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Abstract
Midu levd programming (MLP) technicpons are developed to solve decentralized planning problems with multiple deciaton makers in a hierarchical organization. There are cornunon features of multi level organization interactive decision-making units exist within predominantly hierarchical structure, execution of decisions is sequential, from upper to lower levels, each unit independently maximizes its own net benefits, but is affected by actions of other units drough externalities, the external effect on a decision maker’s problem can be reflected in both objective function and the set of feasible decisions. The basic concepts of multi level programming techniques are as follows an upper level decision maker sets his or her goal and/or decisions and then aske each subordinate level of the organization for their optima which are calculated in isolation, the lower-level decision makers’ decisions are then submitted and modified by the upper level decision maker with consideration of the overall benefit for the organization, and the process is continued until a satisfactory solution is reached. This decision making process is extremely practically such decentralized systems as agriculture, government policy, economic systems, warfare, transportation, network designs and is especially suitable for conflict resolution.
During the last four decades, many methodologies have been proposed to solve MLP problems. Most of these methods are based on concepts of vertex enumeration and transformation approaches. The former is to seek a compromise vertex by simplex algorithm based on adjusting higher-level control variables. It is rather inefficient, especially for larger size problems. Although there is a short cut, generality will be lost.