Integrated Multi-criterial Decision Model: a Case Study for the Allocation of Facilities in Chinese Agriculture

J. Agric. Engng Res. (1999) 73, 87d94 Article No. jaer.1998.0393, available online at http://www.idealibrary.com on

Integrated Multi-criterial Decision Model: a Case Study for the Allocation of Facilities in Chinese Agriculture L. S. Guo*; Y. S. He  Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong; e-mail: [email protected]  Zhejiang University, Hangzhou, 310029, People's Republic of China (Received 16 February 1998; accepted in revised form 6 November 1998)

The proposed methodology of integrating the Analytic Hierarchy Process (AHP) and Goal Programming (GP) in this paper provides decision-makers with the #exibility needed to allocate resources by considering both quantitative and qualitative decision criteria. A large-scale linear goal programming model is established in order to optimize allocation of facilities for a grain harvesting and post-harvest system within a province in China. The proposed model includes multiple con#icting goals with inconsistent units requiring prioritization. The Analytic Hierarchy Process is used to set up priorities for strategic goals in a grain harvesting and post-harvest system, including the two most important goals in the linear goal programming model: grain loss and production cost. Multiple-phase Simplex Algorithm for linear goal programming is then used to get a solution. The original data in this case study are collected from an on-site investigation of Chinese agriculture. The results of AHP and the GP model show that decreasing the grain loss is the most important goal in a grain harvesting and post-harvest system, and it would be possible to decrease it to 13%, and even to 10%, but it is impossible to decrease the grain loss rate to 5% under the present conditions for facilities and techniques.  1999 Silsoe Research Institute

model. Millar and Corkum5 proposed a linear goal programming for selecting road paving project, in which weights for the objectives are obtained by the use of AHP. Ehie and Benjamin6 and Benjamin et al.7 employed an integrated approach involving AHP and Linear Goal Programming (LGP) in industry planning for a lowincome developing country and facilities layout planning. The grain harvesting and post-harvest system includes the whole sequence from the grain harvest to the grain consumption, covering a series of production processes, such as cutting, threshing, cleaning, drying, storage, transporting and milling. The grain harvesting and postharvest system is therefore very complex. It is important to study an optimal allocation of facilities in order to achieve two contradictory goals: decrease in grain loss and increase in grain e$ciency. Linear Programming or Non-linear Programming has been used in studying the optimized allocation of machinery in agriculture, but due to single goal and scleronomic constraints, the situation could occur that no solution is obtained in such a problem model.

1. Introduction Goal Programming (GP), an extension of Linear Programming, is a management science technique for resource allocation in a multiple objective environment. Its application areas are numerous, with over 350 references given in the bibliography by Romero.1 A boom in GP application papers occurred in the late 1970s and early 1980s soon after the "rst major textbooks on GP appeared. Since then the level of applications has dropped to a steady, maintainable level.2 Goal Programming types of applications in agriculture were organized into ten di!erent topics by Schniederjans3 which include 63 cases of GP applications. Ramanathan and Ganesh4 evaluated seven energy sources used in lighting in households against 12 objectives representing the energy} economy}environmental system by including the Analytic Hierarchy Process (AHP) in an integrated GP-AHP * Corresponding author. On leave from Zhejiang University, Hangzhou, People's Republic of China. 0021-8634/99/050087#08 $30.00/0

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Zhejiang is a developed province in the coastal area in the east of China, where the types and levels of grain production are typical of those in the developed area in the southern China. The main contribution of the study to be reported in this paper is to establish a goalprogramming model for optimized macro-allocation of grain harvesting and post-harvest system in Zhejiang Province of China. The Analytic Hierarchy Process (AHP) is employed to set up priorities of strategic goals in the grain harvesting and post-harvest system, including two most important goals in the linear goal programming model: grain loss and production cost of grain (harvest and post-harvest). Multiple-phase Simplex Algorithm for linear goal programming is used to obtain a solution. The data is collected from an on-site investigation.

2. Principle of the Analytic Hierarchy Process and Goal Programming The Analytic Hierarchy Process, which was developed by the mathematician, Thomas L. Saaty,8 is a practical and e!ective method for solving multi-criterial decision problems. Its decision model is based on structuring the elements of the problem in terms of how the alternative solutions in#uence decision criteria, satisfaction of which will show how much a particular solution contributes to the accomplishment of the main objective of a decision problem. The AHP uses a multi-level hierarchical structure of objectives, criteria, sub-criteria and alternatives. The pertinent data are derived by using a set of pairwise comparisons. These comparisons are used to obtain the weights of importance of the decision criteria, and the relative performance measurements of the alternatives in terms of each individual decision criterion. The hierarchical organization structure of the AHP arranges a decision problem in clusters at di!erent levels; higher level elements transmit in#uence to lower level ones, or lower level elements contribute to the functioning of the higher level ones. The general expression of the GP model with a preemptive ranking for each of the goals can be described as follows:





LG Minimize: Z" p (w>d>#w\d\) (1) G GI G GI  GZK I L Subject to: a x !d>#d\"b , for i"1, 2, m GH H G G G H d>, d\, x *0, for i"1, 2, m; for j"1, 2, n (2) G G H In the expression above, the substantially useless value of Z is the summation of all deviations; a are techGH nological coe$cients in the constraints; b are the G

right-hand-side coe$cients in the constraints; x are H non-negative decision variables or unknowns; d> is G called a positive deviation variable and d\ a negative G deviation variable; n is the number of the decision variables; m is the number of the constraints; w>, w\*0 and GI GI represent the relative weighting to be assigned to each of the k"1, 2, n di!erent classes within the ith category G to which the non-Archimedean treascendental value of p is assigned; n is the number of classes within the ith G G category of goals; and p are the pre-emptive priority G factors that serve only as a ranking symbol and can be interpreted to mean that no substitutions across categories of goals will be permitted. It is assumed that the ordering of deviation variables in a goal function will be minimized in order such that p 'p 'p '2 and G G> G> so on for as many priorities as may exist in a model. Furthermore, it is assumed that no combination of relative weighting attached to the deviation variables can produce a substitution across categories in the process of choosing the x . H The "rst LGP solution method was detailed by Charnes and Cooper,9 and implemented as computer code by Jaaskelainen10 in 1969, and this code was limited to the models with 50 or less number of variables. The next generation of LGP codes treated each priority level as a separate LP and added augmenting constraints at each priority level to safeguard the minimal value obtained at the previous level. This type of algorithm is known as sequential simplex and is described by Ignizio and Cavalier.11 Other related algorithms were reported by Authur and Ravindran12 and Schniederjans and Kwak.13 Ignizio14 introduced a primal}dual method that allows dropping of dual constraints at each priority level. Multiple-phase Simplex Algorithm for GP (MPGP),15 based on Simplex Algorithm, is an extension and re"nement of a Two-Stage Algorithm for GP,14 which has advantages of less iterations in computation, high computational accuracy and quick convergence.

3. A case study in Chinese agriculture Grain production consists of crop establishment, crop production and post-harvest operations. Much attention is paid to the establishment and production of the grain, whereas post-harvest operations are often neglected. However, according to the estimate of FAO, the average grain loss rate in grain post-harvest was about 10% in the whole world, and the loss rate in some developing countries was as high as 20}40%. Therefore, a decrease in grain loss during both harvesting and post-harvest operations can be considered as a good opportunity to increase the grain output, especially in some developing countries.

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3.1. ¹he analytic hierarchy process in a grain harvesting and post-harvest system The AHP is applied to analyse the grain harvesting and post-harvest system because the decision problem concerned is related to various elements across many "elds, some of which could not be quanti"ed. In the case study, the elements relating to the grain harvesting and post-harvest system were "rst developed in conjunction with grain producers in China. Then, the problem was segregated into a three-level hierarchy that represents the overall goal of the decision process, the decision criteria, and the decision alternatives (Fig. 1). In particular, in Fig. 1, Level 1 is the overall goal that describes the function of the system, the decrease in grain loss and the increase in the value of the available grain. Level 2 represents the criteria such that: C is the decrease in the grain  loss; C is the reduction in the production cost of grain  harvesting and post-harvest operations; and C is the  increase in the value of the available grain. Level 3 represents the alternative measures including: M , raising the  farmers' management ability; M , putting more materials  and equipment into grain production; M , enlarging the  scale of management for grain production; M , enhanc ing farmer awareness of the need to reduce grain losses; M , raising the price of grain and reforming the system  for the purchase and sale of grain; M , selecting better  grain seed; M , establishing an extension service to  provide advice on techniques and equipment for farmers; M , improving and developing techniques and  equipment used in grain harvesting and post-harvest operations; M , polishing grain products; and M ,   avoiding deterioration and wastage in distribution and consumption. Based on this three-level hierarchy of the grain harvesting and post-harvest system, several questionnaires were then designed and answered by the specialists who are engaged in agricultural management, agricultural economics, agricultural engineering, system engineering, agronomy and biological engineering, and management

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sta! and farmers. The Delphi method was employed to collect and analyse information from the questionnaires15 after which the judgement matrices with pairwise comparisons were constructed. A method known as the eigenvector method8 was applied to compute single criterion weighting, composite weighting and their priorities in the AHP for grain (harvest and post-harvest), which are presented in Table 1. A consistency index and a consistency ratio were used as a means for checking consistency of the elicited matrices. The consistency ratio measures the consistency of the judges or the decision makers who assign relative scales in a pair wise fashion (forming a pairwise comparison matrix of size n) with the attributes A , A , 2, A   L of one level given the attributes of the next higher level of hierarchy associated with a decision problem. Essentially, a consistency ratio of 0)10 or less was considered acceptable as a guideline to use in evaluating matrix consistency.8 As shown in Table 1, all of the consistency ratios (CR) are below 0)10. After the overall goal, criteria and alternative measures, and their priorities in the AHP for grain (harvest and post-harvest) had been suggested, the optimized allocation of facilities was carried out.

3.2. Goal programming model to study the case The purpose of this section is to establish the goalprogramming model for the grain harvesting and postharvest system in Zhejiang Province, China with the objective to optimize the allocation of all facilities and equipment. The model is solved by means of MPGP algorithm. 3.2.1. Decision variables In this model, the numbers of facilities or labourers that are required in each process in the grain harvesting and post-harvest system are de"ned as decision variables, and in particular: x is the number of labourers required  for cutting grain with sickles, 10 persons; x is the 

Fig. 1. Three-level hierarchy for the grain harvesting and post-harvest system, with the overall goal O achieved by diwerent criteria C, each using various measures M

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Table 1 Weighting of single measures M, and of criteria C combined to give composite weighting for the goal and priorities of the elements in the Analytic Hierarchy Process for the grain harvesting and post-harvest system Measure weighting (level 3)

Goal weighting (level 1)

Criterion weighting (level 2) Measures

C1"0)637

C2"0)105

C3"0)258

M  M  M  M  M  M  M  M  M  M  Consistency ratio

0)078 0)048 0)027 0)136 0)366 0)041 0)112 0)192 0)000 0)000

0)133 0)068 0)128 0)093 0)365 0)078 0)135 0)000 0)000 0)000

0)000 0)000 0)000 0)050 0)267 0)050 0)000 0)165 0)363 0)105

0)0655

0)0816

0)0568

number of combine harvesters used in cutting and threshing grain, 10 machines; x is the number of  swathers used in cutting grain, 10 machines; x is the  number of electric-powered threshers used in threshing grain, 10 machines; x is the number of engine-driven  threshers used in threshing grain, 10 machines; x is the  number of pedal threshers used in threshing grain, 10 machines; x is the number of manual threshers used in  threshing grain, 10 machines; x is the number of wheel  barrows used in transporting grain in the "elds, 10 machines; x is the number of labourers engaged in  carrying grain on their shoulders in the "elds, 10 persons; x is the number of tractors used in transporting  grain from the "elds, 10 machines; x is the number of  farm boats used in transporting grain from the "elds, 10 machines; x is the area of unshaded concrete yard used  in drying grain, ha; x is the area of bamboo mats used  in drying grain, ha; x is the number of fans and bamboo  sieves used in cleaning grain, 10 machines; x is the  number of simple cleaners with engine-driven sieves used in cleaning grain, 10 machines; x is the number of  wooden winnowers used in cleaning grain, 10 machines; x is the volume of storehouses used in open grain  storage, 10 m; x is the volume of storehouses with  bamboo mat bins and sacks used in open grain storage, 10 m; x is the volume of wooden cabinets used in  closed grain storage, 10 m; and x is the number of  rice mills used in milling grain, 10 machines. 3.2.2. Constraints Five types of constraints are constructed for the model, namely: grain loss; production cost; number of labourers; number of various facilities; and production capacity in every step of the harvesting and post-harvest system.

Composite weighting

Composite priorities

0)064 0)038 0)031 0)109 0)340 0)047 0)085 0)165 0)094 0)027

6 8 9 3 1 7 5 2 4 10 0)0322

¹ype I: grain loss constraint  l A E x #d\!d>"¸S (3) G G G G J J G where l is the grain loss rate in percent corresponding to G x ; ¸ is the expected total loss rate in percent in the G complete process; A is the annual production time in G h/machine corresponding to x ; E is the production G G capacity in m/h corresponding to x ; S is the area of the G harvested grain per year in ha; d>, d\ are, respectively, J J positive and negative deviations from the expected total grain loss per year ¸S in ha. ¹ype II: production cost constraint  c A E x #d\!d>"CS (4) G G G G   G where c is the production cost in Yuan/ha corresponding G to x ; C is the expected total production cost in Yuan/ha G for all the grain harvesting and post-harvest operations; d>, d\ are, respectively, positive and negative deviations   from the expected total production cost CS in Yuan, the exchange rate for the monetary unit of China being taken as 8)3 Yuan+US$1. ¹ype III: labour force constraint  w x #d\!d>"= (5) G G   G where w is the number of labourers operating per maG chine in the grain harvesting and post-harvest system corresponding to x ; = is the total number of G labourers who could be engaged in the system (10 persons); d>!d\ are, respectively, positive and negative  

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deviations from the number of labourers who could be engaged in the system (10 persons). ¹ype I<: facility constraint x #d\ !d> "R ( j"2, 3, 2 8) H >H >H H (6) x #d\ !d> "R ( j"10, 11, 2 20) H >H >H H where R is the number of facilities in the grain harvesting H and post-harvest system, corresponding to x (10 maG chines, or m, or m); d> , d> , d\ , d\ are, respec>H >H >H J>H tively, positive and negative deviations from the number of facilities in the system corresponding to x (10 maH chines, or m, or m). ¹ype <: production capacity constraint Harvesting:

 A E x #d\ !d> "S G G G   G

 A E x #d\ !d> "S G G G   G O G   Transporting: A E x #d\ !d> "S G G G   G Threshing:

 A E x #d\ !d> "S G G G   G  Cleaning: A E x #d\ !d> "S G G G   G

Drying:

Storage:

 x #d\ !d> "< G   G

Milling: A E mx #d\ %d> &M     

(7)

(8)

(9)

(10) (11)

(12) (13)

where < is the volume of storage of grain harvested in the whole year in m; M is the total weight of grain milled by farmers in the whole year (10 kg); m is the seasonal grain output milled by farmers in kg; d> , d\ , 2, d> , d\ are,     respectively, positive and negative deviations from the production capacity in each process of the grain system in ha (for d> , d\ , 2, d> , d\ ) or in kg (for d> , d\ ).       3.2.3. ¹he goal function Two goals, namely, the decrease in the grain loss and the production cost for grain (harvest and post-harvest), are considered in the GP model. Besides, a full utilization of facilities and resources for grain (harvest and postharvest) is also assured. According to the previous analysis of the AHP for the grain harvesting and post-harvest system, the priorities p and weightings of goals are arranged as follows. The harvesting and post-harvest grain

loss p is the most important criterion in the AHP for the  system, so it should be considered as the "rst goal in the GP model, that is p d>. The total production cost for   harvesting and post-harvest processing p is considered  as the second goal, that is p d>.   An excess of production capacity p leads to resource  waste, but inadequate production capacity leads to untimely harvesting and higher grain loss, so the third goal is p 



 (a\ d\#a> d>) G G G G G



where a>, a\ are, respectively, the weighting coe$cients G G of positive and negative derivations of production capacity constraints, as determined by the relative importance of production capacity of each process in the grain harvesting and post-harvest system. The fourth and eighth goals p , p are to minimize   spare capacity of facilities. Their weighting coe$cients are equal to the proportion of the quotients of the price and the working e$ciency of the facilities. The facilities with the larger weighting coe$cients are placed into the fourth goal, and the facilities with the smaller weighting coe$cients are put into the eighth goal, giving:









p b d> #p b d> , G G  H H  G H i, j3 [4, 5, 2, 20, 21 ], and iOj where b , b are, respectively, weighting coe$cients for G H positive derivation of the facility number constraints corresponding to d>, d>. G H The actual number of labourers working in grain system p should be less than the permitted number, that is  p d>.   The sixth and the seventh goal p , p are to minimize   negative derivation of various facilities (especially with high price and high e$ciency) in the grain system so as to fully utilize them. The weight coe$cients are equal to the proportion of product of the unit price of facilities and their working e$ciency. The facilities with the larger weighting coe$cients are placed into the sixth goal, and the facilities with the smaller weighting coe$cients are put into the seventh goal, giving:









p c d\ #p c d\ ,  G G  H H G H i, j3+4, 5,2, 20, 21], and iOj where y , y are, respectively, weighting coe$cients of G H negative derivation of the facilities number constraints corresponding to d\, d\. G H

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Table 2 The expected values of goals of various plans in Goal Programming model for the grain harvesting and post-harvest system Plans Grain loss rate (¸), % Production cost (C), 10 Yuan/ha

P1

P2

P3

P4

P5

P6

P7

P8

P9

P10

P11

P12

P13

P14

P15

P16

13

13

13

13

10

10

10

10

8

8

8

8

5

5

5

5

66

50

42

33

66

50

42

33

66

50

42

33

66

50

42

33

Combining these terms, the objective function of GP for the grain system can be developed as follows: min Z"p d>#p d>#p      #p



#p









 (a\d\#a>d>) G G G G G

 









b d> #p d>#p c d\ G G    G G G G c d\ #p b d> H H  H H H H

(14)

3.2.4. ¹he solutions of the Goal Programming model To solve the model described in the last section, it is necessary to set up the following target values according to the on-site measurement and assessment in the "elds of Zhejiang Province, China. First, the average harvesting and post-harvest grain loss rate is 15%. Second, the production cost per season is 5000}6600 Yuan/ha at the present level of grain harvesting and post-harvest operations. Third, under the present conditions and levels, the expected rates of harvesting and post-harvest grain loss l are supposed to be 13, 10, 8 and 5%, respectively. G Fourth, the expected production costs c are supposed to G be 6600, 5000, 4200 and 3300 Yuan/ha. Considering different combinations of the expected grain loss rates and production costs for the grain system, 16 plans for the GP model are presented in Table 2. In addition, the various parameters in the constraints and the objective function in the above GP model for the grain harvesting and post-harvest system can be calculated by means of the measured grain loss rate, the investigated production cost and some relative statistical data in Zhejiang Province, China. Multiphase Simplex Algorithm for Goal Programming (MPGP) is used in solving the above GP model which is coded as a FORTRAN program.

4. Analysis of results The results shown in Table 1 were obtained from the questionnaires using the eigenvector method. From the results of the AHP in Table 1 for grain (harvest and post-harvest) in a province of China, it is shown that

C (decrease in the grain loss) is the most important  criterion (weighting 0)637); the weighting of C (reduction  in the production cost) and C (increase in the value of  available grain) are, respectively, 0)105 and 0)258. In China, the imbalance between the supply and demand for grain is prominent because of very large population and inadequate agricultural resources. A large grain loss in the system, unreasonable use and waste of grain exacerbate this imbalance. Therefore, the improvement of the functions of the system should focus on a decrease in the grain loss, as well as an increase in the e!ective use of the grain available. In China, because the scale of grain production for most of the farmers is relatively small and the market price of grain is relatively low, the economic bene"t from grain production is so small that farmers give little consideration to the relevance of grain losses. Therefore, M (raising the price of grain and reforming the system  for the purchase and sale of grain), M (improving and  developing techniques and equipment used in the grain harvesting and post-harvest operations), and M (en hancing farmer awareness of the need to reduce grain loss) are "rst three most important measures amongst the alternatives, with composite weightings of 0)340, 0)165 and 0)109, respectively. In recent years, the system of purchase and sale for grain has been reformed, and the grain price has gradually been raised to re#ect the rules of market economics. In view of the results of the GP model, the number of facilities in the grain harvesting and post-harvest system in Zhejiang Province, China, is su$cient to achieve the goals in plans P and P . All the goals in these two plans   were achieved except the goals p and p (relating to the   excess of facilities included in these goals) as shown in Table 3. In theory, therefore, it is completely possible to decrease grain loss to 13%, and even to 10%, under the present conditions for techniques and facilities. In practice, however, the average rate of harvesting and postharvest grain loss in Zhejiang Province is 15%. This is because a unit of grain production in China is often represented by a few farmers' families, whose scale of production is not very large, and each unit usually possesses some production facilities for grain. Even though the total number of facilities is enough to decrease the

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Table 3 The achieving extent of goals in various Goal Programming plans P Goal outcomes for various plans (P)

Priorities (p)

p  p  p  p  p  p  p  p 

P1

P2

P3

P4

P5

P6

P7

P8

P9

P10

P11

P12

P13

P14

P15

P16

A A A A A N N A

A A A A A N N N

A A A N A N N N

A A N N A N N N

A A A A A N N A

A A A A N N N N

A A A N A N N N

A A N N N N N N

A A A A A N N N

A A A A A N N N

A A N N A N N N

A A N N A N N N

A A N A A N N N

A A N A A N N N

A A N N A N N N

A A N N A N N N

Note: A"Achieved; N"Not achieved.

grain loss rate to 10%, their macro-distribution within the entire Province may not be completely uniform. In addition, due to inadequate energy resources (oils, electricity), insu$cient utilization of the present facilities, small-scale production and traditional forms of management, the e$ciency and capability of the present facilities are not fully realised. In the GP model, however, it is assumed that the facilities for grain (harvest and postharvest) have optimal macro-allocation within the entire Province i.e. the government or some social organization possesses all facilities. The importance of establishing this kind of social organization can be seen from the results of the AHP. Establishing an Extension Service to provide advice on techniques and equipment to farmers M is the  "fth most important measure (weighting 0)085). With regard to the plans P , P , P , P , P , and P , the       number of two particular facilities, simple cleaners with engine-driven sieves (x in the decision variable de"ni tion) and areas used for open grain storage (x in the  decision variable de"nition) are not su$cient. Furthermore, in order to decrease the production cost to 3300 Yuan/ha (see Table 2 on P , P , P and P ), the     number of combine harvesters (x in the decision variable  de"nition) used in cutting and threshing grain is not su$cient. It is impossible to decrease the grain loss rate to 5% (see Tables 2 and 3 on P , P , P , P ) under     the present conditions for techniques and facilities; goals p , p and p in these plans could not be achieved (owing    to the lack of facilities included in these goals) as shown in Table 3. Therefore, in the long term, it is essential to improve and develop new techniques and equipment used in the grain harvesting and post-harvest system. The results of the AHP also support this conclusion i.e. M (improving and developing techniques and equip ment used in the grain harvesting and post-harvest operations) is the second most important measure (weighting 0)165).

5. Conclusions This research indicates that it is suitable to integrate the powerful decision tool of the Analytic Hierarchy Process (AHP) with Goal Programming (GP) model to consider both quantitative and qualitative decision criteria e.g. optimizing macro-allocation of facilities in agriculture or other "elds. In the illustrative case for the grain harvesting and post-harvest system in Zhejiang, China, the results of AHP and the GP model show that a decrease in the grain loss is the most important goal in the system. It would be possible to decrease the rate of harvesting and post-harvest grain loss to 13%, and even to 10%, but impossible to decrease the grain loss rate to 5% under the present conditions of facilities and techniques. Delphi method is applied to handling the group discussion process and group setting judgement matrices with pairwise comparisons in the AHP so that the obtained results could be more objectives and a high level of consistency could be achieved. The proposed methodology of integrating AHP and GP provides decisionmakers with the #exibility needed to allocate resources by considering both quantitative and qualitative decision criteria. Acknowledgements This research was supported by IDRC in Ottawa, Canada, and conducted in Zhejiang Agricultural University, Hangzhou, People's Republic of China. References 1

Romero C Handbook of Critical Issues in Goal Programming. Oxford: Pergamon Press, 1991

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