Agricultural and Food Science, Vol. 19 (2010): 43-56 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. 19(2010): 43–56. 43 © Agricultural and Food Science Manuscript received June 2008 The impact of distance to the farm compound on the options for use of the cereal plot Kalvi Tamm1*, Taavi Võsa1, Valdek Loko1, Jüri Kadaja1, Raivo Vettik1 and Jüri Olt2 1Estonian Research Institute of Agriculture, Department of Agricultural Engineering and Technology, Teaduse 13, 75501 Saku, Estonia, *email: kalvi.tamm@neti.ee 2Estonian University of Life Sciences, Institute of Technology, Kreutzwaldi 56, Tartu 51014, Estonia In increasingly competitive conditions, the dominant trend of enlarging the production area of farms is causing a growth in transportation costs making the profitability of cultivating distant plots questionable. The aim of this study was to provide a method to evaluate the rationality of using a plot depending on its distance, area and cultivation technology. An algorithm and a mathematical model were composed to calculate the total costs depending on the distance to the plot. The transportation costs of machines and materials, cost of organisational travel and timeliness costs are taken into account in the model to enable determination of the maximum distance or the minimum area of the plot necessary for profitable cultivation. Simulations allow us to conclude that the growth in yield and selling price of the production allow an increase in the limit value of driving costs and, thus, the profitable distance of the plot; on the other hand, it means also an increase of timeliness costs as a limitation for extending distance. Exploitation of more distant plots can be uneconomical in coming years because of increasing fuel costs. Key-words: farm size, plot, distance travelled, intrafarm transport, transport costs, timeliness, economic evaluation, technology, mathematical models, simulation. Introduction Under the conditions of growing competition, the trend towards enlarging the production area of farms is dominating, causing longer driving distances to the plots. During the years 2001−2007, the portion of farms of less than 50 ha decreased; those of over 100 ha increased in the total area of agricultural land in Estonia (Fig. 1). We can observe similar trends elsewhere in the world, for example, in the USA (Schnitkey 2005), Finland (Suomi et al. 2003), England (Burton and Walford 2005), and Hungary (Burger 2001). 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 Tamm, K. et al. The impact of the plot distance 44 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. 19(2010): 43–56. 45 (Bouma et al. 1998) the need for composing a me- thod that would assist determining optimal farm size. Mathematical modeling is an essential method here. In the late 1990s, a research team model- ling the agricultural production from the Estonian University of Agriculture composed a method to calculate the effect of the area of a round-shaped farm to the farm’s profitability (Asi et al. 1999). Kryachkov and Sharova (2005) studied the optimal area of farms in the region of Kursk (Russia), deter- mining factors to prognosticate the transportation costs depending on the area of the given agricultur- al enterprise. A mathematical model was presented 0 100 200 300 400 500 600 700 0 − <5 5 − <10 10 − <20 20 − <30 30 − <50 50 − <100 >=100 Farm size group, ha Agricultural land, thousand ha 2001 2003 2005 2007 Fig. 1. Division of agricultur- al land according to farm sizes in years 2001−2007 (Statistics Estonia, 2009). Table 1. The number of plots depending on plot size group in Estonia by register of area supports of Estonian Agricultural Registers and Information Board in year 2008. Plot size group Number of declared plots Declared area, ha Average plot area, ha <1 ha 46 339 24 333 0.53 1 − <5 ha 61 570 160 791 2.61 5 − <10 ha 23 876 173 126 7.25 10 − <50 ha 23 331 447 576 19.18 50 − <100 ha 951 61 840 65.03 100< 90 12 635 140.39 Total 156 157 880 301 5.64 Farmers buy or rent land primarily to increase profitability of their enterprises (Gwyer et al. 2005), but expanded production tends to have an influence on expenses as well as on income. Enlargement of arable land enables increased effectiveness of ma- chinery use, and in the case of constant machinery equipment, the fixed costs per hectare are decreas- ing. However, it may cause an increase of the costs for maintenance and repair of the machines. In 2007 in Estonia there were 23 257 farms with an average agricultural area of 39 ha; of those larger than 100 ha, 1549 farms have an average area of 405 ha. The number of plots by plots size group is given in Table 1. Aaltonen et al. (1999) reports that most plots are situated closer than 3.7 km to the farm compound in the EU and 6.6 km in Finland. There are no similar statistics for Estonia; studies are needed. The enlargement of production area influences the portion of transportation expenses in the cost price of the yield. Along with increasing distances, transportation expenses are growing as well (Stein- sholt 1997) and, in certain conditions, may exceed the increase of the income created by enlarging of production area; as a result, profitability of the farm begins to decline. The need for increasing the effectiveness of ex- ploitation of land and problems related to the grow- ing costs of energy, labour and other production resources, are calling for the creation of decision support systems that analyse and plan agricultural production. Several researchers have suggested 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 Tamm, K. et al. The impact of the plot distance 44 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. 19(2010): 43–56. 45 to calculate the profitability of the proposed farm depending on its production capacity. The aim of these studies was to compose a method for determining the optimal size of a farm. Nevertheless, using this parameter in real-life man- agement of production is questionable. Should the farmer exclude from production the plots located outside the critical distance, i.e., sell or lease them, and seize the plots located in the vicinity, i.e., buy or rent them? In reality, individual plots have in- dividual properties, different crops, and, thus, dif- ferent operational capacities and production costs (Jabarin and Epplin 1994, Harasimowicz and Ost- ršgowska 2001). One critical factor is the size of the plot. Introduction of a small plot located far away from the farm compound will probably not be economical as the transportation costs will be so high that the production will not be profitable. This may also be true for plots remaining inside the criti- cal border. For planning of production, therefore, a method is required to analyse the costs taking into account the distance, the area and the cultivation technology used there. In an overview of studies in the field of agrolo- gistics, Hahn (2006) denotes that theory-forming contributions to the mentioned research area are still rare in literature. Morlon and Trouche (2005) also find that there is scarcely relevant scientific literature available and the existing materials are generally based on ancient or simplistic schemes and models which are not of practical use in the present conditions. There are, however, references to studies in which distances inside the farm are used as one of the problematical factors of plant production. One of the first contributions in that area was worked out by Johann Hermann von Thünen (1783−1850), who developed the model to describe the land use practices radiating out from a central market loca- tion (Crosier 2009). He theorized that several rings of agricultural land use practices would surround the central market place. The land within the closest ring around the market produces products that are profitable in the market, yet are perishable or dif- ficult to transport. As the distance from the central market increases, the land use shifts to producing products that are less profitable in the market, yet are much easier to transport. The general approach of von Thünen illustrated the use of distance-based gradient analysis (e.g., the change in value for a variable such as land rent with increasing distance from the city center). De Garis De Lisle (1982) has studied the effects of intra-farm distance on farm income and on inter- nal cropping patterns. The research was based on the data of the farms situated in Manitoba (Canada) collected by crop insurance agents. The following conclusions were drawn: 1) the distribution of crops is affected both by the distance of the plot to the farm compound and the soil productivity; 2) adjustments to the organization and intensity of farming compensate the effects of distance on the net income. Myyrä and Pietola (2002) estimated with the help of a switching-type Probit-model the shadow prices for land parcel characteristics in Finland, such as size and distance from the compound, by adding these characteristics to the conditional profit maximization model. Their research concludes that plot size and distances from the farm compound significantly affect the farmer’s choice of allocat- ing most of the land either to grass or to grain. Harasimowicz (1997) describes an evaluation sys- tem, where plot distance to the compound is one factor affecting land value in points characterising the profitability potential of land: a plot situated far away is assessed to be less valuable than a closer one. The literature overview indicates that there is no research available containing a method to esti- mate rationality for exploitation of the plot based on the distance between plot and farm compound. The aim of this study is to compose a mathematical model to calculate these costs and thereby estimate the rationality of exploitation of a plot on the basis of driving distance. The model considers transpor- tation costs of aggregates, hauling costs of materi- als, income loss caused by delays in field work, and the cost of organizational drives. All the factors in- fluencing technology, like crop (Fig. 2), machines or technological materials can be considered with choice of technology. The present model considers the cereals seedbed preparation and sowing opera- tions’ influence on the income loss. 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 Tamm, K. et al. The impact of the plot distance 46 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. 19(2010): 43–56. 47 On the basis of the model, software “Field dis- tance” is composed, enabling, in a relatively short period of time, evaluation of the rationality of using different technologies on a particular plot depend- ing on its area and distance. The paper gives an overview of the composed model and its practical use with different tillage technologies. The simulations are used to estimate the influence of the price of fuel and yield, as well as the yield level on the economical maximum of plot distance. The model Economical parameters depending on plot distance Following the aim of composing the mathematical model for evaluating the rationality of exploitation of a plot taking into account the driving distance, we concentrated on the economical parameters depending on that factor. The expenditures arising from distance were separated from other production costs; these are the costs related to the transporta- tion of the field aggregates and the technological materials, and the costs of all organizational trips to the plot (Tamm 2006). In addition to the expenses, we need to look at the effect of driving distance on income. If the distance increases, the daily perform- ance of the field aggregate will decrease and work periods will lengthen; as a result, the working time will increasingly deviate from the optimal and the average yield will decrease. The consequent income loss is considered a cost, as well. Thus: Kh=Ks+Kv+Ko+ΔT, (1) where Kh is the sum of costs depending on distance to the plot (€ ha-1), Ks is the driving cost of aggregate to and from the plot for one production year (€ ha- 1), Kv is the cost of hauling the materials to or from the plot (€ ha-1), Ko is the driving cost of service vehicles per one production year (€ ha-1), and ΔT is the income loss caused by driving duration (€ ha-1). The evaluation of options of exploitation of the plot Using a plot within a certain distance is rational in cases when the cost Kh related to distance is less than the maximum value Kh,max (Kh≤ Kh,max). The last one is found with formula Kh,max =T–Km (2) where T is predicted income (€ ha-1) and Km are the costs independent of distance (€ ha-1). If the model user wants take into account the profit or the production risk, these factors can be added to Km. In order to determine the economically reason- able maximum distance between farm compound and the plot considering its area and technology, the distance in the case of Kh,max must be found. While the distance cannot be analytically found by the system of formulas composed for calculating Kh, then the iterative method is used. The method enables finding the distance in which the sum of the costs is the nearest to the limit value. i.e., Kh→ Kh,max. The plot area and the technology are fixed while seeking distance d. In the case of the iterative method, it is necessary to define the tolerance δ; when it has been achieved, the calculation proce- dure will be completed. In other words, the follow- ing condition should be fulfilled: |Kh– Kh,max |≤δ. (3) If the condition (3) is met, then the distance used for finding the parameter Kh is the economi- cally reasonable maximum distance between the farm compound and the plot, considering its area and technology. There are three phases of the iterative method: we used the determination of the initial solution, the secant method (Weisstein 2006a) and bisec- tioning (Weisstein 2006b). The calculations thus far show that the 50 cycles are enough to reach a satisfying solution. After having tested the model, the following schema is composed to search solu- tion: 1) 1st Cycle – calculating the initial solution, 2) 2nd −5th Cycle – secant method, and 3) 6th – 50th Cycle – method of bisecting of interval. That mathematical construction also enables the search for minimum area of plot at known 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 Tamm, K. et al. The impact of the plot distance 46 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. 19(2010): 43–56. 47 distance. The machines would still drive back and forth at least once even for a tiny plot. Thus the farmer has transportation costs, independent of plot size. However, the plot can be so small that the income does not cover the transportation costs, especially when the distance is long. It means that Kh>Kh,max – the transportation costs are larger than the amount of money available for transportation expenses. The larger the plot, the smaller the trans- portation costs per ha (costs are divided with the area) unless two trips are made – then the sum of transportation costs per ha jerk upward and then start to decrease again, etc. (Fig. 4). If the mar- ket conditions are favourable for the farmer, then with increasing the plot size the income for the whole plot grows faster than costs; at some point, the value of the area is Kh