IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

39 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

ANALYTIC HIERARCHY PROCESS APPLICATION FOR

MULTIPLE PURPOSE FOREST RESOURCES MANAGEMENT

BUDGET ALLOCATION IN DURANGO, MEXICO

Aregai Tecle

Professor, College of Engineering, Forestry and Natural Sciences,

Northern Arizona University

Flagstaff, Arizona

aregai.tecle@nau.edu

Gustavo Perez-Verdin

Associate Professor,

Instituto Politecnico Nacional, Sigma 119

Durango, Mexico

ABSTRACT

A very important aspect of natural resources management is determining optimal budget

allocation to satisfy the needs and aspirations of multiple stakeholders. This is especially

the case in developing countries like Mexico where budgetary funds are in short supply.

There has been an increasing debate in Durango, Mexico, for example, about determining

the most efficient way of allocating a budget for multi-purpose forest management. The

debate has been triggered by a growing number of interests and stakeholders, which in

addition to optimal timber production, have the desire to improve environmental

conditions, water resource development, range and other non-timber resources

production, and to provide better amenity values and expanded recreational opportunities.

CONAFOR (COmisión NAcionale FORestal), the Mexican agency in charge of

allocating funds to promote sustainable forest resources development, has been

implementing four national programs: developments of forest resources, tree plantations,

non-timber products, and water resources. In addition to these programs, the forest

resources management decision-making process involves four interest groups and six

management objectives independently connected in a hierarchical framework.

Accordingly, the most suitable multi-objective/multi-criterion decision-making

(MODM/MCDM) technique for optimal allocation of scarce budgetary funds among the

four natural resources development programs is the Analytic Hierarchy Process (AHP).

The two programs that receive the most funds are forest resources development and

water resources/ environmental services development. In this way, the AHP can be used

to optimally distribute scarce financial resources among competing programs to improve

regional economic development and better satisfy the needs of various interest groups.

Acknowledgements: The authors wish to express their gratitude to Dr. Ciro Hernandez-Diaz of

Silviculture and Wood Research Institute and Ramon Silva-Flores, a resource planner with

CONAFOR-Durango, for their invaluable help in getting the data used in the pairwise comparison

matrices and making the CONAFOR budget available. This project was partially funded by the

state of Arizona’s Prop 301 funding and Mexico's CONACYT.

mailto:aregai.tecle@nau.edu

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

40 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

Keywords: Multi-objective forest management; CONAFOR; forest budget allocation;

Mexican community forestry; ejido; utility model

1. Introduction

In the past, Mexican forest management decision-makers and consultants focused their

allocation of funds primarily on agroforestry-related resource management activities.

The intention was to support forestland farming communities who depended on timber

production, cattle grazing and crop farming for their livelihood. Recently, however, there

is a growing interest among stakeholders on improving other land-based goods and

services such as environmental protection, water production, natural resources

conservation, as well as promoting biodiversity, and cultural and recreational values. This

in principle is multi-objective forest resources management. In this regard, the concept of

multiple-use forestry is being revised by Mexican federal and local governments to more

efficiently allocate scarce funds. The revision entails adopting a forest resources

management approach that incorporates the views and aspirations of multiple, some of

them conflicting, stakeholders. Such stakeholders in a forest ecosystem management may

include community and individual landowners, the logging industry, wildlife enthusiasts,

forest-related resources managers, non-government organizations (NGOs), the general

public, and federal and local institutions (Tecle et al., 1995, 1998; Jenkins, 2005; Niemela

et al., 2005; Hossain & Robak, 2010).

A considerable portion of the necessary funds for managing Mexican natural resources

comes from the National Forest Commission (or CONAFOR which stands for its Spanish

equivalent acronym). CONAFOR is a relatively recent Mexican federal agency created

by a Presidential Decree on April 4, 2001. Its main objectives are to promote efficient

forest management and restoration activities and to enforce and monitor sustainable

forest development policies. To achieve these objectives, CONAFOR has recently been

engaged in projects that increase forest stock levels. The projects include development of

plantation forestry and improved management of native forests, improvement of

landowner’s resource management skills, development of forest system management for

non-timber products such as resins, oregano and mushrooms, and rewarding landowners

whose efforts have improved water quality and environmental protection (Perez-Verdin

et al., 2011). For instance, recently combined federal and state funds equivalent to US

$4.1 million were issued in the budget to support 1,200 projects in the state of Durango,

Mexico (see Figure 1). The aims of the projects were grouped into nine categories: (1)

managing timber, (2) developing plantation forestry, (3) increasing non-timber products,

(4) expanding recreational opportunities and ecotourism, (5) protecting water quality and

quantity, (6) enhancing environmental quality, (7) fostering skilled manpower

development, (8) providing technical assistance, and (9) reducing operational costs.

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

41 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

Figure 1 Location of the State of Durango in Mexico (Rhoda and Burton, 2010)

Allocating a budget to such a complex problem consisting of different resources with

non-commensurable values, and involving numerous interested parties some with

incompatible and conflicting objectives like those stated above is a multi-objective

problem (Tecle et al., 1995; Zanakis et al., 1995; Schmoldt et al., 2001a, 2001b). Such a

problem tends to become more complex as it usually involves evaluating the

performances of numerous alternative management programs using a set of criteria to

arrive at the most preferred decision outcome(s) (Tecle & Duckstein, 1994; Duckstein &

Tecle, 2002; Vaidya & Kumar, 2006). In the problem under study, the alternatives are the

varying ejido forest management budget allocation levels, and the preferred outcome is

the most optimal budgetary allocation to achieve the various management objectives that

can produce the most satisfying mix of forest resources products and services.

In general, there are numerous types of multi-objective/multi-criterion decision-making

(MODM/MCDM) techniques that have been used to solve various types of multi-

objective problems (Tecle, 1992; Tecle & Duckstein, 1994; Triantaphyllou, 2000;

Duckstein & Tecle, 2002; Hajkowicz & Higgins, 2006; Vaidya & Kumar, 2006; Moseley

et al., 2009; Sadeghi et al., 2012; Mardani et al., 2015). A typology of the many different

available techniques is summarized in Duckstein and Tecle (1993a), while their solution

approaches are described in Duckstein and Tecle (1993b). There are many

MODM/MCDM techniques that have specifically been used to analyze and solve varying

types of multi-objective forest resources management problems (Kangas, 1992; Tecle et

al., 1995, 1998; Kangas et al., 2001; Jenkins, 2005; Krcmar et al., 2005; Niemela et al.,

2005; Phua & Minowa, 2005; Hajkowicz & Higgins, 2006; Balteiro & Romero, 2008;

Ananda & Herath, 2009; Balteiro et al., 2009; Šporčić et al., 2010; Šporčić, 2012, to

mention some). Very few of these problems involve costs and budget allocations in

multiple objective forest resources management projects; yet, to the best of our

knowledge, this study is the only one specifically dedicated to optimally allocate scarce

budgetary funds to a multi-objective community level forest resources management

Mexico

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

42 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

(Kangas, 1992; Tecle et al., 1998; Balteiro et al., 2009; Chiou et al., 2009; Poff et al.,

2010, 2012; Bradford & D'Amato, 2012; White & Bordoloi, 2015).

As noted previously, there are numerous multi-criterion decision-making approaches that

have been used to evaluate and solve various types of multi-objective forest resources

management problems (Mendoza & Prabhu, 2000; Kangas et al., 2001; Balteiro &

Romero, 2008; Poff et al., 2010, 2012; Šporčić et al., 2010; Šporčić, 2012; Tecle &

Jibrin, 2014). However, the formulation of the different parts of the problem in an

interconnected hierarchical structure makes this particular problem a candidate for

evaluation using either the Analytic Hierarchy Process (AHP) or the Analytic Network

Process (ANP). But, since the different levels in an Analytic Network Process show

interactions and dependence among themselves as described, for example, in Cheng and

Li (2004), Ozdemir et al. (2011), Thangamani (2012), Sadeghi et al. (2012), Napoli and

Schilleci (2014), and Saaty (2017), the ANP is excluded in favor of the AHP. The latter

is so because the different levels in the budget allocation problem are independent of each

other to justify and favor the use of the AHP (Leskinen, 2000). The AHP evaluates the

multi-objective forest resources management budget allocation problem by incorporating

public values to indicate preferences in the decision making process (Saaty, 1977, 1980,

1988, 1990; Schmoldt et al., 2001a; Niemela et al., 2005; Proctor, 2005; Saaty & Vargas,

2006; Ishizaka & Labib, 2011). Furthermore, we found the AHP to be a relatively simple

and effective method with an ability to deal with both quantitative and qualitative criteria

to determine the most efficient budget allocation for the multi-objective ejido forest

management problem under consideration.

2. Problem description

In the past, Mexican planners and resource managers rarely focused on developing

strategies that strengthen multiple use and sustainable land resource development

practices. Hence, federal programs resulted in poor resource management scenarios that

jeopardized sustainable development, which eventually led to a decrease in resource

productivity and an increase in environmental degradation as stated herewith.

The lack of a consistent policy to strengthen ejidos [common properties]

has grave social and economic implications that result in the degradation

of natural resources, which consequently prevents rural communities

from making sustainable use of land resources such as forests leading to

a decreased quality of life. This creates the vicious cycle of degradation,

poverty and poor quality of life. (Semarnat, 2000, p. 43)

Recent changes have improved the management of natural resources by developing new

forest policies and their enforcement to promote not only sustainable resource

management but also improve important environmental services. These in turn have led

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

43 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

to improved research, and more efficient decision-making. Such changes are necessary to

alleviate the disparities between farmers and forest landowners. Previously, crop farmers

received a government subsidy to cultivate their lands, while forest landowners did not

receive any funds to help them improve management of their natural resources; instead,

they were blamed for the deterioration in land productivity and the poor quality of water

coming from the forested areas. To ameliorate the situation, the Mexican government

through CONAFOR has decided to manage the ejido forest system by developing four

different forest resources/service programs to improve and optimize sustainable forest

resources productivity. The programs are forest development (FD), plantations

development (PD), non-timber products development (NTP), and water

resources/environmental services development (WH). Table 1 shows a one year U.S. $4.1

million Mexican government budget allocation to these four different forest resources

management programs.

Table 1

A one-year federal budget allocation to manage the four forest resources/service

development programs.

Programs Budget (mill $) %

Forest development (FD) 2.16 53

Plantations development (PD) 1.45 35

Non-timber products development (NTP) 0.49 12

Water resources/ environmental

services development (WH)

Total $4.10 100

The main objectives for developing the four different forest resources /services programs

are: (1) to promote the sustainability of primarily timber-related products, (2) to improve

landowner’s resource management skills and (3) to reduce operational costs. Of the four

programs, forest resources development (FD) was considered the most important one

receiving the largest share of the budget with the largest number of individual projects

funded. The plantation development program (PD) was designed to increase forest stocks

through establishing new commercial plantations, by producing seedlings and reforesting

burned areas and former agricultural or pasture lands. The non-timber products

development program (NTP) was not given as much importance as the first two

programs, and was meant to focus on the production of items such as oregano and

mushrooms and the development of fisheries and improved ecotourism projects. Though

these kinds of multiple programs development plans were designed to operate in only six

wetter and more forested states of Mexico, the state of Durango was included because of

its enormous potential to generate similar products in its temperate and semi-arid forested

areas. The fourth program, water resources/ environmental services development (WH),

was the latest program created by the federal government to protect and enhance amenity

values, improve water quality and quantity, increase carbon sequestration, promote

recreation, and reduce the pressure on timber-based products. It was not funded during

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

44 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

the above budget year, but both federal and state authorities expect its importance to

grow quickly as the public becomes more aware of and familiar with it.

The mandate to develop these programs involves providing monetary resources directly

to landowners to help them achieve sustainable forest management. The fundamentals of

these Mexican national programs are fully described in the “2001-2006 National Forest

Program”. The main aspects of the program consist of seven national strategies and 14

objectives which are designed to promote sustainable forest management in Mexico. To

satisfy the objectives, the four national programs (FD, PD, NTP, and WH) were

developed as the feasible programs to compete for the limited funds. But, first the 14

objectives and nine project categories are reduced into six management objectives

specifically designed to: (1) improve economic benefits, (2) increase water yield, (3)

increase recreational or other environmental benefits, (4) increase forest stocks, (5)

reduce operational costs, and (6) increase yield of non-timber products. Note that some

important biological objectives such as maintaining biodiversity or protecting wildlife

habitat which are not within CONAFOR’s areas of responsibility are not included in the

above list. On the other hand, all the interested parties in Durango who are involved in

multi-purpose forest resources management are considered part of the study. Those

parties are grouped into those members of the public or government sector (PUB),

landowners (LND), those who belong to the private sector (PRV), and members of non-

governmental organizations (NGOs). The latter includes environmental groups and non-

profit forest-interest organizations. Landowners, the most dominant group in Durango,

consist of both common and private land owners. The common properties or ejidos are

collectively owned expanses of land, which occupy up to 70 percent of the forestlands in

the state of Durango (Alcorn & Toledo, 1998). Thus, the essence of this study is to

determine the most efficient budgetary distribution among the four national programs in

ejido forest lands, taking into account the views and aspirations of the four interest

groups and the achievement of the six forest resources management objectives.

3. Methodology
3.1 The Analytic Hierarchy Process

Our interest in this paper is to optimally allocate a limited budgetary resource among four

competing programs to achieve six ejido forest resources management objectives. A

convenient multi-objective decision-making technique that can handle such a

hierarchically-structured level of independent elements is the Analytic Hierarchy Process

(Saaty, 1977, 1980, 1988, 1990, 1997, 2008b). This is a well-known technique, which

has been successfully used to solve numerous multi-objective management problems

(Kangas, 1992, 1994, 1999; Saaty, 2001; Duke & Aull-Hyde, 2002 to mention a few).

The Analytic Hierarchy Process formulation of a problem involves describing the

elements in a lower level in terms of some or all of the elements in the next higher level

of the hierarchy (Saaty, 1980, 1988). Altogether, the process consists of the following

steps: (1) describing an overarching objective in terms of an overall and ultimately

desired direction (e.g. maximizing the overall utility); (2) identifying the interested

parties, stakeholders, or decision makers involved; (3) defining the specific objectives

that represent the wishes and aspirations of every interested party (or parties) (e.g.

maximizing desired objectives, minimizing undesired outcomes and project costs,

improving economic benefits and environmental conditions, etc.); and (4) articulating

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

45 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

feasible alternatives that can be used to achieve the desired objectives (Saaty, 1998,

2008a, 2008b, 2010; Ansah 2015). Criteria and sub-criteria are used to articulate the

specific objectives in step (3) especially when the objectives represent complex problems

that need to be expressed in more detailed and ordinal forms (Duckstein & Tecle, 2002).

The theoretical foundation behind the AHP is the utility theory of value. Zahedi (1987)

showed that the process of selecting alternatives is consistent with maximizing a decision

maker’s either single or multi-attribute utility functions (Saaty, 1998, 2003). Results

implied that the AHP and the utility maximization process can be combined to solve

decision problems. The problems can be multi-objective forest resource management

approaches such as the problem under study that involves multi-attribute utility functions.

The utility functions are usually described in terms of weights and relative rankings of

alternatives that can be evaluated using AHP (Saaty & Vargas, 1982; Duke & Aull-Hyde,

2002; Proctor, 2005; Balteiro & Romero, 2008; Ford et al., 2017).

The overarching objective of this multi-objective forest resources management planning

problem is maximizing the overall utility U of the system. Such maximization of the

overall utility occupies the highest level in the hierarchical formulation of an AHP

approach of solving a multi-objective problem. A utility model is a mathematical tool

that describes a problem in terms of features such as goals or objectives that express the

wishes and aspirations of individuals and/or groups. A very simple utility model can be

described in terms of the overall utility value U, which is the sum of the products of the

individual objective weights (ai) and the decision variable Xi. Algebraically, this can be

expressed as


i

ii
XaU (1)

in which i stands for an individual alternative. In a multi-objective problem, the

alternative that produces the highest utility value becomes the most preferred

management option (Tecle, 1992; Saaty, 1998, 2003; Tecle et al., 1998; Schmoldt et al.,

2001a; Poff et al., 2012).

The solution process includes arrangement of pairwise comparisons of the relative

weights of the different objectives. This would allow the decision maker to determine a

preferred management alternative where the weights represent the decision maker’s

preference structure on the objectives. Saaty (1988) used weights of 1,3,5,7, and 9 to

respectively represent equal (or the preference of an objective weighted against itself),

moderately dominant, strongly dominant, very strongly dominant, and extremely

dominant of one objective over the other in a pairwise comparison. The weights of 2, 4,

6, and 8 represent the intermediate values between two consecutive pairs of the above

values. Reciprocal values are entered in the transpose position and values between

integers are permitted when desired. Use of this methodology is based on extensive

research on the psychology of human preference behavior, which demonstrated that an

individual cannot simultaneously compare more than five objects fairly and without

having some confusion (Tversky & Kahneman, 1981; Kangas, 1994; Ford et al., 2017).

To do a pairwise comparison, the relative weights (importance / preference) of elements

at each hierarchical level are determined (Saaty, 2001). The analyst uses this to create the

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

46 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

matrix of pairwise comparisons, A, in Equation 2 from which an eigenvector is computed

(Saaty, 1998, 2003).

A a

w w w w

n n

 





















1 2 1

2 1 2

1 2

/ ... /

(2)

Here aij represents the pairwise comparisons of elements i and j; when i = j, then aij =1.

The ratio wi/wj is the relative importance or weight of element i over element j, while n is

the total number of elements being compared. Because the AHP involves subjective

assignment of values to utilities, the process may lead to some inconsistencies. To deal

with this problem, Saaty (1980, 2003) proposed an eigenvector method for testing

inconsistencies. For example, the inconsistency in the matrix A can be estimated using a

Consistency Index (CI), which can be described in the form of Equation 3, which is

)1/()( max  nnCI  (3)

where
m ax

 is the largest eigenvector in matrix A. This value (
m ax

 ) is obtained using

Equation 4, which involves multiplying the matrix aij by the vector of relative importance

or weights, wi.

𝜆𝑚𝑎𝑥 = ∑ ∑ 𝑎𝑖𝑗
𝑗𝑖

𝑤𝑖 (4)

The vector of relative weights, wi, is obtained by first normalizing each column and then

each row in the matrix A (Saaty, 1988). Such a matrix has to be estimated for each

decision variable at all levels of the system. In each level, the eigenvector is scaled to add

up to one to obtain level-wise priorities. We developed a basic approach using a

spreadsheet to calculate both the relative weights and the eigenvectors. If the pairwise

comparisons in the n × n matrix include no inconsistencies, then
m ax

 = n; otherwise A is

simply the reciprocal of the matrix (Saaty, 2001). The more consistent the comparisons

are the closer the value of the computed
m ax

 becomes to n. A consistency ratio (CR)

determined using Equation 5 indicates the coherence of the pairwise comparisons

(Alonso & Lamata, 2006):

CR = 100 (CI / ACI) (5)

where ACI is the average consistency index for randomly generated comparisons, which

varies with the size of the developed matrix (Saaty, 1988). Kangas (1994) considers the

appropriate value for CR to be 0.10 or less.

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

47 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

3.2 Data acquisition and problem formulation

A questionnaire was used to obtain the basic data for this study. Twenty representative

individuals involved in forest resources management were identified and asked to answer

an online questionnaire to reveal their personal preferences on the way the budget for

forest resources management in Durango should be allocated. The identified individuals

belong to each one of the four interested groups described above. However, seven of the

20 refused to participate in the study. Hence, we used only the responses from the 13

consenting respondents to construct the decision matrix used in the pairwise comparisons

(see Appendix AI). Of the 13 individuals, four were from the public sector, three were

landowners, three were members of non-government organizations, and three were from

the private sector. The questionnaire started with self-identification of the respondents,

followed by questions on their knowledge of the four national programs and others

related to the desired management objectives.

To use the information for the intended decision making process, the data were averaged

and then formulated into a matrix of preferences for each interested party. This was

followed by calculating the eigenvectors and determining the consistency indexes to

check for potential inconsistencies (Saaty, 2003). A similar process was followed for the

management objectives. But, in this case, we made pairwise comparisons of each

management objective with each interested party and for which a consistency test was

also made. The arrangement of the data in the form of a matrix, calculations of the

eigenvector and consistency indexes, making the pairwise comparisons for alternative

preferences and arriving at optimal budgetary allocation are done step by step in a

hierarchical framework.

Formulation of the problem in an AHP framework follows four hierarchical steps (see

Figure 2). The first step consists of identifying an overarching objective of the study.

The purpose is to allocate a one year forest management budget in the state of Durango,

Mexico to achieve optimal resources productivity. The second step is to determine the

relative importance or weights of all interested parties that represent the various resources

and arrange them as level two in the hierarchically structured framework. Kangas (1994)

suggested that the assignments and pairwise comparisons of the weights may be done by

the office staff administering the resource management since its members may have a

better understanding of the relative importance of each resource type and the interested

parties involved (Saaty & Vargas, 1982). As such, pairwise comparisons of the weights

of the parties and the resources involved were based on personal knowledge of the area

and the role the interested parties play in the management of natural resources as in

Proctor (2005). We also considered the scope of the forest law, which gives more

importance to forest landowners than to any other groups in the management of forest

resources.

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

48 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

Figure 2 An AHP flow chart of optimal budget allocation for multi-objective forest

resources management in Durango, Mexico

The third step consisted of describing the six management objectives and their relative

weights. The latter came from the responses to the survey questionnaires. The last one in

the hierarchy, level 4, consists of arranging the national forest resources/service

development alternative programs. Starting from the bottom, the elements in each level

are usually linked with the elements in the level above it. However, we also find that not

every element in a lower level is linked with every element in the level above it. For

example, the plantation development program is not linked with the improve economic

benefits objective in the level above it (see Figure 2). This usually takes place when an

element in the lower level is not related to one or more elements in the upper level as

described in Saaty (1988). In any case, the hierarchical structure in an AHP links one

level with the immediate levels above and below it (if there are any), thereby

mathematically tying the entire decision-making process together (Saaty, 1988, 2010,

2017).

4. Results

Optimal allocation of the available budget in this study is made by evaluating the four

national resources development programs with respect to their performances in achieving

the six desired management objectives. Normally, expert consultants and actual

management decision-makers are involved in assigning the preference structures or

weights to the objectives (Saaty & Vargas, 1982; Zanakis et al., 1995; Duckstein &

Tecle, 2002; Ford et al., 2017). In this study, the authors first assumed the roles of both

the expert consultants and the decision-makers and calculate the weights using Kangas’

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

49 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

(1994) methodology. The matrix of interested parties’ responses and the relative weights

assigned to each interested party are shown in Appendix AI. The relative weights are

0.18 for the public sector (PUB), 0.51 for the landowners (LND), 0.17 for the private

sector (PRV), and 0.14 for the non-government organizations (NGO). In this

arrangement, the relative importance given to landowners is much higher than that

assigned to the other stakeholders (see the Table in Appendix AI). This makes the values

of
m ax

 = 4.25, ACI = 0.90, CI = 0.08, and CR = 0.09. The CR value here is within the

standards recommended by Kangas (1994), i.e., CR ≤ 0.1.

The next step consists of determining the relative importance of each objective to the

various interested parties. Here, the responses to the questionnaires are first averaged,

then normalized and arranged in a matrix format to indicate objective-interested party

relationships as shown in Table 2. The Table also shows the relative importance of each

objective where the objective that receives the highest overall weight of 0.97 is

increasing forest stocks.

Table 2

Objective values and weights given by each interested party involved in the multi-

objective forest management decision process

Objectives Interested Parties

PUB LND PRV NGO Overall

Weights

Improving economic benefits 0.10 0.26 0.18 0.09 0 .63

Increasing water yield 0.25 0.12 0.12 0.24 0 .73

Increasing recreation or other

environmental benefits
0.23 0.07 0.19 0.22 0 .71

Increasing forest stocks 0.24 0.28 0.24 0.21 0 .97

Reducing operational costs 0.06 0.18 0.13 0.07 0 .44

Increasing non-timber products yield 0.12 0.09 0.14 0.17 0 .52

m ax 6.50 6.37 6.60 6.16

CR 0.08 0.06 0.10 0.03

On the other hand, reducing operational costs receives the lowest overall weight of 0.44.

In a similar manner, the relationships between the four alternative forest resources

development programs and the desired objectives are given in Table 3. Using values

from Table 2, Table 3 and the weights in Appendix AI, the global utility (or budget

allocation) value with respect to a particular management alternative program is

determined using Equation 6.


i

GP 



















)(
6

1 k

ikjk

j
LPMSLPOLPIG (6)

where GPi is the desired global budgetary ratio (or global utility value) obtained using

management alternative program i, LPIGj is the specific utility level or relative weight

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

50 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

assigned to interest group j, LPOjk is the local utility or relative weight of objective k

from the point of view of interest group j, and LPMSik is the specific utility level or

relative weight of management alternative i (national program) with respect to objective

k. Note that a special attention should be paid in determining GPi because all

management objectives do not have links with all management alternatives. Hence, there

are no LPMSik values reported for some of the cells in Table 3. In such a situation, Saaty

(1988) recommends to follow a procedure similar to that we have done in this paper. In

any case, the sum of all GPi's must be equal to one.

Table 3

Local priorities of management alternatives (national programs) with respect to decision

objectives (level 3 to 4)

Objectives

Management alternatives

(National Programs)*
m ax

 CR
FD PD NTP WH

Improving economic benefits 0.44 ----- 0.17 0.39 3.03 0.02

Increasing water yield 0.20 0.20 ------ 0.60 3.00 0.00

Increasing recreation or other

environmental benefits
0.17 0.39 ------ 0.44 3.03 0.02

Increasing forest stocks 0.16 0.42 0.14 0.27 4.07 0.03

Reducing operational costs 0.67 ----- 0.33 ------ 2.00 0.00

Increasing non-timber products yield 0.30 0.16 0.54 ------ 3.01 0.01

* Dotted cells represent the management objectives that do not have costs associated

with a particular national program.

Also, note that Equation 7 is the numerical application of Equation 6 that determines the

global utility value (0.307) for the forest development program (FD).

GPFD = [0.18 × {(0.10 × 0.44) + (0.25 × 0.20) + (0.23 × 0.17) + (0.24 × 0.16) + (0.06 ×

0.67) + (0.12 × 0.30)}+ 0.51 × {(0.26 × 0.44) + (0.12 × 0.20) + (0.07 × 0.17) + (0.28 ×

0.16) + (0.18 × 0.67) + (0.09 × 0.30)} + 0.17 × {(0.18 × 0.44) + (0.12 × 0.20) + (0.19 ×

0.17) + (0.24 × 0.16) + (0.13 × 0.67) + (0.14 × 0.30)}+ 0.14 × {(0.09 × 0.44) + (0.24 ×

0.20) + (0.22 × 0.17) + (0.21 × 0.16) + (0.07 × 0.67) + (0.17 × 0.30)}] = 0.307 (7)

The global utility values for the other three national resources development programs are

similarly determined to be 0.214 for PD, 0.177 for NTP, and 0.303 for WH. These show

that the resource development program with the highest global utility value is forest

development (FD), very closely followed by water harvesting (WH). The calculated

values are based on the wishes and aspirations (or utilities) of representative groups of

community members (Zanakis et al., 1995; Chiou et al., 2009). Based on this, the

government would allocate the budget for forest resources management among the four

national resources development programs to best achieve the desired management

objectives.

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

51 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

In the past, decisions on budget allocations followed no systematic approach. For

instance, the available funds for the particular budget year considered in this paper were

allocated as 53% for forest development, 35% for plantations development, 12% for non-

timber products, and zero to water harvesting. However, if the budget were distributed

among all four national resources development programs water harvesting and

environmental service development program would take some part of the budget. Such an

arrangement would proportionally reduce the funds that would be allocated to forest

development and the other two programs. Figure 3 compares this revised budget

allocation with the actual budget distribution above. The hypothetical allocations of the

annual budget of $4.10 million among the four resources development programs (FD,

PD, NTP and WH) for one year were obtained using Equation 6 and in a manner similar

to the calculation for FD using Equation 7.

Figure 3 Comparing actual (current) and hypothetical budget allocations to the four

resources development programs in the state of Durango, Mexico; the actual budget

allocation does not include funding to the water harvesting program (WH) in the year

5. Sensitivity analysis

An important aspect of any modeling effort is testing the reliability and robustness of the

model in performing as desired under varying input variables/parameters. This is

sensitivity analysis and it can be done by testing the effects of changes in one or more of

the utilities of the interested parties on the desired budget allocation among the four forest

resources management programs (see Figure 3). Performing sensitivity analyses on all

the decision variables would be repetitive, very tedious, and unnecessarily time

consuming. Hence, we only performed a sensitivity analysis on the effect of changes in

the utilities of one interested party (or decision-maker), the Landowners, on the global

utility values (see Figure 4). In this analysis, the utilities of the other three decision-

makers are kept constant.

0.50

1.00

1.50

2.00

2.50

FD PD NTP WH

Alternatives (National Programs)

M
il
li
o

n
s

o
f

D
o

ll
a
rs

Current Desired

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

52 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

The results of the sensitivity analysis show that the Analytic Hierarchy Process is very

reliable for optimal budget allocation among the different and competing forest resources

management programs in Durango, Mexico. This reliability is indicated by the small

variation in the global utility values of each natural resources development program with

changes in the landlord's utility values (see Figure 4). As shown in the figure, the change

in the global utility value for water harvesting is very little, ranging from 0.350 to 0.370,

as the landlord's utility value decreases from 0.5 to 0.0. On the opposite side, when the

landowner’s utility value is between 0.5 and 1.0, there is a slight rise, from 0.350 to

0.385, in the global utility for forest development. Likewise, the global utility values for

development of plantation and the non-timber products development programs are lower

than those of the above and do not change significantly with changes in the landlord's

utility values. Also the basis for providing the necessary budget is related to the land

tenure system prevailing in the State of Durango, Mexico, where new forest policies are

formulated to help landowners. Hence, it makes sense that the preference for budget

allocation favors landowners, albeit slightly, compared to the other interested parties

involved. In spite of the latter, however, there is little or no sensitivity in the derived

utility levels of the resource development programs with changes in the decision-maker’s

utility values. Hence, for the little difference observed between the outcomes of the two

most desirable forest resources management alternatives, forest development and water

harvesting.

Figure 4 Effect of changes in landowner’s utility values on global priority values.

In this test, the utility values of the other interested parties are assumed to be

equal

To corroborate the sensitivity analysis results, we performed a t-test, along with a test for

homogeneity of variances, by dividing the landowner’s utility values into two classes:

0.0

0.1

0.2

0.3

0.4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Landowners' utility values

G
lo

b
a
l

p
ri

o
ri

ty
v

a
lu

e
s
FD PD NTP WH

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

53 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

those having utility values less than 0.50 as class 1, and those with utility values greater

than or equal to 0.50 as class 2. In the process, the four resources development programs

of FD, PD, NTP and WH are considered to be dependent variables while their utility

values are classes or factors of independent variables. In the end, a result of the t-test

indicates existence of no significant differences between the two classes. This means that

changing the utility values of landowners does not have a significant effect on the overall

preference or on the prioritization of one resource development program over the others

under consideration.

6. Conclusions and recommendations

This study used the multi-criterion decision-making technique, AHP, to optimally

allocate a scarce forest management budget among the different forest resources

development programs in the state of Durango, Mexico. We analyzed the attitudes of four

representative decision-making groups toward an optimal allocation of a scarce budgetary

fund among four national programs to achieve six management objectives. Two of the

four programs, forest development and water harvesting/environmental services, received

the highest budget allocation in accordance with their higher global utility values.

However, since water harvesting/environment services constitutes a new program, its

funding has to come by reducing the budgetary share of the other programs, especially

that of forest development. This should lead to a fair and optimal allocation of the entire

budget among the four national forest resources management programs in Durango,

Mexico.

There are at least three major reasons for the need for optimal forest resources

management budget allocation. First, since the money comes from taxes, its distribution

should make it possible to provide the greatest amount of goods and services to the

largest number of people in the State. Second, an optimal budgetary distribution process

can help resources managers put their scarce budgetary funds where they are most needed

and efficiently used. Third, the developed approach must be a convenient technique for

simultaneous management of multiple forest resources to achieve multiple objectives as

in Tecle (1992), Balteiro and Romero (2008), Saaty (2008b), and Perez-Verdin et al.

(2009). The multi-objective approach is more advantageous than a traditional and

inefficient, single objective and single resources management approach (Tecle, 2007).

Using the multi-objective decision-making approach in this study water harvesting and

environmental services can be handled simultaneously with forest and non-timber

development programs to benefit not only landowners but the entire ejido community

who uses the resources as a whole. Hence, we recommend the use of the AHP not only

because it enables optimal allocation of scarce resources to do the greatest good for the

largest number of people, but because it also engenders active participation of the public

in resolving natural resources management-related conflicts (Balteiro et al., 2009;

Nordstrom, 2010; Groselj et al., 2016; Nilsson et al., 2016). This is possible because AHP

is capable of handling numerous types of qualitative as well as quantitative information

such as ordinal data from public opinions and cardinal and ratio data types generated

using all sorts of research endeavors (Saaty, 2008a; Šporčić, et al. 2010; Šporčić, 2012).

One method such as that of Duke and Aull-Hyde (2002), for example, can be used to

gather a large amount of public opinions. An additional strength of the AHP is its ability

to normalize non-commensurable data and express it in the form of ratio scale to make

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

54 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

handling of a complex multiobjective problem analysis easy (Tecle, 1992; Mendoza &

Prabhu, 2000; Saaty, 2008a).

The AHP is widely used to evaluate and solve many different kinds of multi-objective

decision problems (Saaty, 1990, 2001, 2008a, 2008b; Schmoldt et al., 2001a, 2001b;

Duke & Aull-Hyde, 2002; Macharis et al., 2004; Hajkowicz & Higgins, 2006), in

general, and various types of forest resources management problems such as those in

Balteiro and Romero (2008), Ananda and Herath (2009), Perez-Verdin et al. (2009,

2011), Šporčić et al. (2010), Poff et al. (2010, 2012), to mention some. But, to the best of

our knowledge, this is the first time the AHP has specifically been used to optimally

distribute scarce budget resources among four ejido-based forest resources management

programs designed to achieve six objectives of four interested parties. A sensitivity

analysis was conducted on the effects of varying the utility values of landowners on the

global utility values that determined the budget distribution among the four competing

forest resources management programs. The analysis results show the reliability and

robustness of the AHP in allocating the budget.

Another benefit of using the AHP is its integrative assessment of numerous interacting

and at times competing forest resources components. It takes advantage of not only the

synergistic relationships among the various components of a multi-objective decision

problem, but also incorporates the risks and uncertainties inherent in such a complex

problem to reach a realistic and acceptable decision outcome (Macharis et al., 2004).

Weights and public preferences are heavily used to hierarchically interconnect various

decision-makers, their objectives and the different alternative management schemes

involved. These aspects of the AHP are the reasons for its desirability, wide use and

success to solve various types of multi-objective forest resources management problems.

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

55 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

APPENDIX A

AI. Pairwise comparisons (A) of stakeholder’s utilities and vector of weights (w)

A w

























12/13/11

213/12/1

3314

124/11

NGPRLDPU

aAw
ik



















14.0

17.0

51.0

18.0

; m ax =4.25; CR=0.09

PU = Public Sector; LD = Landowners; PR = Private Sector; and NG = Non-government organizations

AII. Pairwise comparisons of stakeholders’ management objective values and vector of

weights

Public sector preferences

EE WY REC FS OPC NTP

EE 1.00 0.33 0.33 0.33 3.00 1.00

WY 3.00 1.00 2.00 0.50 3.00 3.00

REC 3.00 0.50 1.00 2.00 4.00 1.00

FS 3.00 2.00 0.50 1.00 3.00 2.00

OPC 0.33 0.33 0.25 0.33 1.00 0.50

NTP 1.00 0.33 1.00 0.50 2.00 1.00



























12.0

06.0

24.0

23.0

0.25

0.10

; m ax =6.50; CR=0.08

Landowners preferences

EE WY REC FS OPC NTP

EE 1.00 3.00 3.00 1.00 2.00 2.00

WY 0.33 1.00 2.00 0.50 0.33 2.00

REC 0.33 0.50 1.00 0.25 0.33 1.00

FS 1.00 2.00 4.00 1.00 3.00 2.00

OPC 0.50 3.00 3.00 0.33 1.00 2.00

NTP 0.50 0.50 1.00 0.50 0.50 1.00



























09.0

18.0

28.0

07.0

0.12

0.26

; m ax =6.37; CR=0.06

Private Sector preferences

EE WY REC FS OPC NTP

EE 1.00 3.00 1.00 1.00 0.50 1.00

WY 0.33 1.00 1.00 0.50 1.00 1.00

REC 1.00 1.00 1.00 0.50 3.00 2.00

FS 1.00 2.00 2.00 1.00 3.00 1.00

OPC 2.00 1.00 0.33 0.33 1.00 1.00

NTP 1.00 1.00 0.50 1.00 1.00 1.00

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

56 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

Non-governmental organizations preferences

EE WY REC FS OPC NTP

EE 1.00 0.33 0.33 0.33 1.00 1.00

WY 3.00 1.00 1.00 1.00 3.00 2.00

REC 3.00 1.00 1.00 1.00 4.00 1.00

FS 3.00 1.00 1.00 1.00 3.00 1.00

OPC 1.00 0.33 0.25 0.33 1.00 0.33

NTP 1.00 0.50 1.00 1.00 3.00 1.00



























17.0

07.0

21.0

22.0

0.24

0.09

; m ax =6.16; CR=0.03

EE = Improve economic benefits; WY = Improve water yield; REC = improve recreation/

environmental services; FS = Increase forest stocks; OPC = Reduce operational costs; and NTP =

increase non-timber products yield.

AIII. Pairwise comparisons of forest resources management programs, and corresponding

vector of weights (w) and other parameters related to each objectives.

Improve Economic Benefits

FD NTP WH w

FD 1.00 3.00 1.00 0.44

NTP 0.33 1.00 0.50 0.17

WH 1.00 2.00 1.00 0.39

m ax

 =3.03; CR=0.02

Improve Water Yield

FD PD WH w

FD 1.00 1.00 0.33 0.20

PD 1.00 1.00 0.33 0.20

WH 3.00 3.00 1.00 0.60

m ax =3.00; CR=0.00

Improve Recreation and

Environmental Services

FD PD WH w

FD 1.00 0.50 0.33 0.17

PD 2.00 1.00 1.00 0.39

WH 3.00 1.00 1.00 0.44

m ax =3.03; CR=0.02

Increase forest stocks

FD PD NTP WH w

FD 1.00 0.50 1.00 0.50 0.16

PD 2.00 1.00 3.00 2.00 0.42

NTP 1.00 0.33 1.00 0.50 0.14

WH 2.00 0.50 2.00 1.00 0.27

m ax =4.07; CR=0.02

Reduce operational costs

m ax =2.00; CR=0.00

FD NTP w

FD 1.00 2.00 0.67

NTP 0.50 1.00 0.33

Increase non-timber products

FD PD NTP w

FD 1.00 2.00 0.50 0.30

PD 0.50 1.00 0.33 0.16

NTP 2.00 3.00 1.00 0.54

m ax =3.01; CR=0.01

FD = Forest Development; PD = Plantations Development; NTP = Non-timber products; WH = Water Harvesting

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

57 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

REFERENCES

Alcorn, J.B. and Toledo, V.M. (1998). Resilient resource management in Mexico's forest

ecosystems: the contribution of property rights. In F. Berkes and C. Folke (Eds), Linking

social and ecological systems: management practices and social mechanisms for building

resilience (216-249). Cambridge, U.K: Cambridge University Press.

http://www.consecol.org/vol4/iss2/art5/

Alonso, J.A., and Lamata, M.T. (2006). Consistency in the Analytic Hierarchy Process: A

new approach. International Journal of Uncertainty, Fuzziness and Knowledge-Based

Systems, 14(4). Doi: 10-1142/S0218488506004126.

Ananda, J. and Herath, G. (2009). A critical review of multi-criteria decision making

methods with special references to forest management and planning. Ecological

economics, 68(10), 2535-2548. Doi: https://doi.org/10.1016/j.ecolecon.2009.05.010

Ansah, R.H., Sorooshian, S. and Bin Mustafa, S. (2015). Analytic Hierarchy Process

decision making algorithm. Global Journal of Pure and Applied Mathematics, 11(4)

2015. http///ssrn.com/abstract=2683706.

Balteiro, L.D., and Romero, C. (2008). Making forestry decisions with multiple criteria:

A review and assessment. Forest Ecology and Management, 255(2008), 3222-3241. Doi:

https://doi.org/10.1016/j.foreco.2008.01.038

Balteiro, L.D., Gonzalez-Pachon, J. and Romero, C. (2009). Forest management with

multiple criteria and multiple stakeholders: An application to two public forests in Spain.

Scandinavian Journal of Forest Research, 24(1), 87-93. Doi:

https://doi.org/10.1080/02827580802687440

Balteiro, L.D. Romero, C. (2001). Combined use of goal programming and the Analytic

Hierarchy Process in forest management. In D.L. Schmoldt, J. Kangas, G.A. Mendoza,

and M. Pesonen (Eds), The Analytic Hierarchy Process in Natural Resource and

Environmental Decision-Making (81-95). Norwell, MA : Kluwer Academic Publishers.

Doi: https://doi.org/10.1007/978-94-015-9799-9_6

Bradford, J.B and D’Amato, A.W. (2012). Recognizing trade-offs in multiple-objective

land management. Frontiers in Ecology and the Environment, 10(4), 210-216. Doi:

10.1890/110031. Doi: 10.1890/110031

Cheng, E.W.L., and Li, H. (2004). Contractor selection using the Analytic Network

Process. Construction Management and Economics, 2004(22), 1021-1032. Doi:

https://doi.org/10.1080/0144619042000202852

Chiou, C.W., Chen, C.C. and Chiou, S.C. (2009). A decision-making model of budget

allocation for the restoration of traditional settlement buildings. International

Conference on Management and Service Science on 20-22 Sept. 2009 in Wuhan, China.

Doi: 10.1109/ICMSS.2009.5303265

https://doi.org/10.1016/j.ecolecon.2009.05.010
https://doi.org/10.1016/j.foreco.2008.01.038
https://doi.org/10.1080/02827580802687440
https://doi.org/10.1080/0144619042000202852
http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5300802
http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5300802
https://doi.org/10.1109/ICMSS.2009.5303265

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

58 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

Duckstein, L. and A. Tecle. (1993a). Multiobjective Analysis in Water Resources: Part

II - A New Typology of MCDM Techniques. In: Marco, Harboe and Salas (eds.),

Stochastic Hydrology and its Use in Engineering. Kluwer Academic Publishers,

Dordrecht, The Netherlands. pp. 333-344. Doi: https://doi.org/10.1007/978-94-011-

1697-8_21

Duckstein, L., and Tecle, A. (1993b). Multiobjective analysis in water resources: Part I

– Numerical versus non-numerical and discrete versus continuous alternatives. In: Marco,

Harboe and Salas (Eds.), Stochastic Hydrology and its Use in Engineering (319-332).

Dordrecht, The Netherlands: Kluwer Academic Publishers. Doi:

https://doi.org/10.1007/978-94-011-1697-8_20

Duckstein, L. and Tecle, A. (2002). Multicriterion analysis in water resources

management. In H.H.G. Savenije and A.Y. Hoeksta (Eds.), Water resources

management, Encyclopedia of life support systems (EOLSS), Oxford, UK: UNESCO,

EOLSS Publishers. Doi: https://doi.org/10.1061/(ASCE)0733-9496(1990)116:6(840)

Duke, J.M., and Aull-Hyde, R. (2002). Identifying public preferences for land

preservation using the Analytic Hierarchy Process. Ecological Economics, 42, 131-145.

Doi: https://doi.org/10.1016/S0921-8009(02)00053-8

Ford, R.M., Anderson, N,M, Nitschke, C., Bennet, L.T. and Williams, K.J.H. (2017).

Psychological values and cues as a basis for developing socially relevant criteria and

indicators for forest management. Forest Policy and Economics, 78(2017), 141-150. Doi:

https://doi.org/10.1016/j.forpol.2017.01.018

Forman, E. and , Peniwati, K. (1998). Aggregating individual judgments and priorities

with the Analytic Hierarchy Process. European Journal of Operational Research,

108(1),165-169. Doi: https://doi.org/10.1016/S0377-2217(97)00244-0

Groselj, P., Hodges, D.G. and Stirn, L.Z. (2016). Participatory and multi-criteria analysis

for forest (ecosystem) management: A case study of Pohorje, Slovenia. Forest Policy and

Economics, 71(2016), 80–86. Doi: https://doi.org/10.1016/j.forpol.2015.05.006

Hajkowicz, S., and Higgins. A. (2006). A comparison of multiple criteria analysis

techniques for water resource management. European Journal of Operational Research,

184(2008), 255–265. Doi: https://doi.org/10.1016/j.ejor.2006.10.045

Hossain, S.M. Y., and Robak. E.W. (2010). A forest management process to incorporate

multiple objectives: a framework for systematic public input. Forests, 1, 99-113. Doi:

10.3390/f1030099

Ishizaka, A., and Labib. A. (2011). Review of the main developments in the Analytic

Hierarchy Process. Expert Systems with Applications, 38(11), 14336–14345. Doi:

https://doi.org/10.1016/j.eswa.2011.04.143

Jenkins, T. (2005). Multi-objective forest planning. Forestry, 78(4),457-458.

Doi:https://doi.org/10.1093/forestry/cpi051.

https://doi.org/10.1061/(ASCE)0733-9496(1990)116:6(840)
https://doi.org/10.1016/S0921-8009(02)00053-8
https://doi.org/10.1016/j.forpol.2017.01.018
http://www.sciencedirect.com/science/journal/03772217
https://doi.org/10.1016/S0377-2217(97)00244-0
http://www.sciencedirect.com/science/article/pii/S1389934115300058
http://www.sciencedirect.com/science/article/pii/S1389934115300058
http://www.sciencedirect.com/science/journal/13899341
http://www.sciencedirect.com/science/journal/13899341
http://www.sciencedirect.com/science/journal/13899341/71/supp/C
https://doi.org/10.1016/j.forpol.2015.05.006
https://doi.org/10.1016/j.ejor.2006.10.045
http://www.sciencedirect.com/science/journal/09574174
http://www.sciencedirect.com/science/journal/09574174/38/11
https://doi.org/10.1016/j.eswa.2011.04.143

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

59 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

Kangas, J. (1992). Multiple-use planning of forest resources by using the Analytic

Hierarchy Process. Scandinavian Journal of Forest Research, 7, 259-268. Doi:

https://doi.org/10.1080/02827589209382718

Kangas, J. (1994). An approach to public participation in strategic forest management

planning. Forest Ecology and Management, 70, 75-88. Doi: https://doi.org/10.1016/0378-

1127(94)90076-0

Kangas, J. (1999). The Analytic Hierarchy Process (AHP): Standard version, forestry

applications and advances. In F. Helles, P. Holten-Andersen, and L. Wichmann (Eds),

Multiple use of forests and other natural resources (96-105). Norwell, MA: Kluwer

Academic Publishers. Doi: https://doi.org/10.1007/978-94-011-4483-4_8

Kangas, J., Kangas, A., Leskinen, P. and Pykalainen, J. (2001). MCDM methods in

strategic planning of forestry on state-owned lands in Finland: applications and

experiences. Journal of Multi-Criteria Decision Analysis, 10(5), 257-271. Doi:

10.1002/mcda.306

Krcmar, E, Van Kooten, G.C., Vertinsky, I. (2005). Managing forest and marginal

agricultural land for multiple trade-offs: compromising on economic, carbon and

structural diversity objectives. Ecological Modelling, 185(2), 451-468. Doi:

https://doi.org/10.1016/j.ecolmodel.2004.12.014

Leskinen, P. (2000). Measurement scales and scale independence in the Analytic

Hierarchy Process. Journal of Multicriteria Decision Analysis, 9(4), 163. Doi:

10.1002/1099-1360(200007)9:4<163::AID-MCDA274>3.0.CO;2-L

Macharis, C., Springael, J., De Brucker, K. and Verbeke, A. (2004). Promethee and AHP:

The design of operational synergies in multicriteria analysis. Strengthening Promethee

with ideas of AHP. European Journal of Operational Research, 153, 307−317. Doi:

https://doi.org/10.1016/S0377-2217(03)00153-X

Mardani, A., Jusoh, A., Nor, K., Khalifah, Z., Zakwan, N. & Valipour, A. (2015).

Multiple criteria decision-making techniques and their applications – a review of the

literature from 2000 to 2014. Economic Research-Ekonomska Istraživanja, 28(1), 516-

571. Doi: https:/doi/full/10.1080/ 1331677X.2015.1075139.

Mendoza, G., and Prabhu, R. (2000). Multiple criteria decision making approaches to

assessing forest sustainability using criteria and indicators: A case study. Forest Ecology

and Management, 131(1-3), 107-126. Doi: https://doi.org/10.1016/S0378-

1127(99)00204-2

Moseley, K.R., Ford, W.M., Edwards, J.W. and Strager, M.P. (2009). A multi-criteria

decision making approach for management indicator species selection on the

Monongahela National forest, West Virginia. USDA Forest Service Northern Research

Station, Research Paper NRS-12. Doi: https://doi.org/10.2737/NRS-RP-12

https://doi.org/10.1080/02827589209382718
https://doi.org/10.1016/0378-1127(94)90076-0
https://doi.org/10.1016/0378-1127(94)90076-0
https://doi.org/10.1016/j.ecolmodel.2004.12.014
https://doi.org/10.1016/S0377-2217(03)00153-X
http://www.tandfonline.com/author/Mardani%2C+Abbas
http://www.tandfonline.com/author/Jusoh%2C+Ahmad
http://www.tandfonline.com/author/MD+Nor%2C+Khalil
http://www.tandfonline.com/author/Khalifah%2C+Zainab
http://www.tandfonline.com/author/Zakwan%2C+Norhayati
http://www.tandfonline.com/author/Valipour%2C+Alireza
http://www.tandfonline.com/toc/rero20/28/1
https://doi.org/10.1016/S0378-1127(99)00204-2
https://doi.org/10.1016/S0378-1127(99)00204-2
https://doi.org/10.2737/NRS-RP-12

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

60 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

Napoli, G., and Schilleci, F. (2014). Application of an Analytic Network Process in the

planning process: The case of an urban transformation in Palermo (Italy). A conference

paper. Doi: 10.1007/978-3-319-09150-1_22.

Nilsson, H., Nordstrom, E.M. and Ohman, K. (2016). Decision support for participatory

forest planning using AHP and TOPSIS. Forests, 7(5), 100. Doi: 10.3390/f7050100.

Niemela, J., J. Young, D. Alard, M. Askasibar, K. Henle, R. Johnson, M. Kurttila, T.B.

Larsson, S. Matouch, P. Nowicki, R. Paiva, L. Portoghesi, R. Smilders, A. Stevenson, U.

Tartes, and A. Watt. (2005). Identifying, managing and monitoring conflicts between

forest biodiversity conservation and other human interests in Europe. Forest Policy and

Economics, 7(2005), 877-890. Doi: https://doi.org/10.1016/j.forpol.2004.04.005

Nordstrom, E.V. (2010). Integrating multiple criteria decision analysis into participatory

forest planning. A doctoral thesis for the Department of Forest Resources Management,

Swedish University of Agricultural Sciences, Umea, Sweden. Doi:

https://doi.org/10.1016/j.forpol.2010.07.006

Ozdemir, Y., Basligil, H. and Karaca, M. (2011). Aircraft selection using analytic

network process: A case for Turkish Airlines. Proceedings of the World Congress on

Engineering, II, London, U.K.

Perez-Verdin G., Navar-Chaidez, J.J., Kim, Y-S and Silva-Flores, R. (2011). Valuing

watershed services in Mexico's temperate forests. Modern Economy, 2(5),769-779. Doi:

10.4236/me.2011.25085

Pérez-Verdín, G., Hernández-Díaz, J.C., Márquez-Linares
,
M.A. and Tecle, A. (2009).

Aplicación de técnicas multicriterio en el manejo integral forestal en Durango, México.

Madera y bosques, 15(1), 1405-0471. Doi: http://dx.doi.org/10.21829/myb.2009.1511195

Phua, M.H., and Minowa, M. (2005). A GIS- based multi-criteria decision making

approach to forest conservation planning at a landscape scale: A case study in the

Kinabalu area, Sabah, Malaysia. Landscape and Urban Planning, 71(2-4), 207-222. Doi:

https://doi.org/10.1016/j.landurbplan.2004.03.004

Poff, B., Tecle, A. Neary, D.G. and Geils, B. (2010). Compromise programming in forest

management. Journal of the Arizona-Nevada Academy of Science, 42(1), 44-60. Doi:

https://doi.org/10.2181/036.042.0107

Poff, B., Tecle, A. Neary, D. and Geiles, B. (2012). Spatio-temporal multi-objective

decision making in forest management., In C. Van Riper III, M. Villarreal, C. van Riper,

and M. Johnson (Eds.), The Colorado Plateau V: Research, environmental planning, and

management for collaborative conservation (121-129). Tuscon, AZ: The University of

Arizona Press. Doi: 10.2307/j.ctt183pc7f

Proctor, W. (2005). Valuing forest resources using multi-criteria decision analysis and

stakeholder participation. In. Michael Getzner, M., C. Spash, and S. Stagl (Eds.),

https://doi.org/10.1016/j.forpol.2004.04.005
https://doi.org/10.1016/j.forpol.2010.07.006
http://www.scielo.org.mx/scielo.php?script=sci_serial&pid=1405-0471&lng=es&nrm=iso
https://doi.org/10.1016/j.landurbplan.2004.03.004
https://doi.org/10.2181/036.042.0107

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

61 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

Developing alternatives for valuing nature: Part II: Taking multiple criteria into account.

London, UK: Routledge.

Rhoda, R. and Burton, T. (2010). Geo-Mexico: the geography and dynamics of modern

Mexico. Canada: Sombrero Books.

Saaty, T.L. (2017). The Analytic Network Process. Download from iors.ir at 0:40+0430

on Wednesday April 26, 2017. https://iors.ir/journal/article-1-27-en.pdf.

Saaty, T. L. (2010). Principia Mathematica Decernendi: Mathematical Principles of

Decision Making. Pittsburgh, PA: RWS Publications. ISBN 978-1-888603-10-1.

Saaty, T. L. (2008a). Measurement and its generalization in decision making: Why

pairwise comparisons are central in mathematics for the measurement of intangible

factors - The Analytic Hierarchy/Network Process. RACSAM (Review of the Royal

Spanish Academy of Sciences, Series A, Mathematics), 102 (2), 251–318. Doi:

https://doi.org/10.1007/BF03191825

Saaty, T. L. (2008b). Decision making with the Analytic Hierarchy Process.

International Journal Services Sciences, 1(1), 83-98. Doi: 10.1504/IJSSCI.2008.017590

Saaty, T.L. (2003). Decision-making with the AHP: Why is the principal eigenvector

necessary. European Journal of Operational Research, 145(1), 85-91. Doi:

https://doi.org/10.1016/S0377-2217(02)00227-8

Saaty, T. L. (2001). Fundamentals of the Analytic Hierarchy Process. In D.L Schmoldt, J.

Kangas, G.A. Mendoza, and M. Pesonen (Eds), The Analytic Hierarchy Process in

natural resource and environmental decision making (15-35). Norwell, MA: Kluwer

Academic Publishers. Doi: https://doi.org/10.1007/978-94-015-9799-9_2

Saaty, T.L. (1998). Ranking by eigenvector versus other methods in the Analytic

Hierarchy Process. Applied Mathematics Letters, 11(4),121-125. Doi:

https://doi.org/10.1016/S0893-9659(98)00068-8

Saaty, T.L. (1997). That is not the Analytic Hierarchy Process: what the AHP is and

what it is not. Journal of Multi-Criteria Decision Analysis, 6(6), 324-335. Doi:

10.1002/(SICI)1099-1360(199711)6:6<324::AID-MCDA167>3.0.CO;2-Q

Saaty, T.L. (1990). How to make a decision: The Analytic Hierarchy Process. European

Journal of Operational Research, 48, 9-26. Doi: https://doi.org/10.1016/0377-

2217(90)90057-I

Saaty, T. L. (1988). Multicriteria decision making: The Analytic Hierarchy Process.

Pittsburgh, PA: RWS Publications.

Saaty, T. L. (1980). The Analytic Hierarchy Process. Planning priority setting, resource

allocation. New York, NY: McGraw-Hill Inc. Doi: https://doi.org/10.1016/0377-

2217(82)90022-4

http://en.wikipedia.org/wiki/Thomas_L._Saaty
http://en.wikipedia.org/wiki/International_Standard_Book_Number
http://en.wikipedia.org/wiki/Special:BookSources/978-1-888603-10-1
http://en.wikipedia.org/wiki/Thomas_L._Saaty
http://dx.doi.org/10.1504/IJSSCI.2008.017590
http://www.lamsade.dauphine.fr/mcda/biblio/Author/SAATY-TL.html
http://www.lamsade.dauphine.fr/mcda/biblio/Author/SAATY-TL.html
https://doi.org/10.1016/S0377-2217(02)00227-8
http://en.wikipedia.org/wiki/Thomas_L._Saaty
http://www.sciencedirect.com/science/journal/08939659
https://doi.org/10.1016/S0893-9659(98)00068-8
http://www.lamsade.dauphine.fr/mcda/biblio/Author/SAATY-TL.html
http://www.lamsade.dauphine.fr/mcda/biblio/Author/SAATY-TL.html
https://doi.org/10.1016/0377-2217(90)90057-I
https://doi.org/10.1016/0377-2217(90)90057-I
http://en.wikipedia.org/wiki/Thomas_L._Saaty
http://en.wikipedia.org/wiki/Thomas_L._Saaty
https://doi.org/10.1016/0377-2217(82)90022-4
https://doi.org/10.1016/0377-2217(82)90022-4

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

62 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

Saaty, T.L. (1977). A scaling method for priorities in hierarchical structures. Journal of

Mathematical Psychology, 15, 234-281. Doi: https://doi.org/10.1016/0022-

2496(77)90033-5

Saaty, T. L.. and Vargas, L.G. (2006). Decision making with the Analytic Network

Process: Economic, political, social and technological applications with benefits,

opportunities, costs and risks. New York: Springer.

Saaty, T. and Vargas, L.G. (1982). The logic of priorities. Boston: Kluwer-Nijhoff. Doi:

https://doi.org/10.1007/978-94-017-3383-0_1

Sadeghi, M., Rashidzadeh, M.A. and Soukhakian, M.A. (2012). Using Analytic Network

Process in a group decision-making for supplier selection. Informatica, 23(4), 621-643.

Schmoldt, D.L., Kangas, J. and Mendoza, G.A. (2001a). Basic principles of decision

making in natural resources and the environment. In D.L Schmoldt, J. Kangas, G.A.

Mendoza, and M. Pesonen (Eds),The Analytic Hierarchy Process in natural resource and

environmental decision making (1-13). Dordrecht, The Netherlands: Kluwer Academic

Publishers. Doi: https://doi.org/10.1007/978-94-015-9799-9_1

Schmoldt, D.L., Kangas, J. and Mendoza, G.A. and Pesonen, M. (2001b). Strategic and

tactical planning for managing national park resources. In Schmoldt et al. (Eds.), The

Analytic Hierarchy Process in Natural Resource and Environmental Decision-Making

(67-79) Dordrecht, The Netherlands : Kluwer Academic Publishers. Doi:

https://doi.org/10.1007/978-94-015-9799-9_5

Semarnat. (2000). Strategic forest program 2025. (Secretaria de Medio Ambiente y

Recursos Naturales). Available at http://www.conafor.gob.mx/documentos_conafor/

ENG/pdf/19.pdf (last time visited June 7, 2004).

Šporčić, M. (2012). Application of multi-criteria methods in natural resources

management - A focus on forestry: Chapter 22. In Jorge Martin Garcia and Julio Javier

Diez (Eds.), Sustainable forest management - Current research. Casero, Doi:

10.5772/23667

Šporčić, M., Landekić, M. Lovrić, M. Bogdan, S. and Šegotić, K. (2010). Multi-criteria

decision-making in forestry - methods and experiences. Sumarski List, 134(5-6), 275-284.

Tecle, A. (2007). Sustainable natural resources management in an era of global climate

change. Forum on Public Policy, 3(4), 443-454.

Tecle, A. (1992). Selecting a multicriterion decision making technique for watershed

resources management. Water Resources Bulletin, 28(1), 129-140. Doi: 10.1111/j.1752-

1688.1992.tb03159.x

http://www.lamsade.dauphine.fr/mcda/biblio/Author/SAATY-TL.html
https://doi.org/10.1016/0022-2496(77)90033-5
https://doi.org/10.1016/0022-2496(77)90033-5
http://en.wikipedia.org/wiki/Thomas_L._Saaty
http://www.conafor.gob.mx/documentos_conafor/ENG/pdf/19.pdf
http://www.conafor.gob.mx/documentos_conafor/ENG/pdf/19.pdf

IJAHP Article: Tecle, Perez-Verdin/Analytic Hierarchy Process application for multiple purpose

forest resources management budget allocation in Durango, Mexico

International Journal of the

Analytic Hierarchy Process

63 Vol. 10 Issue 1 2018

ISSN 1936-6744
https://doi.org/10.13033/ijahp.v10i1.422

Tecle, A., and Duckstein, L. (1994). Concepts of multicriterion decision- making,

Chapter 3. In H.P. Nachtnebel (Ed.), Decision support system in water resources

management (33-62) Paris, France: UNESCO Press.

Tecle, A., and Jibrin, S. (2012). Incorporating fuzzy logic and stochastic processes in

multiobjective forest management. Hydrology and Water Resources in Arizona and the

Southwest, 41, 41-45.

Tecle, A., Shrestha, B. and Duckstein, L. (1998). Multiobjective decision support system

for multiresource forest management. Group Decision and Negotiation, 7, 23-40. Doi:

https://doi.org/10.1023/A:1008671129325

Tecle, A., Szidarovszky, F. and Duckstein, L. (1995). Conflict analysis in multi-resource

forest management with multiple decision-makers. Nature & Resources, 31(3), 8-17.

Thangamani, G. (2012). Technology selection for product innovation using Analytic

Network Process (ANP) - A ccase study. International Journal of Innovation,

Management and Technology. 3(5), 560-565. Doi: 10.7763/IMT.2012.V3.298.

Triantaphyllou, E. (2000). Multi-criteria decision making methods: A comparative

study. Boston, MA: Springer. Doi: https://doi.org/10.1007/978-1-4757-3157-6

Tversky, A., and Kahneman, D. (1981). The framing of decisions and the psychology of

choice. Science, 211,453-458. Doi: 10.1126/science.7455683

Vaidya, O.S., and Kumar. S. (2006). Analytic Hierarchy Process: an overview of

applications. European Journal of Operational Research, 169(1), 1-29. Doi:

https://doi.org/10.1016/j.ejor.2004.04.028

White, S.W., and Bordoloi, S.K. (2015). A review of DEA-based resource and cost

allocation models: Implications for services. International Journal of Service and

Operations Management, 20(1). 86-101. Doi: 10.1504/IJSOM.2015.065973

Zahedi, F. (1987). A utility approach to the Analytic Hierarchy Process. Mathematical

Modeling, 9, 387-395. Doi: https://doi.org/10.1016/0270-0255(87)90497-0

Zanakis, S.H., Mandakovic, T., Gupta, S.K., Sahay, S. and Hong, S. (1995). A review of

program evaluation and fund allocation methods within the service and government

sectors. Socio-Economic Planning Sciences, 29(1), 59-79. Doi:

https://doi.org/10.1016/0038-0121(95)98607-W

https://doi.org/10.1016/j.ejor.2004.04.028
http://dx.doi.org/10.1504/IJSOM.2015.065973
https://doi.org/10.1016/0270-0255(87)90497-0
https://doi.org/10.1016/0038-0121(95)98607-W