A goal programming model for planning the development of newly reclaimed lands

Agricultural Systems 26 (1988) 245-261

A Goal Programming Model for Planning the Development of Newly Reclaimed Lands

Hisham E1-Shishiny

IBM Cairo Scientific Center, 56 Gameat, E1 Dowal El Arabia Street, Mohandessin, Cairo, Egypt

(Received 12 January 1987; revised version received 30 July 1987; accepted 31 July 1987)

S U M M A R Y

A large-scale, multi-objective single-time-period model for planning the development of reclaimed lands is proposed. The period considered is a typical year at the most developed stage of the agricultural complex. Given specific development goals and a set of resource constraints, the model determines the optimal land allocation for the integrated agricultural development of a region, including agricultural and livestock production as well as agri- industries.

Linear Goal Programming is the multi-objective technique used for model formulation. The technique proposed for the solution is a multi-phase simplex algorithm which is based on the IBM-MPSX/370.

1 INTRODUCTION

Due to the high cost and effort associated with land reclamation development projects, and the variety and complexity of the different factors related to them, comprehensive and integrated planning is required prior to initial development.

One of the most effective planning tools in this respect is agricultural modelling. It provides a framework for the evaluation of alternative planning scenarios.

Determination of policies for handling newly-reclaimed lands along with specific objectives of reclamation is a complex exercise since objectives are

245 Agricultural Systems 0308-521X/88/$03-50 © Elsevier Applied Science Publishers Ltd, England, 1988. Printed in Great Britain

246 Hisham El-Shishiny

usually conflicting. Decision-makers are usually faced with many important objectives when planning for the integrated development of a region or subregion. Examples of those objectives are:

Employment generation Resource development Self-sufficiency Export promotion Net income increase Environmental enhancement

Such objectives may be non-commensurable and often conflicting. For instance, we cannot maximize simultaneously net income, employment and food exports. The production of a crop that gives the highest net income may not generate the highest employment opportunities or provide the country with agricultural exports. In such cases, decision-makers, when selecting a course of action, try to achieve more than one objective, taking into consideration the constraints dictated by the resources and the environment.

The problem under consideration is multi-objective in nature and has to be addressed by multi-objective programming techniques rather than by conventional single objective Linear Programming (LP). Although the literature of applying programming techniques, especially LP, to agricultural planning problems is extensive (Lee, 1972; Day & Sparling, 1977; E1-Kheshen, 1977), yet the reported attempts to use Multi-Objective programming methods in that area are still very limited both in number and in scope (Wheeler & Russel, 1977; Bazaraa & Bouzahar, 1981; E1-Shishiny 1983; Romero, 1986; Zanakis & Gupta, 1985).

Goal Programming (GP) is an optimization technique for solving problems involving multiple non-commensurable conflicting goals. These are rank-ordered according to their priority to the decision-maker. GP considers the goals, one at a time, from highest to lowest priority and attempts to achieve them by minimizing the deviations from the goal levels. For a more detailed description of GP the reader is referred to Lee (1972) and Ignizio (1976).

This paper aims at describing in detail an agricultural planning model particularly conceived to address issues pertaining to the integrated development of newly-reclaimed lands in developing countries. Decision makers, planners, and analysts interested or involved in land development programs may benefit from examining the proposed model when planning for sub-regional or regional integrated agricultural development. They can learn from a real experience in model building for regional planning, developed through actual in-depth analysis of agricultural development needs in a typical developing country. The proposed model is flexible and

Model for planning the development of newly reclaimed lands 247

can be modified and used as a tool for the analysis of Complex regional planning problems in other developing countries.

2 THE M O D E L

The formulated model is a single time period which is a typical year at the developed stage of the agricultural complex.

For implementing the model, the region or subregion under study is divided into a number of subregions according to the special characteristics of the region. Each subregion is considered as a human settlement administrative unit. The soil of the region or subregion is differentiated into soil classes, and crops suitable for each soil class identified.

The model indices, variables, coefficients, constraints and goals are defined as follows:

2.1 Indices

The following is a list of the indices used in the formulated model:

b water quality j subregion under study s soil class a agricultural technology f farm type i irrigation method t time period c crop commodity q feed type l livestock type p livestock product n agri-industry type e labor type e' machine type k fertilizer type

2.2 Variables

The following is a list of the variables used in the formulated model:

Xjs,lic acreage of crop c in subregion j, soil type s, agricultural technology a, farm type f, irrigation method i

Ijt quantity of water allocated to subregion j at period t


H j,

M ,j,

M ,j

Fkj

LS u PFqj POPj PPFqj SAL~pj

SALcj RINLp,zj

RINC.~.j

INDLvntj

INDC~cj

ENGjt

ENGTj TC sj INC fs APj, VAj NPSj NRSj NSSj NHTj NCHj NIHj NSUj NPOj NPTj TFA f j

total person days of labor type e required by subregionj at period t total hours of equipment type e' required by subregion j at period t total hours of equipment type e' required by subregion j per year total quantity of fertilizer type k required by subregion j total chemical cost required by subregion j quantity of seeds required by subregion j for crop c number of livestock type l in subregion j quantity of feed type q available at subregion j population of subregion j quantity of feed type q purchased from outside subregion j quantity available for sale outside subregion j of livestock product p of livestock type l quantity of crop c available for sale outside subregion j available raw materials for agri-industry type n for livestock product p of livestock type 1 in subregion j total yield of crop c in subregion j available raw materials for agri-industry type n for crop c" in subregion j processing capacity of agri-industry type n for livestock product p of livestock type l in subregion j processing capacity of agri-industry type n for crop c in subregion j total energy required for irrigation by subregion j during month t total energy required by subregion j total annual cost of farm type f i n subregion j total net income of farm type f in subregion j total animal power required by subregion j in time t total value added for subregion j number of primary schools in subregion j number of preparatory schools in subregion j number of secondary schools in subregion j number of hospitals in subregion j number of clinics in subregion j number of integrated clinics in subregion j number of social units in subregion j number of police stations in subregion j number of telephone and telegraph units in subregion j total area cultivated using farm type f in subregion j


2.3 Coefficients

The following is a list of the coefficients used in the formulated model:

PRtc WAjsbict

M A e, safict

FTksa.fic

PSsaf~c

SE.y~

YDsaflcb

F q c

enc

Pp.t E L S l TI,, EDU CPFIq CONll,

CONc RT MN~

MRs.c

proport ion of land occupied by crop c at time t average water requirements of one acre cultivated by crop c on soil type s and irrigated on water quality b, irrigation method i in subregion j, at time t person days of labour type e required to cultivate one acre, soil type s, agricultural technology a, farm type f and irrigation method i by crop c at time t number of hours of equipment type e' required to cultivate one acre, soil type s, agricultural technology a, farm type f and irrigation method i by crop c at time t quantity of fertilizer type k required to fertilize one acre of soil type s cultivated by crop c using agricultural technology a, farm type f and irrigation method i cost of chemicals required per acre of soil type s cultivated by crop c using agricultural technology a and farm type f and irrigation technique i quantity of seeds required per acre cultivated by crop c using agricultural technology a and farm type f yield per acre of soil type s cultivated by crop c using agricultural technology a, farm type f and irrigated by irrigation method i and water of quality b quantity of feed type q obtained from one unit of crop c quantity of agri-industrial product type n obtained from one unit of crop c quantity of agri-industrial product type n obtained from one unit of product p of livestock I energy consumed per head of livestock type l yield of livestock product p per livestock type l per capita consumption of energy for domestic use consumption of livestock type l of feed type q per capita consumption of livestock product p of livestock type l per capita consumption of crop c ratio of the active population to total population quantity of manure produced from one unit of livestock type I manure requirements per acre of soil type s cultivated by crop c using agricultural technology a

250 Hisham EI-Shishiny

HU, HU..I

HU.c

ElMtsafic

EPL,pl

EPC,c

COsafic

INsayic

ARafct

VLs~ii~

VPL,pl

VPC,c

PS RS SS HT CH IH SU PO PT

person hours of labor required per unit of livestock type l person hours of labor required per unit capacity of agri- industry type n for livestock product p of livestock type l person hours of labor required per unit capacity of agri- industry type n of crop c energy requirements for irrigation per acre of soil type s cultivated by crop c using agricultural technology a, farm type f and irrigation method i during month t energy requirements per unit capacity of agri-industry type n for livestock product p of livestock type l energy requirements per unit capacity of agri-industry n for crop c annual cost per acre of soil type s cultivated by crop c using agricultural technology a, farm type f and irrigation method i net income per acre of soil type s cultivated by crop c using agricultural technology a, farm type f and irrigation method i animal power required per acre cultivated by crop e using agricultural technology a, farm type f at time t value added per acre of soil type s cultivated by crop c using agricultural technology a, farm type f and irrigation method i value added per head of livestock type l value added per unit capacity of agri-industry type n for livestock product p of livestock type l value added per unit capacity of agri-industry type n for crop c ratio ratio ratio ratio ratio ratio ratio ratio ratio

of primary schools to population of preparatory schools to population of secondary schools to population of hospitals to population of clinics to population of integrated clinics to population of social units to population of police stations to popula t ion of pos t office units to population

2.4 Constraint set description

2.4.1. Land occupation Each crop occupies land according to its crop calendar. The total cropped area of each soil class at each subregion should not at any time exceed the


total area of that particular soil class:

~ f R t c . Xjsaf ic~Zjs

a,i,f,c

V j, t, s

2.4.2 Crop diversification Areas occupied by certain groups of crops are constrained in order to assure the diversification of crops in the region:

L c, <_ <_Ljc, s,a,i,f ,c ~ c'

V j, e'

2.4.3 Water duties The total monthly water duties for each subregion is expressed as:

lit = ~ WAjsblct" Xjsafic = 0

s,a,f ,i,c V j, t

The limits on the quantity of water available for irrigation are:

WL, < ~ , Ij~ < WU~

J V t

2.4.4 Agricultural labor The total agricultural labor required every month from each type of labor for each subregion is expressed as:

Hej t -- ~ HUesafict" Xjsafic : 0

s,aJ, i,c

Vj , t ,e

2.4.5 Animal power The total monthly requirements of animal power given in animal days of work for each subregion is expressed as:

APJ t ~ ARaf ~t" Xj~ayi~ : 0

s,a,f ,i,c

V j, t


2.4.6 Agricultural machinery The total machine hours required monthly from each machine for each subregion is represented by:

V~ Me'jr -- 2 , MAe'sayict. X;sallc = 0

s,a,f,i,c

Vj, e', t

The total annual machine hours required from each machine type for each subregion is represented by:

M'e,j - ~ M e ' i t = 0 t

V j, e'

2.4.7 Fertilizer supply Fertilizer requirements from each fertilizer type for each subregion is expressed as:

Fkj -- ~ FTk~fi~. Xj~afic = 0 s,a,f,i,c

V j, k

2.4.8 Chemical cost The total cost of chemicals for each subregion is expressed as:

e j -- ~ easafic" Xjsafic = 0

s,a,f,i,c v j

2.4.9 Seed supply Seed requirement for each crop for each subregion is expressed as:

s,a,f ,i

SEcy.. Xj~yi~ = 0

V j , c


2.4.10 Crop yield The total crop yield of each crop type for each subregion is expressed as:

s,a,f,i

YD~,,fi~ b . Xj~.fi~ = 0

W, c

2.4.11 Livestock-Feed Balance The livestock-feed balance for each subregion is expressed as:

PFqj + PPFqi - ~ CPFIq. LStj = 0

l

V j, q

2.4.12 Crop-feed balance The balance between crop products and type of livestock feed produced for each subregion is expressed as:

For crops producing green fodder

PFqj -- y YDsaficb. X j s a f i c = 0

s ,a , f ,l,c

vj

For crops producing straw as a by-product

eFqj -- ~ VFq~. X j s a f i c = 0

s,a,f,i,c

vj

For processed feed

PFqj -- IND Cnc j = 0

v j

254 Hisham EI-Shishiny

2.4.13 Manure balance The manure balance for each subregion is expressed as:

l s ,a , f , i ,c

v j

2.4.I4 Agri-industries The balance between agricultural and livestock products, population consumption, agri-industries and products available for sales outside each subregion is expressed as:

Tzp . LSIj - CONtp. P O P j - SALlpj - R I NLp , zj -~ 0

Ppnl" RINLp,I i - INDLp,t j = 0

Vp, n , l , j

Y~,j - CONe°. P O P j -- SALc,~ - R I N C , e,j = 0

P,c" . RINC,¢°j - I N D C , c,,j = 0

V c", n, j

c": agri-industrial crops

2.4.15 Set t lement opportunities

The total settlement opportunities created by agricultural, livestock and agri-industrial activities is related to the active potential population of each subregion as follows:

te l p ,n , l

+ y , HU.c. INDC.~j -- R T . POPi = 0

n , c

V j

2.4.16 Energy needs Monthly energy expressed as:

requirements for irrigation for each

ENGjt -- y j EIMtsayic. X j s a f i c ~ - 0

s ,a , f , i ,c

v j, t

subregion are


Total energy needs for livestock production, agri-industries and domestic use is expressed as:

ENGTj--2EPLnpt . INDLnpl j - -2EPCnc. INDCnc j n,p,l n,c

-- ED U. POPj -- ~ ELSz. LStj = 0 l

vj

2.4.17 Farm cost The total annual variable cost of each subregion for each farm type is expressed as:

T C f j - 2 s,a,i,c

COsafi c . X)~ali ~ = 0

V f j

2.4.18 Farm income The total annual net income of each subregion for each farm type is expressed as:

I N C f j - 2 INsaf ic 'Xjsaf ic :O

s,a,i,c

Vf, j

2.4.19 Total value added The total value added for each subregion is expressed as:

VAj- ~ VLsafic..Xjsafic-2vgt. LSlj s,a,f ,i,c 1

- - 2 VPL'wl ' INDLnplJ-2 n,p,l n,c

v j

VPC, c. INDC, ci = 0


2.4.20 Farming areas The total farming area for each farm type for each subregion is expressed as:

T F A f j - 2 XjSafic ~-0 S,a,[,c

Vj, f

2.4.21 Infrastructure The infrastructure required by the potential population of each subregion is expressed as:

NPSj -- PS. POPj = 0

NRSj - - R S . P O P j = O

NSSj -- SS. POPj = 0

N H r j - HT. POPj=O

N C H j - - C H . POPj=O

NIHj- - I H . P O P j = O

NSUj -- SU. POPj = 0

NPOj - PO. POP~ = 0

NPTj -- PT. POPj = 0

v j

2.4.22

Ljc,

L)c,

wut

WLt

Right-hand-side definitions

total area of soil type s at subregion j upper limit on surfaces cultivated by the group of crops c' at subregion j lower limit on surfaces cultivated by the group of crops c' at subregion j upper limit on the volume of water available for irrigation at time t lower limit on the volume of water available for irrigation at time t

2.5 Goals and priority structure

In order to complete the formulation of the Goal Programming model, a set of goals for the development of a region or a subregion have to be identified and an ordinal ranking of these goals according to their priorities is required.


Therefore, a number of articulated and prioritized goals for the development of a region or a subregion in line with national objectives have to be defined. The following goals are considered by the formulated model:

(a) Population Absorption: To create permanent settlements in order to attract people from the overpopulated areas.

(b) Resource Development: To use efficiently the resources of each settlement in a way that serves its permanent activities and achieves its rapid growth.

(c) Economic Viability: To develop productive economic activities that will result in producing goods and services that meet the settlement and the national needs.

2.5.1 Goal's mathematical representation In order to incorporate the mentioned goals into the model, each goal should be expressed in the form of a goal constraint as follows:

2.5.1.1 The population absorption goal: This goal is represented in the model by setting a targeted population level for the settlement under consideration. This is expressed as follows:

where:

LPOPj Pl~ and nlj

POPj + nlj-- Plj = LPOPj

v j

the targeted population level at subregion j the positive and the negative deviations from the targeted population level at subregion j

The activities created for the targeted population will be determined endogenously by the model according to the available resources of each subregion.

2.5.1.2 The resource development goal: This goal is represented by setting targeted levels for the production of those activities in the subregion that depend on local resources such as agri-industries. This is expressed as:

INDLp, tj + n2pntj -- P2pnlj = INDLTpnlj

Vp, n , l , j

INDC, c,j + n3,c° s -- P3,~,,~ = INDCT,~,j

V n, c", j


where

IND L Tpnl j

INDCT,~,j

n2p,,l j and P2pntj

n3,e, j and P3,~°j

The resources required

targeted processing capacity of agri-industry type n for livestock product p of livestock type 1 at subregion j targeted processing capacity of agri-industry n for crop c" at subregion j the negative and positive deviations from the targeted processing capacity of agri-industry n for livestock product p of type l at subregion j the negative and positive deviations from the targeted processing capacity of agri-industry n for crop c" at subregion j

for these activities will be determined by the model.

2.5.1.3 The economic viability goal: This goal is represented in the model by setting a high target value added for the subregion as well as targeted values for the production of certain activities that meet a national need. This is expressed as:

VAj + n4j -- P4j = TVAj v j

Ycj + n5cj - P5cj = Yrcj V j

for crops that meet a national need.

LSIj + n61j -- P61j = STzj v j

for livestock that meet a national need.

where

YT~j ST~j TVA j n4j and P4j

n5j and P5j

n6j and P6j

targeted yield of crop c from subregion j targeted number of livestock type l in subregion j targeted value added for subregion j negative and positive deviations from the targeted value added for subregion j negative and positive deviations from the targeted yield of crop c from subregion j negative and positive deviations from the targeted number of livestock type l in subregion j


2.6 The objective function

The objective function is to minimize the positive and negative deviations for the given set of goals according to the priority structure assigned to them.

3 THE SOLUTION ALGORITHM

Basically, there are two methods for solving Linear Goal Programming models; namely, the multi-phase modified simplex algorithm and the sequential or iterative approach where the problem is solved as a sequence of interrelated single-objective Linear Programming problems.

The technique adopted for the solution of the formulated Goal Programming model is the Linear Multi-Objective Programming System (LMPS) (Cortes, 1980) which is based on the IBM MPSX/370, LMPS is a multi-phase method with a phase for each defined priority level. The main advantage of this method is that it requires less pivots to find the optimal solution.

4 MODEL-GENERATED SOLUTIONS

The model-generated solutions consist of: For each subregion:

Acreages and yield of crops in each season Annual livestock production Annual agri-industry production Resettlement opportunities Total agricultural value added Total annual energy needs Required infrastructure

Monthly requirements of:

Irrigation water Agricultural labor Agricultural machinery Animal power Irrigation energy

Annual requirements of:

Fertilizers Chemicals Seeds Fodder

260 Hisham E1-Shishiny

For each farm type:

Total annual cost Total annual net income Total cultivated area

The model has been applied to a number of case studies and the generated solutions were examined critically using common-sense. The solutions were sensible and conform with what we might expect in practice.

Among these case studies is the planning for the development of Sinai Northern Plain in Egypt, where about 300000 acres are expected to be reclaimed and irrigated by the Nile water, which will be extended to Sinai through siphons under the Suez Canal.

In this paper we do not intend to describe the application of the model to case studies: however, this has been the subject of other publications (E1- Shishiny & Attia, 1985).

5 CONCLUDING REMARKS

The proposed model is a valuable planning tool formulated to assist decision makers in evaluating alternative plans for the integrated development of newly reclaimed lands.

The model analyzes important issues pertaining to the development of newly reclaimed sites such as:

The appropriate cropping pattern Saline water use for irrigation Intensive use of mechanization Land tenure structure

The model can also be used to answer important questions related to the establishment of new communities such as:

What is the number of created settlement opportunities? What is the required infrastructure? What are the energy needs for the community?

It is to be pointed out that the final choice of an adequate development plan for a region or a subregion is decided by the human decision maker after having carefully examined the model generated solutions.

REFERENCES

Bazaraa, M. S. & Bouzahar, A. (1981). A linear goal programming model for agricultural planning in developing economies with an illustration from the agricultural sector in Egypt. Management Science, 27 (4), 396413.


Cortes, A. (1980). Linear Multi-Objective Programming System--Program De- scription. IBM Madrid Scientific Center.

Day, Richard H. & Sparling, E. (1977). Optimization models in agricultural and resource economics. In: A survey of agricultural economics literature, Vol. 2. (Martin, U R. (Ed.)), University of Minnesota Press, Minneapolis.

E1-Kheshen, K. S. (1977). A survey of the use of linear programming in national planning. Paper prepared for Economics 216, University of California, Davis.

E1-Shishiny, H. (1983). A goal programming land use model for the Mediterranean desert ecosystems of Egypt. Egyptian Journal for Operations Research and Applied Statistics, 9 (1), 59-78.

El-Shishiny, H. & Attia, B. (1985). Multi-objective modelling for the planning and management of 'New Lands' in Egypt. A case study. In Proceedings of the IFA C Conference on Systems Analysis Applied to Water and Related Land Resources, Lisbon, Portugal, 2-4 October.

Ignizio, J. P. (1976). Goalprogramming and extensions, D. C. Heath and Company, Lexington, Massachusetts.

Lee, G. E. (1972). The use of linear programming in national models of agriculture decisions. Canadian Department of Agriculture Publications, Vol. 72/9.

Lee, Sang M. (1972). Goal programming for decision analysis, Philadelphia, Auerbach Publishers.

Romero, Carlos (1986). A survey of generalized goal programming (1970-1982). European Journal of Operational Research, 25, 183-91.

Wheeler, B. M. & Russel, J. R. M. (1977). Goal programming and agricultural planning. Operations Research Quarterly, 28 (l), 21-32.

Zanakis, Stelios, H. & Gupta, Sushil K. (1985). A categorized bibliographic survey of goal programming. Omega, 13 (3), 167-73.

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A goal programming model for planning the development of newly reclaimed lands