Linear programming with iterative modification of the objective function and restraints vector

Abstract

Development of land resources poses many problems for the planning agency. From the viewpoint of the economist perhaps the most important problems are those relating to the desirability of a project in terms of some income or efficiency objective. Typically, a project objective is stated as the maximization of individual, regional, or national income depending upon the jurisdiction of the developing organization. To effectively evaluate a land development, in terms of its objectives, it is necessary to anticipate the pattern of land use that will likely result in the project area. This study presents a quantitative approach for estimating land use patterns when use of the project land is restricted to agriculture. Planning problems concerned with agricultural as compared to non-agricultural uses, project financing, conditions of repayment, and form of tenure are ignored. The empirical application of the estimating procedure consists of estimating land use patterns for a project currently being undertaken by the State of Hawaii. Objectives: The primary objective is to develop a procedure for estimating the perfect competition equilibrium production of several crops, on lands of varying quality, in spatially separated producing areas. Market supply and demand equations are include in the model so that the patterns of land use will be established by market forces. The model indicates, by physical land productivity class and project area, the acreage used to produce each crop. It also gives the equilibrium market price and quantity supplied for each included commodity. The objective of the empirical applications of the model was to estimate patterns of land use based on different wage rate, labor availability, and unit size assumptions for several tracts of state-owned land that are included in a current development project. These lands, which are located at Waimanalo and Waianae Kai on the Island of Oahu and at Hoolehua on the Island of Molokai, make up the three project areas considered in this study. Procedure: The first step was to construct cost of production and yield budgets, by land productivity class, for a group of crops that represent most of the production alternatives faced by prospective farmers in the project areas. These budgets are based upon existing cost of production studies supplemented by interviews with crop specialists. Because of limited resources, only those crops for Which cost studies are presently available are included in the analysis. This group of crops includes pineapple, pasture, papaya, apple banana, tomatoes, snap-beans, cantaloupe and Manoa lettuce. Market supply and demand functions were developed for each crop and included in the estimating model. This was done in an effort to duplicate the market forces that actually contribute to the establishment of a land use pattern. For the purposes of this analysis, it is assumed that all vegetable crop production will be sold on the Honolulu market. This market restriction is imposed because producers will not export until the Honolulu market price falls to a point Where export offers the most profitable outlet. This price would probably be somewhat lower than the West Coast price less transportation charges. Available information suggests that under prevailing management practices, which are assumed, this price would not be sufficient to cover production costs (39; 49, p. 11). The estimating model is an iterative linear programming system that allows for adjustments in supply from existing producers as price changes and does not permit production to exceed quantity demanded at any given price. This model constructs a static equilibrium for a specified number of crops while allowing them to compete with one another for scarce resources as they would in the market. The scarce resources are allocated to their most profitable use.