Linear Goal Programming Model Research Articles

A Linear Goal Programming Model for Planning the Exports of Emerging Countries

A linear goal programming model for planning the exports of emerging countries is formulated in this paper. The model includes some economic factors which may affect the exports, e.g. industrial structure, labour force, value added in exports, capital efficiency, imports of raw material used for manufacturing goods designated for exports, investment plan, etc. An illustrative example is presented. A sensitivity analysis was performed in order to examine the effect of various changes made in the model on the results. It is felt that the model presented in this study would be useful to economic planners in emerging countries.

A Linear Goal Programming Model for Planning the Exports of Emerging Countries

A Linear Goal Programming Model for Planning the Exports of Emerging Countries

Duality and transformations in multiphase and sequential linear goal programming

We consider herein a specific type of goal programming model, namely the lexicogrpahic linear goal programming model. Although the two most common methods of solution, the sequential process and the multiphase process, produce the same solutions, the interiors of the final tableaus will differ. We present algorithms which allow one to transform the sequential tableau into the multiphase tableau and vice versa and, in doing so, demonstrate the respective mathematical duals and their relationships. These results are particularly important when performing sensitivity analysis.

A Linear Goal Programming Model for Developing Economies with an Illustration from the Agricultural Sector in Egypt

In this study we formulate a multi-regional single time period linear goal programming model for agricultural planning in a developing economy. In addition to specifying different levels of input and output for each activity, we describe explicit crop interdependencies which account for rotational requirements. Constraints are developed for land, labor, water, machinery, fertilizer, and capital resources. Economic aspects are addressed through the use of different production functions and the incorporation of several objectives. This last point marks a departure from conventional models which stress maximization of “economic welfare” defined as efficiency through maximum social product without consideration for income distribution. The emphasis on income distribution is reflected in our model in delineation of regional employment goals. In addition, foreign exchange expenditures and regional demand satisfaction goals reflect the importance of limiting foreign trade deficit and providing basic nutrition for the population. The decisions suggested by the solution include acreage allocated to different crops, sequences of crop rotations, fertilization levels, and transportation and distribution of crops and livestock among the regions. We illustrate the model using data from the agricultural regions with three cropping seasons: winter, summer, and nili (autumn). The activities covered by the model consist of ten winter crops, seven summer crops, three nili crops, two permanent crops, two pasture types, four livestock types, and three types of fertilizers. The crops are modeled in sequences to minimize the detrimental effects of cotton. The results suggested by the model show the need for using improved farming techniques through labor-intensive means to obtain a relatively higher degree of specialization and a relatively lower cotton production. This latter conclusion confirms that reached by an independent study of the U.S. Agency for International Development and the Ministry of Agriculture in Egypt. Several computer runs are conducted to test sensitivity of the results to major assumptions and goal targets. It is felt that the model presented in this study would be useful to management scientists, agricultural planners, especially those in developing countries, and to various United Nations organizations such as the International Bank for Reconstruction and Development.