Agricultural and Food Science, Vol 15 Supplement 1 A G R I C U L T U R A L A N D F O O D S C I E N C E A dynamic programming model for optimising feeding and slaughter decisions regarding fattening pigs Jarkko K. Niemi MTT Agrifood Research Finland, Economic Research, Luutnantintie 13, FI-00410 Helsinki, Finland e-mail: jarkko.niemi@mtt.fi ACADEMIC DISSERTATION To be presented, with the permission of the Faculty of Agriculture and Forestry of the University of Helsinki, for public criticism in Auditorium XII, Unioninkatu 34, Helsinki, on April 21st, 2006, at 12 o’clock. Supervisors: Docent Kyösti Pietola Economic Research MTT Agrifood Research Finland Professor Matti Ylätalo Department of Economics and Management University of Helsinki, Finland Reviewers: Professor Ruud Huirne Business Economics Group Wageningen University, The Netherlands Professor Anders Ringgaard Kristensen Department of Large Animal Sciences Royal Veterinary and Agricultural University, Denmark Opponents: Professor Pekka Ilmakunnas Department of Economics Helsinki School of Economics, Finland Professor Asko Mäki-Tanila Biotechnology and Food Research MTT Agrifood Research Finland A G R I C U L T U R A L A N D F O O D S C I E N C E Preface Several persons have contributed to this thesis and supported me. I take this opportunity to thank those people. First, I wish to express my gratitude to my two supervisors, Docent Kyösti Pietola (MTT Eco- nomic Research) and Professor Matti Ylätalo (University of Helsinki). Docent Pietola encouraged me to start post-graduate studies, supported me throughout, and assisted me in my efforts to deal with a variety of methodological and theoretical issues. Professor Ylätalo supported me during my studies in several ways, provided guidance during my research, and made constructive comments on this study. In addition, I would like to express my gratitude to Marja-Liisa Sévon-Aimonen (MTT Animal Production Research), who provided biological data and helped me to formalise the model. I thank Professor Ruud Huirne (Wageningen University, The Netherlands) and Professor Anders Ring- gaard Kristensen (Royal Veterinary and Agricultural University, Denmark) for their careful pre-examina- tion of the thesis and for their many valuable comments. I am also grateful to Professor Pekka Ilmakunnas (Helsinki School of Economics) and Professor Asko Mäki-Tanila (MTT Biotechnology and Food Re- search) who agreed to be my public examiner. I wish to acknowledge my colleagues at MTT Economic Research as well as several people who have participated in this research project at MTT Animal Production Research: Esa Mäntysaari (Ph.D.), Hilkka Siljander-Rasi (M.Sc.), Ismo Stranden (Ph.D.), Jarmo Valaja (Ph.D.) and Kaarina Vuori (M.Sc.). I also thank Saara Raulo (Ph.D.) (the National Veterinary and Food Research Institute) and Marie-Josée Mangen (Ph.D.) (Agricultural Economics Research Institute, The Netherlands) for suggestions concerning early versions of Chapter 7. I am also grateful to the supervisors of the research project “Economic comparison of feeding strategies in pigs” for their remarks. This study is based on research projects which were funded by Ministry of Agriculture and Forestry, MTT Agrifood Research Finland and Raisio Group Plc., with additional support provided by the Finnish Animal Breeding Association (FABA). In addition, the August Johannes and Aino Tiura Foundation of Agricultural Research, the Science and Research Foundation of the Finnish Association of Academic Agronomists as well as the Finnish Cultural Foundation provided financial support for this thesis. I gratefully acknowledge the funding and information provided by these organisations. I am also grateful to MTT for giving me the op- portunity to work on this topic and for providing me with excellent facilities for this study. I thank Emeritus Professor Henry Fullenwider (Ph.D.) for reading the manuscript for English-language usage. I’m also grateful to the editorial board of Agricultural and Food Science for accepting this study for publication in their journal. Finally, I wish to express my gratitude to my friends and relatives for their support. Warm thanks go to my parents Erkki and Raila, who have encouraged and supported me throughout my life. My warmest thanks go to my wife Sari for her love, care and understanding, and to our sons, Ville and Jere, who have always brought sunshine into my life. Kurikka, February 2006 Jarkko Niemi 4 A G R I C U L T U R A L A N D F O O D S C I E N C E Contents Abstract ........................................................................................................................ 6 1 Introduction ............................................................................................................. 7 1.1 Background of the study .................................................................................. 7 1.2 Modelling feeding and the timing of slaughter decisions ................................ 8 1.3 Objectives and structure of the study ............................................................... 10 2 Previous studies on pig production management and optimisation ........................ 11 2.1 Production and pricing of pig meat in Finland ................................................. 11 2.2 Features of optimised pig management ............................................................ 12 2.2.1 The planning horizon ............................................................................. 12 2.2.2 Choosing the optimal feeding patterns .................................................. 12 2.2.3 The optimality of slaughter timing ........................................................ 16 2.2.4 Uncertainty of slaughter income ............................................................ 19 2.3 Methods for optimising pig fattening ............................................................... 20 2.3.1 The optimality of an allocation .............................................................. 20 2.3.2 Production and cost functions ................................................................ 21 2.3.3 Convex and concave sets and functions ................................................. 22 2.3.4 Dynamic programming .......................................................................... 24 2.4 Scope and method of the study ........................................................................ 26 3 A dynamic programming model for pig fattening ................................................... 29 3.1 Model specification problems .......................................................................... 29 3.2 The optimisation problem ................................................................................ 31 3.3 Decomposing the control variables .................................................................. 32 3.4 The pig growth model ...................................................................................... 33 3.5 Restricting pig growth ...................................................................................... 35 3.6 One-period returns function ............................................................................. 36 4 Precision feeding – a benchmark scenario .............................................................. 37 4.1 Data and scenarios ............................................................................................ 37 4.2 Estimation method ............................................................................................ 41 4.3 Results .............................................................................................................. 44 4.4 Summary .......................................................................................................... 49 5 Adjusting pig production management to market conditions ................................. 50 5.1 Data and scenarios ............................................................................................ 50 5.1.1 Price movements .................................................................................... 50 5.1.2 Quality price premiums .......................................................................... 52 5.2 Results .............................................................................................................. 52 5.2.1 The effects of price changes .................................................................. 52 5.2.2 Elasticity estimates for price movements .............................................. 56 5.2.3 The effects of quality price premiums ................................................... 58 5.3 Summary .......................................................................................................... 61 5 A G R I C U L T U R A L A N D F O O D S C I E N C E 6 The value and management implications of animal genetics .................................. 63 6.1 Data and scenarios ............................................................................................ 63 6.2 Results .............................................................................................................. 66 6.2.1 The effects of animal genotype .............................................................. 66 6.2.2 Split-sex feeding .................................................................................... 69 6.3 Summary .......................................................................................................... 72 7 The importance of slaughter timing ........................................................................ 74 7.1 Data and scenarios ............................................................................................ 74 7.1.1 The case of exogenously delayed slaughter ........................................... 74 7.1.2 Modelling the value of slaughter timing ................................................ 76 7.2 Results .............................................................................................................. 78 7.2.1 Adjusted feeding patterns when the slaughter is delayed ...................... 78 7.2.2 Income losses in the event of a short slaughter delay ............................ 79 7.2.3 Income losses in the event of a long slaughter delay ............................. 82 7.3 Summary .......................................................................................................... 83 8 Conclusions and discussion ..................................................................................... 85 8.1 Management implications ................................................................................ 85 8.2 Policy implications ........................................................................................... 89 8.3 Suggestions for further research ....................................................................... 91 References .................................................................................................................... 93 Selostus ........................................................................................................................ 98 Appendices Appendix A. Computer code of the basic model Appendix B. Sensitivity analysis of two-phase feeding Appendix C. Feeding patterns of female pigs and castrated male pigs Appendix D. Sensitivity analysis for genotype scenarios 6 A G R I C U L T U R A L A N D F O O D S C I E N C E A dynamic programming model for optimising feeding and slaughter decisions regarding fattening pigs Jarkko K. Niemi MTT Agrifood Research Finland, Economic Research, e-mail: jarkko.niemi@mtt.fi Costs of purchasing new piglets and of feeding them until slaughter are the main variable expenditures in pig fattening. They both depend on slaughter intensity, the nature of feeding patterns and the technological constraints of pig fattening, such as genotype. Therefore, it is of interest to examine the effect of production technology and changes in input and output prices on feeding and slaughter decisions. This study examines the problem by using a dynamic programming model that links genetic characteristics of a pig to feeding decisions and the timing of slaughter and takes into account how these jointly affect the quality-adjusted value of a carcass. The state of nature and the genotype of a pig are known in the analysis. The results suggest that producer can benefit from improvements in the pig’s genotype. Animals of im- proved genotype can reach optimal slaughter maturity quicker and produce leaner meat than animals of poor genotype. In order to fully utilise the benefits of animal breeding, the producer must adjust feeding and slaughter patterns on the basis of genotype. The results also suggest that the producer can benefit from flexible feeding technology. Typically, such a technology provides incentives to feed piglets with protein-rich feed. When the pig approaches slaughter maturity, the share of protein-rich feed in the diet gradually decreases and the amount of energy-rich feed increases. Generally, the optimal slaughter weight is within the weight range that pays the highest price per kilogram of pig meat. The optimal feeding pattern and the optimal timing of slaughter depend on price ratios. Particularly, an increase in the price of pig meat provides incentives to increase the growth rates up to the pig’s biological maximum by increasing the amount of energy in the feed. Price changes and changes in slaughter premium can also have large income effects. Key words: barley, carcass composition, dynamic programming, feeding, genotypes, pig fattening, preci- sion agriculture, productivity, slaughter weight, soybeans 7 A G R I C U L T U R A L A N D F O O D S C I E N C E Vol. 15 (2006): Supplement 1. 1 Introduction 1.1 Background of the study Decisions related to feeding regimen and slaugh- ter timing in pig meat production have vital sig- nificance because they affect economic perform- ance of pig farms and more broadly, the economic performance of the pork industry. Both decisions can significantly affect the value of pigs sold for slaughter and the income flows of a pig farm, es- pecially as the prices of feed and of piglets are the major variable production expenses. Tuppi (2004), for instance, estimates that on ProAgria Rural Advisory Centres’ sample farms specialised in pig fattening, the average feed cost in 2003 was 22% (€39 per pig) and the purchase cost of pig- lets was 32% (€57 per pig) of the total produc- tion cost of pig meat. Taken together, these two items account for 93% of the total material cost incurred in bringing a pig to slaughter. Therefore, changes in the allocation of feeds, the length of the fattening period, and factors that determine the optimality of these decisions, can have large impact on production cost and profitability of pig fattening. The effects of prices and technological con- straints on production management and the value of a capacity unit are inextricably related to choice of feeding patterns and to slaughter decisions. The genetic production potential of an animal (i.e. gen- otype) can have a particularly large impact on the market value of a carcass and as well as on input efficiency of feeds. It is known that the pig’s re- quirements for protein (Fuller et al. 1989) and en- ergy (Whittemore 1983) depend on its maturity stage and genotype (Boland et al. 1999). Hence, producer can benefit from using feeding schemes that have two or more phases, each of which has a different feed composition (two or three-phase feeding), as opposed to schemes that have the same feed composition (one-phase feeding) throughout the fattening period (Boland et al. 1999, Campos 2003, p. 80) and from adjusting the timing of slaughter of pigs in a batch according to their weight and leanness (Kure 1997, Chapter 4). Stud- ies even suggest that providing an efficient supply of nutrients according to the pig’s genetic growth potential requires continuous rather than discrete adjustment of feed ratios (Glen 1983). The benefits of continuous adjustments are, however, quite un- known. Studies suggest that improvements in genotype can significantly increase returns to pig farming. Since a pig’s genotype and carcass leanness are correlated and since carcass is priced according to its weight and leanness, increases in returns have been observed above all to improvements that in- crease the growth rate of lean meat (Boland et al. 1993). Full utilisation of production potential of improved genotypes can require the adjustment of slaughter and feeding patterns accordingly (cf. Boland et al. 1999). Therefore, it is important to examine how genotype affects pig production management, and how management and genotype jointly affect the value of a capacity unit. This can be important particularly when aiming at obtaining unbiased assessment of economic advantages of a particular animal breeding strategy. An example of a segregated feeding pattern is the case where the producer has an option to group pigs into batches according to their sex, and there- after to optimise feeding and slaughter decisions separately for both sexes (split-sex feeding). Since feeding and slaughter decisions frequently involve interactions (Chavas et al. 1985), it is important to take into account also the income that simultane- ous adjustment of feeding and slaughter decisions can contribute to the capacity unit through im- proved carcass quality as a result of the enhance- ment of the genetic characteristics of the animal. This aspect is often omitted and an inflexible feed- ing technology is used instead. Successful pig management entails the ability to find solutions to problems arising from uncer- tainty and biological variation. Pigs are often managed as groups where individuals may have different growth patterns. This causes variation in carcass value, with the results that it becomes op- 8 A G R I C U L T U R A L A N D F O O D S C I E N C E Niemi, J.K. Optimising feeding and slaughter decisions regarding pigs timal to adjust the timing of slaughter of pigs ac- cording to their weight and leanness (cf. Kure 1997, Roemen and de Klein 2000). Measurement of carcass quality can also be inaccurate and affect the optimal timing of marketing (Jorgensen 1993, Boland et al. 1996). Furthermore, it may take time to observe changes in growth rates of pigs (White et al. 2004), and manager may not always reach desired carcass composition (Parsons et al. 2004). Studies such as Jorgensen (1993), Boland et al. (1996) and Kure (1997) have carefully examined the impacts of uncertainty and biological varia- tion in pig fattening. Less work has been done to analyse the connections between feeding and slaughter decisions and carcass quality. Hence, this study emphasises these linkages and shows how to estimate to the value of genetic improve- ments by taking their management effects into ac- count. From an economic point of view, price ratios of inputs and outputs largely determine the opti- mality of feeding and slaughter decisions for a given production technology (Dent et al. 1970, Sonka et al. 1976, Jolly et al. 1980, Glen 1983, Chavas et al. 1985, Broekmans 1992, Rydstedt and Andersson 1993, Kure 1997, Boland et al. 1999). The factors affecting the optimal pig production management patterns include price adjustments that depend on carcass weight and leanness (Boland et al. 1993). Although a producer can ben- efit from adjusting feeding and/or slaughter pat- terns according to the markets, studies have gener- ally found that input substitution is inelastic with respect to input and output prices. Income, on the other hand, has responded very elastically to changes in input and/or output prices (Chavas et al. 1985, Boland et al. 1993, Sipiläinen and Ryhä- nen 1996, Kure 1997). Feeding and slaughter decisions are also in- volved in several policy issues such as the subsi- dising of pig fattening and regulations affecting the choice of inputs, outputs and production tech- nology. An example of a regulatory problem in- volving the need to evaluate the impact of regula- tions on production is whether to prohibit the use of genetically modified (GMO) soy meal in feeds. GMO soy meal is less expensive than non-GMO soy meal. Dros and Kriesch (2003, p. 10–11), for instance, have reported approximately a 10% price difference. The price gap is expected to increase over time. Regulations prohibiting the use of GMO soy meal therefore imply higher feed costs to do- mestic producers than to foreign competitors with less stringent regulations. Thus, estimates of the effects of regulations require taking into account to which extent producers can make adjustments to production through input substitution. Another important policy issue is decoupling subsidies from production. The slaughter premium paid for each slaughtered carcass affects the timing of slaughter, because the amount of premiums paid to the producer depends on slaughter intensity. The premium is also known to have an impact on pro- ducer income (Sipiläinen and Ryhänen 1996). De- coupling the slaughter premium from production so that producer has no obligation to produce meat is the equivalent of removing it from the optimisa- tion problem. Since the decoupled premium is ex- ogenous, decoupling can decrease the profitability of high slaughter intensity. Decoupling can in- crease the value of existing production capacity but decrease producer incentives to invest in new production capacity. This is so because decoupled payment is independent of production capacity. Hence, more consideration could be given to giv- ing the producer incentives to invest in new pro- duction capacity. 1.2 Modelling feeding and the timing of slaughter decisions Economic optimisation of feeding and slaughter decisions requires simultaneous analysis of both decisions. This is mainly due to two aspects. The first is that feeding decisions, conditional on the genotype of an animal, affect both carcass value and daily growth rates (Chavas et al. 1985, Kennedy 1986, p. 11, Burt 1993). Hence, making the optimal feeding decisions requires information on how a pig of a particular genotype responds to 9 A G R I C U L T U R A L A N D F O O D S C I E N C E Vol. 15 (2006): Supplement 1. feeds and how feeding affects the market value of a carcass. The second aspect is that economically optimal production decisions take both allocation of inputs and the timing of replacement of an asset into account (Burt 1965, 1993, Dillon and Ander- son 1990, p. 87–88). No matter how the problem of the optimal timing of marketing of an animal is solved, the general principle is simple: It is opti- mal to market a pig when the marginal net revenue from fattening an additional day is equal to the op- portunity cost of replacement (Chavas et al. 1985, p. 639, Dillon and Anderson 1990, p. 87–94, Bo- land et al. 1993, p. 148). In other words, the re- placement pig can contribute higher profit than the current pig (for analytical solution, see Chavas et al. (1985, p. 639)). In this study, pig fattening is examined with a structural-form optimisation model that is based on characterisation of the growth mechanism of pigs. An optional approach would be to estimate a reduced-form pig growth model. Discussion on how to feed fattening pigs includes solving wheth- er it is optimal to feed the pig according to its bio- logical growth potential (ad libitum feeding) (Dil- lon and Anderson 1990, p. 113). The problem is economically relevant because, as Boland et al. (1999) note, maximisation of live weight growth only does not recognise the impact of diminishing returns on inputs. Even when the growth rates are exogenously given, it is useful to solve feed ratios by maximising profits rather than weight gain. The benefits of restricting the supply of feed below stomach capacity are related to a carcass merit based meat pricing scheme (Boland et al. 1993, Boland et al. 1996, Sipiläinen and Ryhänen 1996) and to the fact that restricting the feed sup- ply gives the producer the option to extract the quality price premium from the markets at the cost of decreased growth rate. Although pig growth it- self is a complex process, the principle of how to control carcass quality through feeding is quite simple. As the amount of protein in feed increases, carcass becomes leaner (i.e. the share of red meat in the carcass increases) and its value (€ per kg) increases. As the amount of energy in feed increas- es, carcass becomes fattier, and as the total amount of feed increases, the daily weight gain increases and the pig reaches the specified live weight quick- er than before the increase. Therefore, the daily feed allowance significantly affects carcass quality (Whittemore 1998, p. 48–52). The growth of a pig and constraints related to its growth can be characterised using a set of equa- tions (Emmans 1995, p. 113N). The idea is to split the pig’s live weight into energy, protein, water and ash and then to model the growth of the com- ponents separately. As Emmans and Kyriazakis (1999) summarise, this can be a very useful form of simplifying pig growth, because most important processes of pig growth can be reduced to a func- tion of either an energy or a protein component. The genotype of a pig plays an important part in this functional approach. In this study, the geno- type of a pig refers to the maximum rate at which the amount of lean and fatty tissue in the pig’s body can increase (i.e. the growth potential). Lean tissue refers to the protein component and meas- ures the amount of all fat-free components in the body, whereas fatty tissue refers to the energy component and measures all fat in the body. When the Gompertz function characterises the maximum growth pattern of a pig, the parameter known as mature weight measures the weight that an animal can reach when it matures, and the pa- rameter known as maturing rate measures the maximum daily weight gain of a tissue component (Whittemore 1998, p. 59–68, Emmans and Kyria- zakis 1999; see also Black 1988, Boland et al. 1993, Sevón-Aimonen 2001). Clearly, these two parameters are of interest when estimating the val- ue of genetic improvements. Generally, an increase in the rate of daily weight gain is associated with an increase in maturing rate, whereas an increase in carcass leanness is associated with an increase in the mature weight of lean tissue. Both increases, however, result in a higher rate of daily weight gain (Whittemore 1998, p. 59–68, Emmans and Kyriazakis 1999). Mature weight is conceptually different from slaughter weight. Mature weight depends on the pig’s genotype, whereas the producer decides the slaughter weight. Since slaughter pigs are valued according to their weight and carcass leanness, in- creasing the probability for the slaughter to be de- 10 A G R I C U L T U R A L A N D F O O D S C I E N C E Niemi, J.K. Optimising feeding and slaughter decisions regarding pigs layed can provide a producer with incentives to minimise reductions in the value of a carcass by marketing the pigs prematurely. Yet, little attention has been paid on examination of the economic im- pacts of delayed timing of slaughter, and of the op- tions available to an individual producer to adjust pig farming to delayed slaughter. This problem is common, because slaughterhouses are generally responsible for the collection of animals for slaughter, and an individual producer cannot al- ways fully control the date of slaughter. Thus, failed co-ordination of the production chain can alter the value of a carcass and the quality of the industry’s product. Similar problem can occur also in special cir- cumstances, such as when animal disease regula- tions expose farms to the risk of a long exogenous delay in the timing of slaughter. Then, producer’s problem is to consider the options to minimise in- come losses through adjusting feeding patterns. The problem of premature slaughter is interesting also from society’s point of view because prema- ture slaughter can have externalities for a large number of farms in the event of an animal disease outbreak, and because it can increase society’s ex- posure to additional disease losses. 1.3 Objectives and structure of the study This study focuses on modelling the production technology of pig fattening in cases where produc- er can observe the technology and state of nature of pig and control feeding and slaughter of a pig accordingly. The objective is to examine changes in pig producer’s production decisions and income when production technology and input and output prices change. In more detail, the goal of this study is to estimate: • How much the producer can benefit from using a flexible feeding technology (‘precision feed- ing’), which allows him/her to continuously control feed ratios and carcass quality, instead of inflexible two-phase feeding technology (Chapter 4) • How the optimal feeding and slaughter policies and the value of a capacity unit change when carcass quality premiums, slaughter premiums or the prices of pig meat, feed and piglets change in a given production technology (Chapter 5) • How much the producer can benefit from changes in production technology such that the genotype of an animal is improved, and how these technological improvements affect the optimal feeding and slaughter patterns (Chap- ter 6) • How much the producer can benefit from opti- mising the timing of slaughter, and how he/she can minimise income losses when there is a possibility that the production technology al- lows timing of slaughter to be delayed (Chap- ter 7) These problems are studied by modelling the producer’s decision making in a finite horizon re- cursive dynamic programming (Bellman, 1957) framework. Dynamic programming provides an efficient tool for linking feeding and feed compo- nents to carcass quality and for optimising feeding and the timing of slaughter simultaneously. The value of a capacity unit depends on both volume and quality of pig meat produced, which is condi- tional on quality price premiums paid according to the share of red meat in the carcass. The scope of this study is practical in the sense that the model characterises the growth mechanism of a pig (cf. Lucas’s critique of the validity of macroeconomic models (Sargent 1987, p. 40–41)). The main contribution of this study to the lit- erature of pig production management is the dy- namic approach that explicitly takes into account carcass quality while simultaneously optimising feeding and slaughter decisions. The model esti- mates the optimal feeding and slaughter patterns and corresponding value functions over time and over subsequent fattening periods. The term fat- tening period refers to the time that is used to feed an individual piglet until slaughter maturity. The model is normalised for a capacity unit. The value of a capacity unit refers to the compensation that 11 A G R I C U L T U R A L A N D F O O D S C I E N C E Vol. 15 (2006): Supplement 1. the producer receives for fixed inputs and other variable inputs than feed cost and cost of replace- ment piglets. The results are based on the data from growth experiments on Finnish low-fat York- shire and Landrace crossbreed pigs, literature and meat market records in 2001–2003. The results are conditional on model formulation factors such as producer’s ability to control carcass quality of an individual pig and that states of nature (i.e. geno- type, carcass composition, prices) are known each period. Hence, the main goal of this thesis is to analyse how changes in model parameters, such as market information, animal genotype or feeding technology, affect feeding and slaughter patterns and the value of a capacity unit rather than to esti- mate absolute feed levels and the timing of slaugh- ter or the parameters themselves. This study is organised as follows. Chapter 2 discusses the optimisation of pig fattening in gen- eral, and results obtained in previous studies. Chapter 3 presents the modelling framework used in this study. Each of the four research problems given above is examined separately, one at a time, in Chapters 4–7. More detailed description of the problem in question is given in the beginning of each of these Chapters, followed by scenario and data description, the results and a summary at the end of the Chapter. Finally, Chapter 8 draws con- clusions and discusses the results. 2 Previous studies on pig production management and optimisation 2.1 Production and pricing of pig meat in Finland Approximately 2.3 million fattening pigs are slaughtered in Finland per year. The average car- cass weight of a slaughtered pig in the past few years has been 82–84 kg. Thus, the annual amount of pig meat produced by fattening pigs in Finland has been 162–187 million kg (Tike 2005). Finnish pig farms house approximately 520,000 fattening pigs (>50 kg) and almost 300,000 young pigs at 20–50 kg live weight, of which most become fat- tening pigs (Tike 2004b). Since 1995, the price of pig meat has been less volatile in Finland than in most member countries of European Union (EU). Both increases and decreases in the EU average price seem to diffuse into Finnish meat markets with lags, and the difference between the highest and the lowest meat price is generally smaller in Finland than in such countries as Denmark, Ger- many, the Netherlands or Spain, which produce large amounts of pig meat (Eurostat 2004). The producer price of pig meat in Finland is adjusted according to carcass weight and the share of red meat in the carcass. The advantage of car- cass component based pricing is that it sends pig meat producers an observable price signal reflect- ing the value of carcass quality at later stages of the marketing chain (Boland et al. 1996, p. 46). Carcass leanness upon slaughter is graded accord- ing to the SEUROP classification scheme com- monly used in European Union. The measurement is carried out with a Hennessy grading probe 4 measure or a pork fat thickness analyser. In 2003, 40.6% of the carcasses qualified as class S (more than 60% red meat), 54.6% as class E (55–59% red meat), and 4.6% as class U (50–54% red meat) carcasses. The share of carcasses in class S was higher in 2003 than in any of the years from 1999– 2002 (Tike 2004a). Major slaughterhouses in Finland use similar principles when pricing pig meat, but the quality 12 A G R I C U L T U R A L A N D F O O D S C I E N C E Niemi, J.K. Optimising feeding and slaughter decisions regarding pigs premiums or discounts may differ from slaughter- house to slaughterhouse. The producer price con- sists of the base price, where no quality adjust- ments apply, and quality premiums or discounts that depend on carcass weight and leanness. In ad- dition, the base price can be differentiated accord- ing to producer category. For instance, producers contracted to produce a certified quality generally receive a higher base price than producers without a contract. Often, the base price is paid for carcasses con- taining 59–59.9% lean meat and being within cer- tain weight range (such as 75–80 kg). Each addi- tional percentage point of red meat increases above (below) the reference receives an additional pre- mium (discount). Each kilogram of carcass weight that is below or above the target weight range, re- sults in a price discount. The discount increases as the carcass is lighter or heavier. For instance, when the discount is €0.02 per additional kg and the car- cass weight is 2 kg above the target, the price per kg is discounted €0.04 below the base price. 2.2 Features of optimised pig management 2.2.1 The planning horizon Farm management is often defined as the alloca- tion of limited resources to maximise the farm’s satisfaction. The management functions include planning the allocation, implementing the plans, and finally controlling the activities. Agricultural producers can have different objectives in the short run and in the long run. Planning in the short run involves the operational planning and implemen- tation of a chosen strategy whereas strategic plan- ner expands decisions to long run planning and to fundamental issues of firm operations (Boehlje and Eidman 1984, p. 6–27 and 242–261). Interme- diate length horizon planning is known as tactical planning. Feeding and slaughter decisions, for in- stance, can be adjusted at relatively short intervals whereas investments in costly new production technology require planning for a period of several years, because the new technology can increase ef- ficiency of input use and thus contribute value added in the long run. Management decisions can be represented as a cyclical process (Figure 1) in which strategic, tac- tical and operational decisions combine to affect the implementation and control of management plans. After the plans have been developed, the managers are concerned with implementing the plans, controlling and monitoring the outcome over time, as well as with adjusting the plans if conditions change. The decisions examined in this study mainly relate to strategic and operational de- cision-making. 2.2.2 Choosing the optimal feeding patterns The biological basis of examining the optimality of feeding patterns is usually the partitioning of the nutritional needs of the growing pig into additive parts, the maintenance needs being met first, fol- lowed by growth needs. In addition, nutritional needs can be separated into protein (i.e. amino ac- ids), energy and minerals needs. If an animal con- sumes just enough nutrients to meet the mainte- nance requirements, then no growth occurs. Thus, nutritional information is critical in the dynamic modelling of animal growth. Furthermore, the Strategic planning Tactical planning Operational planning Implementation Control Fig. 1. The management cycle (Huirne 1990). 13 A G R I C U L T U R A L A N D F O O D S C I E N C E Vol. 15 (2006): Supplement 1. amount of feed an animal can eat is limited by its stomach capacity (a genetic constraint) (cf. Black 1995, Emmans 1995, Whittemore 1998, Sevón- Aimonen 2001). Therefore, it is important to know whether the actual growth meets the poten- tial. If not, then other factors, such as feed avail- ability, restrict growth (Emmans and Kyriazakis 1999). Both maximum rate of protein retention at dif- ferent stages of growth and mature weights of the animal can differ by sex (Whittemore et al. 1988, Emmans and Kyriazakis 1999, Sevón-Aimonen 2001). Similarly, changes in such factors as quality of feed, housing environment, animal health, diet composition, the number of pigs in a pen, and floor allowance can affect the growth rates obtained with a given amount of feed (Kornegay and Knot- ter 1984, Heikkonen 1997, Whittemore 1998). Animals having the freedom to choose their diet may prefer, for instance, large amounts of energy feed (such as barley) and dislike diets that contain a very high or very low share of protein (Arsenos et al. 2000). In addition, the producer can control feed intake causing the pig to eat less that its stom- ach capacity allows and hence, reducing growth rates below the genetic potential. Studying potential and actual growth rates re- quires knowledge of growth as a function of weight and feed intake, and of growth potential. When carcass leanness needs to be taken into account, growth needs to be further separated into energy and protein needs (cf. Chavas et al. 1985, Glen 1983, Boland et al. 1993, Emmans 1995, Kure 1997, Sevón-Aimonen 2001). According to Whit- temore (1998, p 50), the ratio of fat growth to lean growth responds quite steadily to increased use of feeds when growth of fatty and lean tissue is re- stricted below the maximum. When lean growth reaches its maximum, the growth rate of fatty tis- sue increases with respect to the growth rate of lean tissue. Even if feeding is initially restricted so that tissue grows below the potential, the pig can have the capacity to partly compensate for reduced weight gain afterwards if the amount of feed is in- creased up to the level where the pig can utilise the nutrients up to its growth potential (Valaja et al. 1992, Kyriazakis and Emmans 1999). Finnish feeding recommendations advise that young piglets be fed with a protein-rich diet. As the recommended amount of energy in feed in- creases almost every week, pigs approaching slaughter maturity are fed with energy-rich feed. The daily amount of energy supplied to young pigs increases by 0.2 fodder units each week. At later stages of growth, an increase of 0.1 fodder units is typical, and eventually the amount supplied stabi- lises at a constant level. In addition, the recom- mendations suggest discretionary reduction of the share of protein in feed once or twice during the fattening period. The first reduction is recom- mended at 55 kg live weight and the second at 80 kg live weight (MTT 2004). Changes in recommended feeding patterns are linked to the fact that economically optimal feed- ing decisions change as growth rates change (Fig- ure 2). Figure 2 illustrates the fact that an increase in the daily feed allowance affects the three factors measured in the vertical axis, viz. the share of red meat in the carcass, the amount of daily weight gain and the feed cost per additional kilogram of meat for a given feed allowance. The daily weight gain increases when feed allowance increases, but the marginal weight gain is smaller when the al- lowance is large than when it is small. This can be due, for instance, to limits in stomach capacity and the fact that the daily weight gain starts to decrease when the animal becomes mature enough. Simul- taneously, the average feed cost per kilogram of marketed meat decreases. At a certain inflection point, and thereafter, the efficiency of converting feed into meat decreases and average feed cost in- creases. Furthermore, increasing a feed allowance causes trade-off between carcass leanness and dai- ly weight gain. The shaded box between the two vertical lines illustrates the region where an eco- nomically optimal feed allowance is likely to be found. The optimum is where the feed allowance and the three components are suitably balanced. In general, if the daily feed allowance is excessively high (low), then decreasing (increasing) it results in higher returns to producer. The exact location of the profit-maximising optimum in the shaded re- gion, however, depends on such factors as feed and piglet prices. 14 A G R I C U L T U R A L A N D F O O D S C I E N C E Niemi, J.K. Optimising feeding and slaughter decisions regarding pigs Optimal region fodder units of feed per pig per day *)Share of red meat *)Daily weight gain *)Feed consumption Th e am ou nt of m ea su re d va ria bl es *) Fig. 2. The impact of daily feed allowance (fodder units per pig per day) on feed consumption (fodder units per additional kilo- gram of meat), daily weight gain (kg), the share of red meat in car- cass at slaughter (%), and the re- gion where the economically op- timal daily feed allowance with respect to the combination of the three factors can be found (Source: Danske slagterier 2001, p. 1). Since interactions frequently occur between feed inputs, it is important to consider different in- put combinations over a feasible operational range. Both static and dynamic analyses of the optimal feeding patterns suggest that it is optimal to de- crease the share of protein in feed as the pig grows. Dent et al. (1970) examined the effect of feed in- take in different combinations on pig growth and economic outcomes using static regression analy- sis. They observed that response of lean meat and live weight gain to both lysine and protein intake was almost linear for young pigs. Response of live weight gain to increased amount of energy was continuous though diminishing in the later stages of growth, and a connection between low response to protein and low intake of energy was observed. In early stages of growth, lean growth showed positive though a diminishing response to energy. As the ratio of energy intake to dietary lysine decreases along the iso-growth line, the cost of producing a daily weight gain simultaneously de- creases. Thus, under conditions orientated purely to achieving live-weight gain at the minimum feed cost, nutrient combinations should be selected to- wards the high energy-low lysine end of the iso- growth curve (Dent et al. 1970, p. 202). These re- sults, however, do not permit the construction of a continuous growth curve. Sonka et al. (1976), ob- served a similar change in the feeding pattern as the pig grows. They estimated that the optimal share of protein in the diet varies between 12–18% depending on the growth stage of the animal as well as on input prices. Sonka et al. (1976, p. 473) also observed that when the price of protein is low in comparison with the price of corn, the cost ad- vantage of using low amounts of protein decreas- es. Chavas et al. (1985) estimated the optimal feeding pattern of fattening pigs using optimal control theory1. They concluded that pig meat pro- ducers have incentives to feed high protein ration for young pigs, but to use lower protein ration in the finishing phase. The result was quite robust to changes in relative prices. They observed that the marginal product of each nutrient had a negative relationship with respect to the level of the other nutrient. They also observed a diminishing mar- ginal utility of growth with respect to feed intake. 1 For further details on the method, see for instance, Kamien and Schwartz (1992, p. 109–243), Seierstad and Sydsaeter (1993, p. 69–410) or Bertsekas (1995a, p. 97– 112). 15 A G R I C U L T U R A L A N D F O O D S C I E N C E Vol. 15 (2006): Supplement 1. Chavas et al. (1985) have characterised the op- timal feeding pattern as follows. The amount of soybean meal increases until the pig reaches ap- proximately 73 kg live weight. Thereafter, the amount of soybean meal in feed decreases. The amount of corn, on the other hand, increases dur- ing the fattening period. During the finishing stage, the amount of corn increases very rapidly and the share of protein in feed decreases linearly. In addi- tion, Chavas et al. (1985) computed positive cross- price elasticity estimates with soybean meal and corn. Thus, the feeds were substitutes for each other. When the price of one feed increased by one percent the amount of the substitute feed increased less than 0.15%. Increasing the price of a piglet by one percent, however, increased the demand for corn by 1.84% and the demand for soybean meal by 0.94%. Glen (1983), studied another dynamic pro- gramming application by optimising feeding pat- terns of fattening pigs for the entire fattening pe- riod. The pigs had a specified slaughter weight. Glen (1983) divided feeding and live weight into energy and protein (for development of the pig growth model see Whittemore and Fawcett (1976), and for use of the growth model to determine the least costly feed ratio see Fawcett et al. (1978)). Glen (1983) estimated that with a diet consisting of soy and barley it is optimal to increase the amount of feed throughout the fattening period. The optimal diet for 20 kg piglet contained 9.7% soy whereas the optimal diet for 25–50 kg pig con- tained 19.3–21.6% soy. Thereafter, on pigs heavier than 50 kg, the share of soy decreased approxi- mately to 2%. Also Boland et al. (1999) showed that it is economically optimal to decrease the share of protein in feed when the pig approaches the optimal slaughter maturity. Using a production and cost theoretical ap- proach, Sipiläinen and Ryhänen (1996, p.157–200) estimated that at the price ratios observed in 1993– 1996, and at the price ratios estimated for 2000, a producer could achieve a higher income per slaughtered pig by using unrestricted feeding in- stead of restricted feeding. When the analysis fo- cused on maximising the daily surplus, the result was more ambiguous. At price ratios for 1996, re- stricted feeding yielded a higher surplus than unre- stricted feeding, whereas at price ratios for 1995, this was the case only for castrated male pigs. In general, these results suggest that castrated male pigs benefited more, in terms of returns, from re- stricted feeding than female pigs. Kure (1997, p. 71–72) also showed substantial income effects of changes in input and output pric- es. An increase of 10% in the base price of pig meat increased annual net revenues by 81.7% and decreased the optimal slaughter weight by 2 kg. A similar increase in feed prices decreased annual net revenues by 40% and slaughter weight by 0.2 kg. Studies suggest that a producer can increase profits by adjusting the composition and amount of feed according to the pig’s current needs. The ad- justment can be done continuously or, as Boland et al. (1999) and Campos (2003, p. 73–100) illus- trate, in phases. The advantage of allowing adjust- ment of feeding patterns in economic analysis is that it recognises the impact of diminishing returns on feed ratios (Boland et al. 1999). In other words, using two- or three-phase feeding instead of a sin- gle feed ration increases the cost of replacement (i.e. opportunity cost of feeding) (Campos 2003, p. 98). This is due to the fact that under two or three- phase feeding, the loss of nutrients and the cost of an additional day of fattening period are smaller than under one-phase feeding. Wet feeds, for instance, allow producers more flexibility than dry feeds in adjusting feeding pat- terns. Use of wet feeds can also decrease the amount of wasted feed. Thus, using a flexible feed- ing technology, such as wet feeds, can improve the efficiency of inputs use and both increase and sta- bilise income (Campos 2003, p. 61–66, Campos and Andersson 2003, p. 41–42). As adjustments include reducing the share of protein in feed in ac- cordance with the pig’s needs, the adjustments can also reduce environmental externalities such as nutrient leakages (Boland et al. 1998, Campos 2003, p. 20–21, 83–84 and 98–100). Hence, fewer nutrients are excreted and higher returns for pro- ducers are obtainable under flexible feeding tech- nology than under inflexible feeding technology (Boland et al. 1999). 16 A G R I C U L T U R A L A N D F O O D S C I E N C E Niemi, J.K. Optimising feeding and slaughter decisions regarding pigs 2.2.3 The optimality of slaughter timing Economically optimal production decisions take both allocation of inputs and the timing of replace- ment of an asset into account (Burt 1965, 1993, Dillon and Anderson 1990, p. 87–88). The prob- lem of timing is related to the fact that extracting an output from a resource system exchanges a fu- ture loss for an immediate gain, whereas allocating an input into a resource system exchanges an im- mediate loss for a future gain (Kennedy 1986, p. 11). Several studies have elaborated on the opti- mality of the timing of slaughter or on the timing of marketing pigs for slaughter (Jolly et al. 1980, Chavas et al. 1985, Giesen et al. 1988, Broekmans 1992, Boland et al. 1993, Burt 1993, Rydstedt and Andersson 1993, Lloyd et al. 1994, Kure 1997, Toft 2000, Roemen and de Klein 2000, Campos 2003). Chavas et al. (1985, p. 639, for further ap- plication, see Campos and Andersson 2003, p. 32– 35) derive a principle that it is optimal to keep the animal until the age at which the marginal net rev- enue is equal to the opportunity cost of replace- ment. Furthermore, Burt (1993) provides a solu- tion to the dynamic and simultaneous replacement and feeding problem under input and output price uncertainty by extending Hotelling’s replacement and depreciation theory to pig fattening. Another approach is to make feeding and slaughter deci- sions that maximise average profit per unit of time (cf. Dillon and Anderson 1990, p. 87–94, Boland et al. 1993, p. 148). The concept of retention pay-off, despite the fact that it is used for reproduction animals (sows), illustrates the basic idea of the optimal timing of replacement of an animal as a function of time (Figure 3). The optimal timing for replacement is at time t2, when average revenue equals marginal revenue (R2). Any deviation from the optimal tim- ing may result in a loss. Replacing (cf. slaughter- ing) the animals at the optimal time yields higher revenues than replacing them at a later time be- cause the replacement animal can provide higher income than the current animal would provide in the future if no replacement took place. As early replacement leaves some of the current animal’s production potential unused, replacement prior to t2 is also non-optimal. When the replacement ani- mal is non-identical to the current animal, the opti- mum may shift away from t2 (Huirne et al. 1993, Huirne at al. 1997, p. 86). Sipiläinen and Ryhänen (1996) estimated that increasing the price of pig meat 10% above the price of 1996 would decrease the optimal slaugh- ter weight from 81.6 kg to 79.5 kg. Simultaneous- ly, producer’s daily surplus would increase by 32%. If feed price increased by 10%, the optimal slaughter weight would decrease by 2.1 kg and producer’s income would decrease by 12%. If the price of a piglet increased by 10%, the optimal Time Marginal revenue Average revenueN et re ve nu e t1 t2 t3 R1 R2 R3 Fig. 3. The optimal time for re- placement as a function of time in a situation without an alternative opportunity (t3), and in situations of an identical (t2) and a non- identical (improved) (t1) replace- ment animal (Huirne et al. 1997, p. 86). 17 A G R I C U L T U R A L A N D F O O D S C I E N C E Vol. 15 (2006): Supplement 1. slaughter weight would increase by 6.9 kg and producer’s income would decrease by 18%. In other cases, the effect of piglet price on slaughter weight was smaller. In the above cases, feeding was restricted and the carcass quality premiums and discounts applied for carcasses containing less than 59% or more than 61% red meat. When the base leanness (implies no discounts or premiums) was 59–60%, the optimal slaughter weight was generally 76.6 kg, whereas income effects were similar to the previous case. Finally, removing the slaughter premium increased the optimal slaughter weight (Sipiläinen and Ryhänen 1996, p. 191). Giesen et al. (1988) developed a model that op- timised delivery of pigs to the slaughter according to their weight in an all-in/all-out production sys- tem. Their results indicated that producer can ex- tract positive returns by using such an optimisation model. Ross (1980) analysed production function in order to maximise pig meat producer profits. He showed that the optimal slaughter weight varies within relatively narrow range and is generally close to the maximum carcass index. Jolly et al. (1980, p. 809) also provided evidence that market weights of slaughter pigs are rather insensitive to changes in feed or meat prices and that net farm income re- sponds sluggishly to changes in slaughter weights. Kure (1997) analysed the marketing manage- ment of a pig fattening farm. Specifically, he stud- ied how to select and when to market individual pigs from batches, and when to deliver the remain- ing pigs of a batch for slaughter (i.e. terminate the batch). Kure (1997) concluded that selection of the timing of slaughter based on carcass leanness and weight is only slightly superior to selection based on pig’s live weight only. Therefore, very little fi- nancial leeway was left for on-farm leanness meas- urement. The leeway, however, may depend on the meat quality premiums and discounts. Kure (1997) noticed that pig meat producers can benefit from marketing individual pigs of a batch according to their weight. In other words, fast-growing pigs should be marketed before they suffer from discounts in meat price due to excess weight, whereas slowly growing pigs should be kept until they reach sufficient live weight. The optimal delivery patterns were affected by the var- iance of pig traits as well as by the flexibility of piglet supply. The terminal weight of a batch in- creased a little when the variance between traits increased (Kure 1997, Chapter 4). Thus, when a producer has to market a group of pigs of different qualities, he/she benefits from marketing fast- growing pigs when they are close to the upper limit of the target weight range and slowly grow- ing pigs at a lower weight. Similar result has been confirmed in several studies (cf. Jorgensen 1993, Rantala 2004, Toft et al. 2005), which is due to the fact that producers can compensate for the value of lost growth potential of slowly growing pigs by increased rotation of animal stock and improved productivity of replacement pigs. Roemen and de Klein (2000) used a Markov decision model to study the production problem of how to organise delivery of groups of pigs. They took into account that each group consists of sub- groups of pigs with different growth rates and that meat prices vary in time stochastically and interde- pendently. They concluded that the optimal deliv- ery pattern depends on the combination of pig’s age and pig meat price. They concluded that pigs in a larger pig group should be delivered if the ani- mals are sufficiently close to the delivery weight and if the price is in the preferred price set. Other- wise it is optimal to postpone the delivery. Chavas et al. (1985) estimated the optimal marketing time of fattening pigs using the optimal control theory. The results suggest that the optimal marketing time is very close to the maximum of the price premium function. Thus, they conclude that, in a continuous pig operation, the presence of a price premium or discount can be very effective in influencing the marketing weight of pigs. How- ever, they emphasise that further research is re- quired to study the relationship between quality- adjusted market signals and producer response in terms of carcass quality characteristics. The quali- ty price adjustment of Chavas et al. (1985) was based on a quadratic function of live weight, which may not reflect the Finnish policy of basing meat pricing on carcass merit. In contrast to previous studies that neglect op- portunity cost of replacement, Chavas et al. (1985) and Boland et al. (1999) observed that the age and 18 A G R I C U L T U R A L A N D F O O D S C I E N C E Niemi, J.K. Optimising feeding and slaughter decisions regarding pigs weight of a pig upon marketing increased with in- put prices and decreased with output prices. The timing of marketing and the marketing weight re- sponded quite elastically to changes in piglet price, at least when compared to other input prices. Boland et al. (1999) conclude that under optimised feeding, an increase in feed prices has a larger im- pact on average net revenues than on the marginal cost of the timing of replacement. Chavas et al. (1985) and Boland et al. (1999) also observe that prices of inputs and the price of pig meat have a strong impact on producer income. In analyses such as those done by Boland et al. (1993) and Kure (1997), input allocation has responded less elastically to price changes, and income effects have been more elastic than in the analysis of Cha- vas et al. (1985). Boland et al. (1993), for instance, report elasticity estimates of decision variables with respect to price changes to be less than 0.25, whereas income elasticity estimates with respect to price changes are 2.35 or larger. On gilts, in- come elasticity with respect to the price of pig meat is as high as 12.79. The impacts of quality adjustments are also quite large. Female and male pigs have different growth rates and thus require different time periods to reach slaughter maturity. Female pigs have higher yields of lean meat than male pigs. Thus, produc- ers may benefit from marketing female and male pigs separately (Boland et al. 1993, Boland et al. 1996). This view is supported by Sipiläinen and Ryhänen (1996, p. 186), who estimated that, de- pending on the combination of feeding pattern (re- stricted/unrestricted), price ratios and meat quality premiums and discounts, the optimal slaughter weight of female pigs can be higher, lower or the same as the optimal slaughter weight of castrated male pigs. These results emphasise the importance of technological options, such as separate facilities for pig groups, separation of feeding patterns or genotype of pigs (cf. Chavas et al. 1985, p. 643, Boland et al. 1993, p. 161). Some studies (e.g. Jolly et al. 1980), however, estimate that penalties from simultaneous non-optimal marketing of gilts and barrows are small. Returns to management under alternative pric- ing systems vary widely. Boland et al. (1993) ob- served that pigs of lean genotype had heavier opti- mal slaughter weight than pigs of fatty genotype. The heaviest weights were close to the limit above which weight price discounts applied. Further- more, pigs priced according to carcass merits were heavier upon slaughter and they required a longer fattening period, but also contributed higher in- come than pigs priced according to live weight. In addition, pricing based on six size components of hams and loins resulted in slightly heavier pigs than standard carcass merit pricing. The difference was larger for fatty pigs than for lean pigs. The explanation is largely in the efficiency of convert- ing a kilogram of feed into lean meat, because lean pigs and barrows have higher lean and feed effi- ciency than fatty pigs and gilts. The interpretation of the feed efficiency ratio is, however, problem- atic because the choice of diet, length of fattening period and slaughter weight affect the ratio. De- spite improved feed efficiency per kilogram of pig meat, profits can fall if slaughter weight simultane- ously falls (Campos and Andersson 2003, p. 43). Despite this drawback, the positive impact of car- cass merits on producer profits increases when the genetic background of pigs is conducive to the production of leaner meat (Boland et al. 1993). Rydstedt and Andersson (1993) developed a dynamic optimisation model to estimate the batch slaughter pattern that maximises pig meat produc- er income over a given planning horizon. They showed that although slaughter weights differ sea- sonally and an increase in the price of pig meat increases incentives for adjusting the timing of marketing, pig meat producers have insufficient incentives to keep capacity units idle in order to produce pigs specifically for Christmas markets. Only a large increase (+20%) in the price of pig meat over time resulted in seasonal synchronisa- tion of the timing of marketing. Thus, they con- cluded that producing at full capacity is among the most important factors affecting profitability of pig fattening operations. Few of the studies mentioned above have si- multaneously optimised decisions on how to feed and slaughter fattening pigs. Recent studies con- ducted with other animals provide more examples of joint dynamic optimisation of feeding and re- 19 A G R I C U L T U R A L A N D F O O D S C I E N C E Vol. 15 (2006): Supplement 1. placement decisions. Mourits et al. (1999, 2000) optimised nutrition and timing of insemination of dairy heifers using stochastic dynamic program- ming and the hierarchic Markov process technique. Nielsen et al. (2004) optimised winter feed levels, grazing strategy and slaughter policy of organic steer production in Denmark, using a multi-level hierarchic Markov process. Pihamaa and Pietola (2002) used dynamic programming to optimise feeding and slaughter patterns of beef cattle in Fin- land. Vargas et al. (2001) also paid attention to feeding strategies in their dynamic programming model. However, while decisions on replacing the dairy herd were optimised, their model did not ex- plicitly optimise feeding decisions. Earlier work on dynamic optimisation of feeding and timing of marketing include Talpaz et al. (1988) and Kennedy et al. (1976) for broilers, and Kennedy (1972), Yager et al. (1980) and Feinerman and Siegel (1988) for beef cattle. The first three studies have deterministic optimisation models, Yager et al. (1980) presents stochastic optimisation model for beef cows, and Feinerman and Siegel (1988) has a farm-level optimisation model for beef feedlots. 2.2.4 Uncertainty of slaughter income It is known that volatility and uncertainty of in- come can affect optimal production decisions. Broekmans (1992) observed differences in the du- ration of the fattening period when evaluating the effect of price fluctuations on delivery patterns for slaughter pigs. Broekmans (1992) concluded a producer has more incentives for a longer fatten- ing period under fixed prices than under uncertain prices. An exception was the case where the prices were favourable (i.e. low feed prices and/or high pig meat price). When prices became uncertain, producer maximised the net present value of future income flow by slaughtering the pigs as soon as possible, i.e. when prices were still favourable. This was earlier than when prices were fixed and deterministic (Broekmans 1992). The result, how- ever, can depend on the current market conditions so that expectations on whether prices will fall or rise can affect the timing of slaughter. Another source of income uncertainty is that producers cannot always accurately assess current quality of pigs. Accuracy of carcass assessment can affect the optimal timing of marketing (Jor- gensen 1993, Boland et al. 1996) and incentives for preferring genotypes that conduce to carcass leanness at the farm level (Boland et al. 1996). When the number of pigs per pen increases, chanc- es to control animal quality decrease. Thus, ani- mals can be delivered at an inappropriate weight and producer can suffer income losses compared to the case of perfect information. Ignoring possi- ble sources of uncertainty can result in overestima- tion of the value of information. The effect of un- certainty over the pig’s actual weight may not be large in all the cases, however, and depends on the problem under investigation (Jorgensen 1993). Recent advances in precision farming have filled some of the information gaps in swine pro- duction. These include visual analysis of pigs and on-line weighing of animals that are ready for de- livery (see e.g. Schofield et al. 1999, Kristensen 2003) as well as individual-specific feeding tech- nology. Jorgensen (1993) recognised that the opti- mal delivery policy is relatively robust to varia- tions in weighing precision. Weighing precision was measured through variance of weighing. When the pen had more than 16 pigs, the variation was large enough so that improved weighing precision left only very little financial leeway for invest- ments in weighing equipments. Nevertheless, in- creasing the weighing precision could increase slaughter weights at most by 4 kg. An increase in both the variance of pig quality and weighing pre- cision could decrease the net present value of pig fattening by almost 5% (Jorgensen 1993). Among the potential benefits of real-time per- formance measurement of pigs are characterisa- tion of growth response to nutrients in the context of specific pig and farm types, and optimisation of pig performance with reference to a given target (cf. Whittemore 2004). White et al. (2004) ob- served that visual image analysis was able to de- tect a change in pig state after 3–5 days fattening period with 80% confidence, and after 8–10 days fattening period with 95% confidence. The results of Parsons et al. (2004), however, suggest that 20 A G R I C U L T U R A L A N D F O O D S C I E N C E Niemi, J.K. Optimising feeding and slaughter decisions regarding pigs real-time control of weight gain and leanness of pig can be challenging. Parsons et al. (2004), com- pared pig groups that were fed in order to reach 50 kg or 60 kg liveweight and groups that were fed in order to reach 12 mm or 16 mm backfat thickness. They found that it is possible to control carcass quality to some extent. They also found that the proposed management could not reach the target leanness, particularly the 16 mm back fat target. The final example of income uncertainty is that by Toft et al. (2005), who show that the optimal delivery policy depends on such risk factors as the possibility of animal disease. When disease pres- sure increases, producer can benefit from market- ing a larger share of animals at earlier growth stages. This is due to the fact that the producer can slow down the epidemic by early delivery, which reduces the potential shortfall in weight gain due to the disease. Another explanation may be in the expectation that the next batch will be more pro- ductive than the current (infected) batch. There- fore, the opportunity cost of replacement decreases when the number of infected pigs in the current batch increases, and the producer accepts a small immediate loss if he/she expects to gain rewards in the future. Thus, the optimal disease control policy includes delivery policy (Toft et al. 2005, p. 11– 12). This result emphasises the importance of con- sidering slaughter decisions simultaneously with most other pig herd management problems. 2.3 Methods for optimising pig fattening 2.3.1 The optimality of an allocation In the past, the analysis of agricultural production response has heavily relied on static analysis (Heady and Dillon 1972, Kennedy 1986). Live- stock production processes, however, are never instantaneous or static, but occur in a dynamic set- ting in which time can have a decisive impact on outcomes. The major difference between dynamic and static optimisation is the time aspect: while dynamic optimisation takes into account the inter- temporal nature of the problem, static optimisation generally focuses on a single-period optimal solu- tion. Occasionally, a mixture of both methods is used. Linear programming, for instance, can solve least cost ratios within dynamic programming ap- plications (Glen 1983, Bertsekas 1995b, p. 51). Several ways to model production dynamics have been presented. One approach discussed by Dillon and Anderson (1990, p. 87–94) is to specify production response as a function of time and total input used during the response period. Another ap- proach is to characterise production as a dynamic process that follows differential or difference equa- tions. The latter approach allows us to examine a biological process in greater detail than the first approach, but it also has high requirements for data accuracy. No matter which approach is cho- sen, it is important to pay attention to the charac- terisation of dynamic processes. Chavas et al. (1985, p. 640) have criticised some earlier analy- ses of pig growth because their ability to character- ise growth response continuously for all stages of pig growth is impaired due to static bias, and hence they do not facilitate determination of the optimal timing of slaughter and replacement. The fundamental idea of both dynamic and static optimisation is to find the resource allocation that maximises a given objective, such as maxim- ising the value of a capacity unit. A standard ap- proach to obtain the optimal resource allocation for a constrained optimisation problem is to for- mulate the maximisation problem into a La- grangean form and then to characterise the first- order conditions. In general, the optimal resource allocation is such that increasing or decreasing the amount of a particular resource cannot yield addi- tional profits. In other words, marginal revenue is zero (Gravelle and Rees 1992, p. 12–42, Mas- Colell et al. 1995, p. 956–964). In a static framework, the optimal allocation of inputs is such that the marginal rate of technical substitution equals the input price ratio (Dillon and Anderson 1990, p. 11–25, Mas-Colell et al. 1995, p. 129–143). Since the static criteria omit the op- portunity cost of replacement, the result may differ 21 A G R I C U L T U R A L A N D F O O D S C I E N C E Vol. 15 (2006): Supplement 1. in the dynamic framework. Chavas et al. (1985, p. 639) derive a result where the optimal resource allocation in pig fattening is at the point, where the marginal rate of technical substitution between two inputs with respect to growth function equals the ratio of net marginal value product of the two inputs. The ratio at time t is equal to the marginal value of the current product minus input cost. Therefore, both growth rate function and produc- tion function play a role in the optimality condi- tions. The optimal solution holds only momentarily and can be altered by any deviation in any param- eter. On the other hand, when prices change but relative prices remain constant, the optimal solu- tion to the problem can remain. Thus, the optimal allocation of resources primarily depends on rela- tive prices whereas the financial outcome (such as profit) may depend also on the absolute prices (Mas-Colell et al. 1995, p. 50–57 and 129–143). In pig farming, the optimal feeding and slaughter de- cisions can change over time when markets change (Chavas et al. 1985). The aspect of shifting price ratios is particularly important in dynamic optimi- sation, because it takes into account how future decisions and dynamics of production affect cur- rent optimal decisions and vice versa. 2.3.2 Production and cost functions In order to find a global solution to an optimisation problem, the problem has to meet certain condi- tions. These necessary conditions are embodied in the Weirstrass Theorem. The conditions are that the objective function is continuous, and that the feasible set is non-empty, closed and bounded (Gravelle and Rees 1992, p. 25–26). These four conditions are important although in discrete time models the objective function is often a discrete approximation of a continuous function. Without boundedness, for instance, the solution can be infi- nite (Bertsekas 1995b, p. 9–11). Because the con- ditions are closely related to the properties of the functions that characterise underlying processes, Chapter 2.3. briefly examines the issues that fre- quently arise in production economics. One of the fundamental ideas of production economics is that a relationship exists between in- puts z and outputs y. Generally, the relationship is written in a convenient mathematical form called the production function y=f(z). Thus, a corre- spondence between y and z exists (Chambers 1988, p. 7–9). When modelling pig growth, the corre- spondence generally means that growth potential and growth rate can be measured using factors such as the amounts of feed, composition of the diet, live weight and carcass composition as ex- planatory factors. Several models based on such detailed or simplified biological understanding of pig growth have been developed (e.g. Sonka et al. 1976, Whittemore and Fawcett 1976, Glen 1983, Chavas et al. 1985, Black et al. 1986, Emmans 1995, Sevón-Aimonen 2001, Lizardo et al. 2002). A set of assumptions often ensures that the pro- duction function will have the desired properties (Varian 1984, Chambers 1988, Gravelle and Rees 1992, Mas-Colell et al. 1995). The production function has the property of being (strictly) monot- onic. This implies that output does not decrease when the amount of inputs increases. In addition, the input requirement set V(y) is preferably con- cave, which implies that the production function is strictly quasi-concave. Convexity of the produc- tion possibilities set, on the other hand, is required for the law of the diminishing marginal rate of technical substitution. An alternative requirement is the law of diminishing marginal productivity. Further properties of the production function in- clude that a positive output requires the use of scarce inputs; the production possibilities set is closed and nonempty; that the production function is finite, nonnegative, real valued and single-val- ued for all finite and nonnegative inputs; and that the production function is everywhere continuous or twice-continuously differentiable. The last property rules out discontinuous jumps in the pro- duction technology (Chambers 1988, p. 9–18). As an example of the property of the law of diminishing marginal productivity, we may con- sider a producer who keeps on increasing the amount of feed fed to a pig. For small amounts of feed, the growth rate of a pig increases when the amount of feed increases. After having enough 22 A G R I C U L T U R A L A N D F O O D S C I E N C E Niemi, J.K. Optimising feeding and slaughter decisions regarding pigs feed, the pig cannot eat more feed and thus the growth rate no longer increases even if the amount of feed fed increases. The law of diminishing mar- ginal returns holds for a concave production func- tion, because the second derivative of such a func- tion is negative. The law implies that the amount of output gained by using an additional unit of in- put starts decreasing after the marginal product has reached its maximum, whereas the average prod- uct per unit of input reaches the maximum when the marginal product drops below the average product. The marginal product, however, is posi- tive until the total output reaches the maximum (Intriligator 2002, p. 179–189). The cost of producing a certain amount of out- put is another issue that is of interest in the eco- nomic analysis. Hence, the cost function: (1) c(p,y) = min z≥0 {pz:z ∈ V(y)}, where p is a vector of strictly positive exogenous input prices, and pz is the inner product. As Equa- tion 1 illustrates, the cost function represents the minimum cost of producing a given level of output at a given time and given input and output prices (Varian 1984, p. 21, Chambers 1988, p. 50–59). According to Varian (1984, p. 37), the cost func- tion summarises all economically relevant infor- mation about the production technology of the firm. Cost functions also have desirable properties, such as concavity and non-decreasingness in pric- es. Concavity is a direct consequence of the funda- mental inequality of cost minimisation, and sug- gests that the shape of the cost curve with respect to prices is similar to that of an upturned bowl (Varian 1984, p. 44–46, Chambers 1988, p. 50– 59). 2.3.3 Convex and concave sets and functions The properties of production and cost functions can have important implications for optimisation. The property of convexity is closely related to the concepts of half space and hyperplane. A half space is the set of all points lying on one side of a hyperplane in a real space. Graphically this means that drawing a line (hyperplane) across the real space creates half spaces both below and above the line. Since all half spaces and hyperplanes are con- vex sets, a closed convex set can be defined using hyperplanes that support the set. For a convex set it holds that the line az+(1–a)z’, where 05%) of delayed slaughter, or that an 89 A G R I C U L T U R A L A N D F O O D S C I E N C E Vol. 15 (2006): Supplement 1. expected delay will be extended, can result that premature slaughter will maximise the value of a capacity unit. Thus, the optimal delivery policy is affected by risk factors that can reduce slaughter income, such as the risk that the slaughterhouse might be late in transporting the animals. The gen- eral result regarding marketing income risk is in line with that reported for various risk manage- ment problems (e.g. Broekmans 1992, Toft et al. 2005). As the option of premature marketing may be unavailable, the results suggest an optional way to minimise losses due to maintenance feeding. This option, which previous studies do not examine, is to reduce the amount of energy in feed immedi- ately after obtaining the information on the delay. Thus, when producer can control carcass quality, he/she can minimise income losses from excess carcass weight and decreasing carcass leanness. In addition, if excess weight gain is sufficiently large (i.e. the delay is long), then he/she minimises the weight gain and the losses due to costly mainte- nance and protein feeding. 8.2 Policy implications The results support the view that changes in input prices and output prices have large income effects to producers. Several studies share this result (Chavas et al. 1985, Boland et al 1993, Sipiläinen and Ryhänen 1996, Kure 1997, Boland et al. 1999). These results join those of prior research in show- ing that providing a producer with the option of dynamically adjusting management decisions can result in higher management response elasticities and lower income elasticities with respect to price changes than when no such option exists. The elas- ticity estimates imply that depressions and peaks in the price of pig meat have a particularly strong impact on producer income. Therefore, producers and policy makers should extract value added from the markets whenever it is available. The results suggest that completely decoupling the slaughter premium from production decreases producer incentives to invest in new production capacity (i.e. it decreases returns to cover the in- vestment cost), because the producer has no obli- gation to produce pig meat if he/she desires to have the decoupled payment. As a result, the net income that depends on the number of capacity units de- creases significantly. Therefore, decoupling can increase the number of producers that do not invest in new production capacity but exit the industry, and thus decoupling can decrease the amount of pig meat produced in Finland in the long run. On the other hand, when the production capacity is given or when the payment is dependent on the ca- pacity unit (e.g. when investments are subsidised), decoupling can have only a small impact on pro- duction capacity. Then decoupling can even in- crease producer income, because he/she can ex- tract additional income from adjusting meat qual- ity and still obtain a decoupled income transfer as long as the income from markets exceeds the vari- able cost of production (cf. the exit criterion by Ross (1980)). The results suggest that the slaughter premium has a rather small impact on output per capacity unit as long as the producer has no incentive to change his/her behaviour by adjusting the length of the fattening period. Although a slaughter pre- mium fulfils the conditions required for a lump sum transfer (for details, see Mas-Colell et al. 1995, p. 524) better than a price support, an in- crease in slaughter premium increases producer incomes inelastically. Another important policy issue arises in con- nection with regulations that prohibit producers from using certain inputs. If domestic regulations prohibit the use of genetically modified soy meal and foreign regulations do not, domestic producers have to pay a higher input price for soy feed than some of their competitors. The results suggest that pig meat producers as a group suffer approximate- ly €2 million per year (€0.01 per kilogram of pig meat) in higher production costs when using ge- netically non-modified feed instead of less expen- sive modified feed. Hence, farms having high in- put prices suffer from this competitive disadvan- tage when compared to farms benefiting from low input prices even though they can substitute barley 90 A G R I C U L T U R A L A N D F O O D S C I E N C E Niemi, J.K. Optimising feeding and slaughter decisions regarding pigs and synthetic amino acids for soy meal. From the economic point of view, such regulations will re- sult in reduced demand for domestic products when some consumers shift to less expensive for- eign products. Thus, regulations that increase pro- duction costs in Finland decrease the competitive- ness of the Finnish pig meat industry and increase pig meat imports, unless producers can obtain val- ue added from the markets. The findings of this study suggest that efforts made to increase the competitiveness of pig meat production, particularly by increasing the techno- logical productivity of pig fattening, provide value added. For instance, 10% increase in the K-index of a pig increases the value of a capacity init by approximately the same percentage. Hence, the average rate of genetic progress raises the quality- adjusted value of a capacity unit (ceteris paribus) by almost 6% per year. On the other hand, assum- ing that the total number of capacity units with im- proved pigs is 600,000, improving the daily weight gain potential by 100 g at fixed prices, and equals approximately €150 million per year in additional returns to Finnish pig meat producers as a group. Even if this large benefit requires adjustments in both genetics and management, the benefits seem to exceed the costs. The advantage of these tech- nologies is that they provide more or less perma- nent improvements in the efficiency of input use whereas the breeding effort is required only once (although breeding takes several years). These technologies, however, provide only a temporary competitive advantage to producers because pro- ducers with high costs can obtain the same tech- nology over time. Thus, maintaining the competi- tive advantage requires continuous effort. One of the options to improve the genotype of pigs is to improve the productivity of sows. Al- though this study focuses on pig fattening, some implications relate to piglet production. For in- stance, if it is possible to decrease the price of a piglet by increasing the number of weaned piglets per sow, then pig meat producers can gain a com- petitive advantage from having access to less ex- pensive inputs. Such an increase can be profitable even if decreasing the piglet price implies minor reductions in the daily growth potential of pigs or leanness of carcasses compared to other options. From the pig meat producer’s point of view, the decrease in the growth potential or leanness (cete- ris paribus) cannot be very large because, as Cha- vas et al. (1985) and Boland et al. (1999) already noted, the technological and economic possibili- ties of animal genetics are very large. The results suggest that quality adjustments of the price of pig meat provide slaughterhouses with an efficient tool to control carcass quality. This finding is due to the fact that whenever a carcass weight-based price discount exists, it is dominant in optimising slaughter weights. Boland et al. (1993), Sipiläinen and Ryhänen (1996) and Kure (1997) also show that meat pricing affects the slaughter weights. In contrast to previous studies, this study suggests that the most effective way to control the supply of pig meat is to adjust simulta- neously both the target weight and price premium paid for red meat. This is so because as the produc- er’s incentives to increase carcass leanness in- crease, the length of the fattening period increases, and the annual production volume of pig meat per capacity unit also increases. Particularly, produc- ers who introduce a flexible feeding technology have increased options to control carcass quality. Hence, the efficiency of lean meat pricing in con- trolling meat quantities depends how flexible pro- ducers are in controlling carcass quality of a pig. Full utilisation of quality-adjusted pricing schemes also requires that both producers and slaughter- houses have sufficient and symmetric information on how incomes and pig management respond to changes in quality premiums. Since the producer cannot always fully control the timing of slaughter, failures to optimise the timing of slaughter can reduce the performance of quality-adjusted pricing schemes. This is due to the fact that the producer can minimise income losses due to delayed slaughter by marketing the animals prematurely. The result holds particularly when pigs are within the target weight range and producer cannot reduce growth rates enough through feeding. Therefore, it is important to have well defined rules for the timing of collection of animals for slaughter. Such rules can provide pro- ducer higher income and enhance the quality of 91 A G R I C U L T U R A L A N D F O O D S C I E N C E Vol. 15 (2006): Supplement 1. meat sold to slaughterhouses. The rules could in- clude definition of the date at which pigs are col- lected for slaughter if the producer markets them today. In the event of contagious animal diseases, transporting animals can reduce the effectiveness of a disease eradication policy if the transports in- crease the risk of additional infections. Because the expected delay of the timing of slaughter can be very lengthy, even a small probability of a delay can provide the producer with incentives to mini- mise potential costs. In infection areas, premature slaughter implies either a moral hazard problem or that producer suspects that animal movement re- strictions will be imposed on his/her farm. In such circumstances, the producer can increase society’s expected losses by marketing the animals in ad- vance, before the restrictions are imposed. Kuchler and Hamm (2000) and Toft et al. (2005) also have suggested, although in a different context, that management patterns are correlated with animal disease control policies. Hence, any compensation independent of whether it is obtained from the markets or from the government should be condi- tional on non-infectious management practices. Thus the compensation scheme should provide the producer sufficient incentives to minimise the probability of his/her herd being infected. Asymmetric information or the increased risk of infection in regions having an intensive contact structure can exacerbate the incentive problem. One solution to the incentives’ problem could be to take the effect of a reduction in the price of pig meat due to decreased carcass quality into account, and thus losses due to maintenance feeding, when designing compensation and restriction schemes for heavy animals. Another option could be to of- fer the producer an option to sell the animals in a buy-out scheme for economic welfare reasons dur- ing the restriction period. This would both allow epidemiologically safe culling and stabilise pro- ducer income. This study, however, does not focus on the question of whether society should organise such an income stabilisation scheme. In each case, special attention should be paid to producers keep- ing heavy animals (>100 kg) in stock, because they would be better off to interrupt farming in- stead of continuing. Furthermore, as Meuwissen (1999) and Meuwissen et al. (2003) note, the groups which are responsible for actions and their consequences should be agreed before the emer- gency situation occurs in order to avoid misunder- standings and actions due to missing or imperfect information. 8.3 Suggestions for further research The approach used in this study allows us to solve numerically a general dynamic programming problem that cannot be solved analytically. The postulated model takes into account the dynamic and simultaneous nature of pig meat production as suggested by Chavas et al. (1985). It maximises internal rate of return to the capacity unit and al- lows producer to adjust production according to the current pig quality. One major advantage of the structural-form model presented here is that it can explicitly link feed components with carcass com- position and meat quality. As opposed to reduced- form models, this analysis examines marginal changes in cases where genotype and state of a pig is known. The implications of such issues as het- erogeneity of a pig group and unknown production technology have been examined in previous stud- ies (such as Jorgensen 1993, Boland et al. 1996, Kure 1997, White et al. 2004). Further studies could extend this analysis to deal with cases in- volving unknown genotypes. The results are conditional on the functions, prices and growth parameters that are used in the model, and on the ability of producer to control carcass quality of individual pigs on a daily basis. They give information to producers and policy planners on how pig management patterns and the value of a capacity unit change in reaction to changes in relative prices, animal quality, animal growth rates, technology and constraints related to pig fattening. This information provides them with alternatives to adjust feeding regimens instead of 92 A G R I C U L T U R A L A N D F O O D S C I E N C E Niemi, J.K. Optimising feeding and slaughter decisions regarding pigs ignoring these variables by adhering to globally applicable optimal feed levels. One of the potential future applications of this model is in the analysis of production and market- ing contracts in pig production. The model can be extended to include the effects of price uncertainty, price volatility, and other production costs than piglet and feed costs even if the current analysis excludes these effects (for a pig management ap- plication under price uncertainty, see Burt 1993). Another extension might involve analyses in which prices of inputs and outputs are mutually correlat- ed and vary simultaneously but price sets are ran- dom. According to statistics presented in Tike (2003) and elsewhere, however, the price of pig meat in Finland is quite stable. In 2001–2003 the standard deviation of the change in the average price of pig meat over the period of 3 months was approximately €0.036. Furthermore, as some slaughterhouses announce prices in advance for a given period, producers may have quite consistent price expectations in the short run. This helps in planning and implementing feeding patterns. The fact that the results are estimated only for a period of 5 years underestimates the value func- tions. This kind of normalisation has no impact on which scenario producer prefers if he/she is al- lowed to choose between them, because the sce- narios are compared using the same units of meas- ure. However, it would be more useful to extend the length of the estimation period such that the value function also converges. As choice of functional forms is important for modelling, assumptions regarding concavity and decreasing marginal product are occasionally dis- cussed in the literature. Concavity can be particu- larly important when the choice is made between restricted and unrestricted feeding. In pig fatten- ing, the main problem is that biological studies generally postulate pigs to respond linearly or al- most linearly to increasing amounts of feed in the diet (cf. Black 1995). This can result in a corner solution or unstable decision variables in optimisa- tion models. Hence, it increases the importance of growth restrictions. Nevertheless, Emmans and Kyriazakis (1995) critisise the lack of empirical biological evidence to support the assumption that marginal energetic efficiency decreases above maintenance requirements. As the growth equations used in this model are combinations of several functions, it is impossible to ensure that the production function is globally concave. This concavity problem resulted in ir- regular shapes of optimised feeding curves in some scenarios. These irregularities were probably due to the fact that marginal returns from producing an additional unit of lean meat or fatty meat were, in some cases, non-decreasing. A simulation of pig growth in selected scenarios using optional man- agement patterns, however, verifies that under given model formulation, any potential bias of es- timated management patterns is negligible. Boland et al. (1999, p. 92) also noted that their model was not globally concave. For this reason, they per- formed a heuristic matrix test. The results of this test allowed them to conclude that their optimal solution is likely to be also a global optimum. One optional modelling approach to ensure concavity of the production function could be to estimate the transition equations so that they have well defined microeconomic form, such as in Chavas et al. (1985) or Campos (2003). Another issue related to model validity is the consistency of growth parameters. In empirical studies where feeding is unrestricted (ad libitum), it is important to know whether the pig’s growth potential actually restricts pig’s growth. If not, then feeding (or some other factor, such as climate) actually limits the growth, and the data cannot be used to estimate the pig’s growth potential. The parameters used in this study, however, are expect- ed to be valid. One of the strengths of this study is that the parameters of the model are known. In other words, the problem was to estimate pig pro- duction management patterns conditional on pa- rameters, not to determine the parameters them- selves. Therefore, the results provide the best in- formation on how the producer can adjust manage- ment decisions when the values of the parameters change. Future applications could also examine the case where the genotype and the state of nature of a pig are unknown. As the results of Parsons et al. (2004) suggest, this could affect producer’s op- tions to control carcass quality. Taking into ac- 93 A G R I C U L T U R A L A N D F O O D S C I E N C E Vol. 15 (2006): Supplement 1. count the case of unobservable parameters would allow a comparison between full-information man- agement pattern and a limited-information man- agement pattern. The uncertainty aspect includes at least two scenarios. In the first scenario, pro- ducer is unable to observe the true current state of nature. In the second scenario, he/she is unable to observe the next-period state of nature (i.e. sto- chastic growth pattern). This study estimated the optimal feeding and slaughter patterns for an individual pig. Although the results provide information on how non-opti- mal management affects the value of a capacity unit, further research is needed to extend the anal- ysis to large heterogeneous groups of pigs. The problem is interesting because, as Kure (1997) and Jorgensen (1993) point out, variation of the pig’s genetic characteristics can decrease the value of information about large groups of pigs. Taking into account heterogeneity of pigs is important and it requires including the distribution of the states of nature in the model. Such an extension is analyti- cally equivalent to optimising the current model, but it exposes the model to the problem of the curse of dimensionality. Unexploited opportunities may also exist to reduce the problem of the curse of dimensionality by using a more efficient dy- namic programming algorithm or by enhancing the technical performance of the current program. One option to improve the computational efficien- cy of the model could be an approach in which the terminal value of an infinite process is received af- ter marketing the current batch, and where the so- lution to the optimisation problem is obtained by repeating a procedure that updates the terminal value (for details, see Kure 1997). Further research is also needed on appetite control. Chavas et al. (1985, p. 642) discuss a sim- ilar problem. Information is required particularly on how low the ratios of protein to energy in feed can be under suitable markets without affecting the efficiency of feed conversion. Such information could give further insights into the benefits of re- stricted feeding, and the results of this study could be validated with a growth experiment. When optimising production, producers fre- quently use feed inputs efficiency as a measure. Feed efficiency is the ratio of the amount of feed required to produce one kilogram of meat. 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Optimal policies for marketing cull cows. American Journal of Agricultu- ral Economics 62: 456–467. SELOSTUS Dynaamisen ohjelmoinnin malli lihasikojen optimaalisen tuotantokierron ja ruokinnan määrittämiseksi Jarkko K. Niemi MTT (Maa- ja elintarviketalouden tutkimuskeskus), Taloustutkimus Tässä tutkimuksessa tarkasteltiin tarkennetun ruokinnan ja eläinaineksen perinnöllisen laadun parantamisen ta- loudellisia hyötyjä suomalaisilla lihasioilla. Tarkenne- tulla ruokinnalla tarkoitetaan sialle annettavan rehun määrän ja koostumuksen sovittamista sian kasvunvai- heen, perinnöllisten tekijöiden ja hintasuhteiden mukaan niin, että sika voi hyödyntää mahdollisimman tehok- kaasti rehussa olevan energian ja valkuaisen. Lihasiko- jen taloudellisesti optimaaliseen ruokintaan vaikuttavat monet eri tekijät, kuten sian perimä, markkinatilanne ja sika-aineksen vaihtelu. Tämä tutkimus tarjoaa ensisijas- sa tietoa siitä, miten sianlihan tuottaja voi sopeuttaa sian ruokintaa ja teurastuksen ajoitusta tuotantopanosten ja lihan hintasuhteiden, eläimen perinnöllisen tason (mm. päiväkasvu ja ruhon rasvoittumisherkkyys) ja tuotanto- teknologian joustavuuden muuttuessa. Tutkimustuloksia tulisikin tarkastella ensisijaisesti vertaamalla tarkastel- tuja skenaarioita keskenään, sillä tulokset johtuvat erois- ta skenaarioiden lähtötiedoissa. Tutkimusmenetelmänä käytettiin numeerista dynaa- misen ohjelmoinnin mallia. Malli simuloi yksittäisen sian päiväkasvua ja optimoi ruokinnassa käytettävän re- hun koostumuksen ja määrän sekä teurastuksen ajoituk- sen annettujen lähtötietojen (rehujen, porsaan ja lihan hinnat, rehujen laatu, sian perimä) määräämissä rajoissa. Sian teuraspaino, ruhon koostumus teurastushetkellä ja ruokinta optimoitiin niin, että ne antoivat sikapaikalle mahdollisimman suuren tuoton. Tarkastelussa käytetty ruokinta perustui ohra-soijarouhe-aminohappotäyden- nys-seokseen, jonka määrä ja koostumus optimoitiin erikseen kasvatusjakson jokaiselle päivälle. Ruokinta- ja teurastuspäätöksiä määritettäessä otettiin huomioon se, miten sian perimän, ruokinnan ja teurastuksen ajoituk- sen välinen yhteys vaikuttaa ruhon laatuun ja sikapaikan tuottoarvoon. Lisäksi otettiin huomioon se, miten sian syöntikyky ja ravinteiden tarve rajoittavat tuottajan mahdollisuuksia valita rehun koostumus ja rehuannok- sen määrä. Tulokset viittaavat siihen, että lihasikaa kannattaa pääsääntöisesti ruokkia rajoitetulla energiaruokinnalla. Siksi on tärkeää, että rehu sisältää sian tarpeeseen näh- den riittävästi valkuaista. Optimoidun ruokinnan mukai- sesti toimittaessa nuorta lihasikaa ruokitaan korkean valkuaispitoisuuden omaavalla rehulla ja lähes teuras- kypsää sikaa korkean energiapitoisuuden omaavalla re- hulla. Perusskenaariossa (luku 4) soijarouheen osuus rehussa laskee joustavasti niin, että 25 kg painavan por- saan rehuannoksessa soijarouhetta on noin 20 % ja teu- raskypsällä sian annoksessa vajaat 5 %. Samalla ohran määrä rehussa lisääntyy. Porsaan rehuannos sisältää 1,25 kg ohraa päivässä ja teuraskypsän sian rehuannos noin 2,60 kg ohraa päivässä. Tutkimuksen perusskenaariossa 99 A G R I C U L T U R A L A N D F O O D S C I E N C E Vol. 15 (2006): Supplement 1. ohran määrä vakiintuu 2,6–2,7 kg:an päivässä päivässä jo noin kuukausi ennen teurastusta. Lisäksi sialle anne- taan aminohappotäydennyksenä 2,7 g lysiiniä, 0,8 g me- tioniinia ja 1,3 g treoniinia/1 kg ohraa. Perusskenaariossa sika saavuttaa 115 kg teuraspai- non (vastaa noin 85 kg ruhopainoa) 105 päivässä. Pe- russkenaariossa sikapaikka tuottaa vuodessa noin 150 € korvauksen tuotantoon sitoutuneelle työlle, pääomalle ja muille tuotannontekijöille kuin porsaille ja rehulle. Tar- kennettuun kaksivaiheruokintaan verrattuna joustava ruokintateknologia antaa 1,70 € lisätuoton sikapaikkaa kohti vuodessa. Tämän ohella lisätuottoja saadaan sika- kohtaiseen ruokintaan siirtymisestä ja kaksivaiheruokin- nan tarkentamisesta. Tarkennetussa kaksivaiheruokin- nassa sikoja ruokitaan alkukasvatusrehulla 65–75 kg elopainoon asti ja rehun määrää (muttei koostumusta) muutetaan sian kasvun mukaisesti. Lähtötietojen vaikutusta tuloksiin tarkasteltiin ver- taamalla perusskenaarion (luku 4) tuloksia vaihtoehtois- ten skenaarioiden (luvut 5–7) tuloksiin. Tulosten mu- kaan taloudellisesti optimaalinen lihasian ruokinta riip- puu markkinatilanteesta. Malli suosittaa ruokkimaan si- kaa vapaalla ruokinnalla ja energiavaltaisella rehulla silloin, kun sianlihan hinta on korkea suhteessa punai- sesta lihasta maksettavaan laatulisään. Tällöin ruokinta maksimoi sian päiväkasvun. Muissa tapauksissa malli suosittaa rajoittamaan energiaruokintaa. Tällöin ruho kasvaa lihakkaammaksi kuin vapaalla ruokinnalla. Ra- joitetun ruokinnan kannattavuus johtuukin siitä, että tuotantokierron pidentymisestä huolimatta tuottaja voi lisätä sikapaikan tuottoa nostamalla ruhon laatukorjattua arvoa ruokinnan avulla. Rehun valkuaispitoisuutta kan- nattaa lisätä myös silloin, kun kaikkien rehujen hinnat tai teuraspalkkio laskevat. Sen sijaan vain rehun oman hinnan noustessa sitä kannattaa korvata muilla rehuilla. Energiaruokintaa vähennettäessä tulisi huolehtia siitä, että rehun sisältämän valkuaisen määrä ei laske energia- pitoisen rehun määrää vähennettäessä. Toisin sanoen energiapitoisen rehun määrää vähennettäessä myös re- huannoksen sisältämän valkuaisen määrä vähenee, mikä tulisi korvata lisäämällä valkuaispitoisen rehun määrää. Taloudellisesti optimaalinen lihasian ruokinta riip- puu myös sika-aineksen perimästä (genotyypistä). Tu- losten mukaan sikoja, joilla on perinnöllinen taipumus nopeaan päiväkasvuun ja jotka rasvoittuvat helposti, kannattaa ruokkia energiapitoisemmalla rehulla kuin si- koja, joilla on taipumus hitaaseen päiväkasvuun ja jotka säilyttävät lihakkuutensa melko hyvin. Tässä tutkimuk- sessa ei kuitenkaan tarkastella tilanteita, joissa peräk- käisten sikaerien perinnöllinen taso vaihtelee voimak- kaasti. Lihakkuutensa hyvin säilyttävillä sioilla rehun valkuaispitoisuus pidetään melko korkea jopa yli kasva- tusjakson puolivälin, ja ohran määrä rehussa nousee melko suoraviivaisesti. Sen sijaan samaan päiväkasvuun yltävillä sioilla, joiden valkuaisen kasvukyky laskee no- peasti, rehun valkuaispitoisuus laskee melko nopeasti siitäkin huolimatta, että ne tarvitsevat alkukasvatuksessa runsaasti valkuaispitoista rehua. Tulokset viittaavat siihen, että nopeakasvuiset ja vä- härasvaiset siat voivat antaa hidaskasvuisiin ja helposti rasvoittuviin sikoihin verrattuna jopa yli 20 euron lisä- tuoton lihasikapaikkaa kohti vuodessa. Perusskenaarion hintasuhteilla esimerkiksi 10 K-indeksipisteen parannus sian perimässä tuottaa vuodessa 14,51 € lisätuoton sika- paikkaa kohti. Sian biologisen maksimipäiväkasvun noustessa elopainovälillä 20–120 kg keskimäärin 100 g saadaan sikapaikkaa kohti kohti vuodessa 23,54 € lisä- tuotto. Lisätuotto on hieman suurempi, mikäli päiväkas- vua nostettaessa panostetaan niin sanotun aikuistumis- suhteen sijasta aikuispainon nostamiseen. Hyödyt johtu- vat osittain siitä, että keskimääräistä korkeamman ai- kuispainon omaavat siat ovat rasvattomampia kuin muut siat. Koska geneettinen parannus on jokseenkin pysyvä, edellä mainittuja lisätuottoja voidaan saada pitkältä ai- kaväliltä. Eläinjalostuksen tulosten täysimääräinen hyö- dyntäminen kuitenkin edellyttää tuotantopanosten käy- tön tehostamista sian perintötekijöiden mukaan. Tämä johtuu erityisesti siitä, että nopeakasvuisen ja vähäras- vaisen sian tuotanto-ominaisuudet saadaan täysin hyö- dynnettyä vain, mikäli lihakkaan ruhon tuottamiseen tarvittavan valkuaisen määrää rehussa muutetaan sian kasvukyvyn mukaan. Tulokset viittaavat siihen, että sika kannattaa teuras- taa teuraspainon ollessa mahdollisimman lähellä kor- keimman hintaportaan yläpäätä. Siten lihan hinnoittelun muuttuessa myös optimaalinen teuraspaino muuttuu. Jos teurastus jostain syystä uhkaa viivästyä niin että sika kasvaa ”ylipainoiseksi”, tuottajan kannattaa markkinoi- da sika ennenaikaisesti. Tulos johtuu siitä, että ylipainoi- sen sian lihasta maksetaan alennettua kilohintaa. Mikäli sika voidaan teurastaa ennenaikaisesti korkeimman hin- taportaan sisällä, tuottaja välttää lihan hintaan tehtävän laatuvähennyksen ja ennenaikaisen teurastuksen mene- tys jää melko pieneksi. Tämä pätee erityisesti silloin, kun uusi sikaerä saadaan ilman tavanomaista pitempää viivettä heti teurastuksen jälkeen. Jos teurastus kuiten- kin viivästyy, tuottaja voi minimoida laatutappioiden riskin vähentämällä energiaruokintaa. Tällöin hän estää ruhoa rasvoittumasta. Lisäksi tuottaja voi vähentää re- hun kokonaismäärää, jolloin hän minimoi ruhon painon vuoksi lihan hintaan tehtävän laatuhintavähennyksen suuruuden. A G R I C U L T U R A L A N D F O O D S C I E N C E Appendix A: Computer code of the basic model 100 This appendix illustrates functioning of the com- puter code. The optimisation problem is solved recursively by iterating on the Bellman’s equation. The iteration is carried out by discretising the state and control spaces, and thereafter solving the opti- mal controls separately at each point of the state space and at every period of the planning horizon. As Figure A1 illustrates, the model is defined in a three dimensional state space. One of the dimen- Th e am ou nt of le an tis su e (x tle an ) The amount of fatty tissue (xt fat) � (xt fat, xt lean) Th e am ou nt of so y m ea l( u t so y ) The amount of barley (ut barley) The amount of amino acid supplementation (u t aminos ) Fig. A1. The typical model is defined in a three dimensional state space, where one dimension is redundant due to the rela- tionship xt weight(xt fat,xt lean), and in a four dimensional control space, where feed allocations determine three of the dimensions and the binary slaughter variable determines the fourth dimension. The solutions are obtained using backwards re- cursion. This implies that the model solves the op- timal controls of the final period t = T first. There- after, the model solves the optimal optimal control for each period t = t–1 until the time index reaches period t = 0. At each combination of the points of the state space and the time space, the solution en- tails that the model evaluates the value of a capac- sions, the live weight of an animal, is a function of the other state variables, and hence redundant. In addition, the state vector includes several scalars such as input and output prices. Furthemore, the typical model is defined in a four dimensional con- trol space, where three of the control variables re- late to the feed levels. The fourth control variable is the binary slaughter variable, which collapses other controls to scalar when executed. ity unit for all feasible values of the control varia- bles. After the optimal solutions are obtained, the model prints out the optimal control patterns and the value function throughout the time (Figure A2). The computer code below follows a pattern similar to that shown in Figure A2. The text be- tween /* and */ is commented text separated from the computer code. A G R I C U L T U R A L A N D F O O D S C I E N C E Appendix A: Computer code of the basic model 101 Initialisation Step 1: Define input parameters: -Meat pricing scheme and input prices -Feed characteristics -Animal’s genetic characteristics -State and control variables and initial states of nature Step 2: Set up space grids: -State spaces (lean tissue, fatty tissue, live weight) -Control spaces (barley, soy meal, amino acid supplementation, binary slaughter variable) -Quality adjusted meat price and loss ratio of meat upon slaughter at each state of nature Step 3: Specify the terminal value function Step 5: Trace the optimal control paths: -Give the initial state of nature for t=1 -Use the optimal feeding and slaughter decisions from step 4 to simulate pig growth -For each t=1,…,T, find the corresponding values of the value function -Print the optimal paths of the state variables, the optimal controls and the value function over time Terminate computation and save the results reported at step 5 Step 4: Solve the optimal decision rules: -Set up computational variables and matrices and begin with t=T For each control node, repeat: -Compute instantaneous returns at each node of the control space -Solve daily growth of tissue components and live weight -Consider whether the constraints are binding at any control -Solve the next-period state of nature for each node of the control spaces -Find the next-period value function and the value of a capacity unit Repeat step 4 for each time period t=T,…,0 For each given state of nature: -Solve the controls that maximise the value of a capacity unit -Save the optimal controls and corresponding value function R ep ea tf or a ll st at e no de s t= t-1 if t>0 if t=0 If all state nodes at time t evaluated Figure A2. Fig. A2. Flow diagram of the model. 116 A G R I C U L T U R A L A N D F O O D S C I E N C E Appendix B: Sensitivity analysis of two-phase feeding This appendix presents a sensitivity analysis of the two-phase feeding technology. Table A1 illustrates the value of a capacity unit and an approximation of the optimal share of soy meal in both phases of the two-phase feeding when the feed ration is switched at live weight of 45–120 kg. As the pig is always slaughtered below 120 kg live weight, switching at 120 kg live weight in practice is the equivalent of using the same feed ration throughout the fattening period (i.e. one-phase feeding). In addition, Figure Table A1. The value function and approximated optimal share of soy meal in feed under two-phase feeding before (first phase) and after (second phase) switching the feed ratios, when the share of soy meal is adjusted once at 45– 120 kg live weight. Switching weight kg First phase % soy meal Second phase % soy meal Value function € 45 19% 9% 673 55 18% 7% 677 65 18% 7% 678 75 17% 6% 678 85 15% 6% 677 95 14% 4% 673 120*) 14% 4% 658 *) Switching the feed ratios at 120 kg live weight is equal to one-phase feeding, because the pig is slaughtered at 116 kg live weight. Table A2. The value function and approximated optimal share of soy meal in feed under two-phase feeding before (first phase) and after (second phase) switching the feed ratios, when the share of soy meal is adjusted once at 45– 120 kg live weight, and the price of pig meat is €1.62. Switching weight kg First phase % soy meal Second phase % soy meal Value function € 45 17% 7% 974 55 15% 7% 976 65 15% 6% 979 75 15% 6% 978 85 14% 4% 977 95 11% 4% 973 120*) 9% 2% 965 *) Switching the feed ratios at 120 kg live weight is equal to one-phase feeding, because the pig is slaughtered at 116 kg live weight. A3 represents the optimal feeding patterns under two-phase feeding and flexible feeding technology, when producer has incentives to feed the pig ac- cording to its natural growth potential. This scenario is parameterised as the market scenario where the price of pig meat was €1.62. In other words, when the price of pig meat is €1.62 the value of a capac- ity unit for the two-phase feeding in Figure A3 is €979 over the period of 5 years. The corresponding value for the flexible feeding technology is €991. 0 2 4 6 8 10 12 14 16 18 20 1 11 21 31 41 51 61 71 81 91 101 time in days Two phase 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 11 21 31 41 51 61 71 81 91 101 time in days kg feed per day Flexible % of feed Fig. A3. The amount of barley (kg per day, left panel) and the share of soy meal (% of the total amount of feed, right panel) in feed under two-phase feeding and as approximated in the benchmark scenario of the flexible feeding technology. The price of pig meat in both scenarios is €1.62. 117 A G R I C U L T U R A L A N D F O O D S C I E N C E Appendix C: Feeding patterns of female pigs and castrated male pigs 0 5 10 15 20 25 1 11 21 31 41 51 61 71 81 91 101 time in days % of feed Fit of castrated male pig 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 11 21 31 41 51 61 71 81 91 101 time in days kg feed per day Benchmark Castrated male pig This appendix presents the optimised feeding pat- terns for female and castrated male pigs, and their position with respect to the benchmark scenario. The Figures are based on optimising feeding and slaughter patterns separately for female pigs and castrated male pigs. The only difference between these scenarios and the benchmark scenario is that the parameters of the growth potential of the pig and the minimum fat-to-lean growth constraint are given gender-specific values. The price of pig meat in these scenarios is €1.39. The polynomial ap- proximations presented in Figures A4 and A5 cor- respond to the €1.39 curves reported in Figures 28 and 29 in Chapter 6. 1 11 21 31 41 51 61 71 81 91 101 time in days Female pig Fit of female pig 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 11 21 31 41 51 61 71 81 91 101 time in days kg feed per day Benchmark 0 5 10 15 20 25 % of feed Fig. A4. The amount of barley (kg per day, left panel) and the share of soy meal (% of the total amount of feed, right panel) in the benchmark scenario and in the female pig scenario. The fit of female pig represents a polynomial approximation of the female pig scenario. Fig. A5. The amount of barley (kg per day, left panel) and the share of soy meal (% of the total amount of feed, right panel) in the benchmark scenario and in the castrated male pig scenario. The fit of castrated male pig represents a polynomial approximation of the castrated male pig scenario. 118 A G R I C U L T U R A L A N D F O O D S C I E N C E Appendix D: Sensitivity analysis for genotype scenarios This appendix presents sensitivity analyses with respect to constraints used in the model, and additional analyses of the effects of price changes. The results below utilise the growth parameters of the genotype and split-sex feeding scenarios. The price ratios are exactly the same as those used in corresponding market scenarios in Chapter 5. In addition, Figures A6 and A7 represent changes in feeding patterns when the constraint on the mini- mum growth ratio of fat to lean is reduced by 0.2 units below the initial values for female and cas- trated male pigs. The reduced ratios are for pigs of improved genotype (Whittemore 1998, p. 68–70 and 557–558). In other words, the change allows the producer to increase the degree of restricting of feeding. The change increases the convexity of the optimal feeding pattern. As the constraint is locally binding in the benchmark scenario, the change in- creases the share of soy meal in feed and decreases the amount of barley. Notably, the pattern of change in feed ratios is larger for young pigs than for pigs close to the optimal slaughter maturity. 0 5 10 15 20 25 1 11 21 31 41 51 61 71 81 91 101 time in days % of feed Min ratio 0.8 Fit of min ratio 0.8 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 11 21 31 41 51 61 71 81 91 101 time in days kg feed per day Min ratio 1 Fig. A6. The effect of reducing the minimum growth ratio from 1 to 0.8 on the optimal feeding patterns for castrated male pigs. The effects of changes in the minimum fat to lean growth ratio on the numerical results are re- ported in Table A3 for all genotype and split-sex feeding scenarios. The results utilise price ratios similar to those in the benchmark scenario. Tables A4 and A5 represent sensitivity analyses with re- spect to price changes for female and castrated male pigs when changes in price ratios are similar to the market scenarios. Tables A6, A7, A8 and A9 repeat similar sensitivity analyses for pigs having a low K-index, a high K-index, improved maturing rate and improved mature weight. 119 A G R I C U L T U R A L A N D F O O D S C I E N C E Appendix D: Sensitivity analysis for genotype scenarios Fig. A7. The effect of reducing the minimum growth ratio from 0.9 to 0.7 on the optimal feeding patterns for female pigs. 0 5 10 15 20 25 1 11 21 31 41 51 61 71 81 91 101 time in days % of feed Min ratio 0.7 Fit of min ratio 0.7 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 11 21 31 41 51 61 71 81 91 101 time in days kg feed per day Min ratio 0.9 Table A3. Time required to reach slaughter maturity, carcass weight upon slaughter, share of red meat in the slaughtered carcass, and value function over the period of 5 years under alternative growth ratio constraints in genotype and split-sex feeding scenarios. Scenario Time to slaughter Carcass weight Red meat Value function days kg % €/5 years Castrated male pig, ratio is 1 107 85.6 61.3 674 Castrated male pig, ratio is 0.8 107 84.5 61.9 676 Female pig, ratio is 0.9 104 84.3 62.1 696 Female pig, ratio is 0.7 108 85.1 63 698 Improved mature weight, ratio is 1 95 85.2 61.7 779 Improved mature weight, ratio is 0.8 98 85.1 63 784 Improved maturing rate ratio is 1 94 84.8 61.3 772 Improved maturing rate, ratio is 0.8 95 84 62.1 775 Low K-index, ratio is 1 108 85.3 61.4 661 Low K-index, ratio is 0.8 108 83.8 62.2 664 High K-index, ratio is 1 100 85 61.6 725 High K-index, ratio is 0.8 104 85.1 62.9 729 120 A G R I C U L T U R A L A N D F O O D S C I E N C E Appendix D: Sensitivity analysis for genotype scenarios Table A4. Time required to reach slaughter maturity, carcass weight upon slaughter, share of red meat in the slaughtered carcass, and value function over the period of 5 years for castrated male pigs under alternative price parameters. The price ratios used in the scenarios correspond to those used in the market scenarios in Chapter 5. Scenario Time to slaughter Carcass weight Red meat Value function days kg % € per 5 years Benchmark price ratios 107 85.6 61.3 674 High price of pig meat 91 83.7 57.2 979 High price of piglet 107 85.1 61.7 578 High price of barley 107 85.3 61.5 652 High price of soy 103 84.8 60.5 661 High price of all feeds 107 85.3 61.5 620 High slaughter premium 99 84.6 59.3 771 Table A5. Time required to reach slaughter maturity, carcass weight upon slaughter, share of red meat in the slaughtered carcass, and value function over the period of 5 years for female pigs under alternative price parameters. The price ratios used in the scenarios correspond to those used in the market scenarios in Chapter 5. Scenario Time to slaughter Carcass weight Red meat Value function days kg % € per 5 years Benchmark price ratios 104 84.3 62.1 696 High price of pig meat 96 84.4 59.4 994 High price of piglet 108 85.4 62.8 599 High price of barley 104 83.8 62.4 674 High price of soy 104 85.1 61.7 681 High price of all feeds 104 83.8 62.4 641 High slaughter premium 100 84.4 60.7 791 Table A6. Time required to reach slaughter maturity, carcass weight upon slaughter, share of red meat in the slaughtered carcass, and value function over the period of 5 years under alternative price parameters for pigs having improved mature weight. The price ratios used in the scenarios correspond to those used in the market scenarios in Chapter 5. Scenario Time to slaughter Carcass weight Red meat Value function days kg % € per 5 years Benchmark price ratios 95 85.2 61.7 779 High price of pig meat 85 84.4 58.2 1108 High price of piglet 95 85 61.8 671 High price of barley 95 85.1 61.8 757 High price of soy 95 85.5 61.6 762 High price of all feeds 95 85.1 61.8 720 High slaughter premium 95 85.6 61.4 884 121 A G R I C U L T U R A L A N D F O O D S C I E N C E Appendix D: Sensitivity analysis for genotype scenarios Table A7. Time required to reach slaughter maturity, carcass weight upon slaughter, share of red meat in the slaughtered carcass, and value function over the period of 5 years under alternative price parameters for pigs having improved maturing rate. The price ratios used in the scenarios correspond to those used in the market scenarios in Chapter 5. Scenario Time to slaughter Carcass weight Red meat Value function days kg % € per 5 years Benchmark price ratios 94 84.8 61.3 772 High price of pig meat 85 84.6 58 1107 High price of piglet 96 85 61.8 664 High price of barley 96 85.2 61.7 750 High price of soy 92 84.2 60.9 756 High price of all feeds 95 84.9 61.6 713 High slaughter premium 88 83.4 59.8 879 Table A8. Time required to reach slaughter maturity, carcass weight upon slaughter, share of red meat in the slaughtered carcass, and value function over the period of 5 years under alternative price parameters for pigs having a low K-index. The price ratios used in the scenarios correspond to those used in the market scenarios in Chapter 5. Scenario Time to slaughter Carcass weight Red meat Value function days kg % € per 5 years Benchmark price ratios 108 85.3 61.4 661 High price of pig meat 96 84.9 57.7 956 High price of piglet 108 84.6 61.7 566 High price of barley 108 85 61.6 639 High price of soy 104 83.6 61 648 High price of all feeds 108 85 61.6 607 High slaughter premium 100 83.2 59.9 755 Table A9. Time required to reach slaughter maturity, carcass weight upon slaughter, share of red meat in the slaughtered carcass, and value function over the period of 5 years under alternative price parameters for pigs having a low K-index. The price ratios used in the scenarios correspond to those used in the market scenarios in Chapter 5. Scenario Time to slaughter Carcass weight Red meat Value function days kg % € per 5 years Benchmark price ratios 100 85 61.6 725 High price of pig meat 92 84.8 58.9 1037 High price of piglet 100 84.7 61.8 623 High price of barley 100 84.8 61.7 703 High price of soy 100 85.2 61.4 710 High price of all feeds 100 84.9 61.7 669 High slaughter premium 97 85.1 60.5 825 A dynamic programming model foroptimising feeding and slaughter decisionsregarding fattening pigs Preface Contents Abstract 1 Introduction 1.1 Background of the study 1.2 Modelling feeding and thetiming of slaughter decisions 1.3 Objectives and structure ofthe study 2 Previous studies on pig production managementand optimisation 2.1 Production and pricing ofpig meat in Finland 2.2 Features of optimised pigmanagement 2.3 Methods for optimising pigfattening 2.4 Scope and method of thestudy 3 A dynamic programming model for pig fattening 3.1 Model specification problems 3.2 The optimisation problem 3.3 Decomposing the controlvariables 3.4 The pig growth model 3.5 Restricting pig growth 3.6 One-period returns function 4 Precision feeding – a benchmark scenario 4.1 Data and scenarios 4.2 Estimation method 4.3 Results 4.4 Summary 5 Adjusting pig production management to market conditions 5.1 Data and scenarios 5.2 Results 5.3 Summary 6 The value and management implications of animal genetics 6.1 Data and scenarios 6.2 Results 7 The importance of slaughter timing8 7.1 Data and scenarios 7.2 Results 7.3 Summary 8 Conclusions and discussion 8.1 Management implications 8.2 Policy implications 8.3 Suggestions for furtherresearch References SELOSTUS Appendix