LEXICOGRAPHIC GOAL PROGRAMMING APPROACH FOR THE OPTIMIZATION OF CROPPING PATTERN IN YASIN REGION GILGIT, PAKISTAN

Abstract

The prosperity of the agricultural sector is crucial not only for the national economy but also for regional development. For the purpose of agricultural planning and decision making, mathematical programming models are widely used. This paper aims to formulate, apply and evaluate a Lexicographic Goal Programming (LGP) model for the best allocation of land under cultivation for the major crops of central Yasin. It is an extension of the research work [1] which was conducted in this area to maximize the profit of the three crops using Linear Programming (LP). Using the LP model the target was achieved but all the land was allocated for alfalfa being the most beneficial crop among the three. But wheat is a basic need which must be cultivated to a specific amount. Considering this problem we extended the previous work by implementing the LGP approach to satisfy multiple goals such as the allocation of land for wheat, maximization of profit and minimization of capital in the agricultural activity. The LGP model is solved using the Simplex method. The LGP model provided the most satisfactory set of allocations possible and satisfied all three goals. It gave optimum profit of Rs.170003 and capital is minimized to Rs. 73687.678. Compared with the farmer’s plan, the profit of the LGP model increased by 49.39% but compared with the LP model, the profit decreased by 13.11%. Likewise, the total crop production expenditure increased by 4.97% and 1.39% respectively in comparison with the farmer’s plan and LP model.