Linear Three-level Programming Problem With The Application To Hierarchical Organizations

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In many decision processes there is an hierarchy of decision-makers and deci-rnsions are taken at di®erent levels in this hierarchy. The decentralized planningrnproblem has long been recognized as an important decision-making problem.rnIn many practical decision making activities, decision making structure hasrnchanged in the last few decades, from a single person (or decision maker) andrnsingle criterion (or constraint factor) to multi-person (or decision maker) andrnmulti-criteria and even to hierarchical (or multi-level) situations. In any or-rnganization with hierarchical decision systems, the sequential and preemptivernnature of the decision process makes the problem of making an optimal de-rncision, and it is di®erent from the usual operations research methods.rnIn hierarchical decision process decision-makers are often arranged within arnhierarchical administrative structure, each with his/her objective (perhapsrncon°icting). A planner at one level of the hierarchy may have an objec-rntive and a set of feasible decision space determined, in part, by other levels.rnHowever, his control instruments may allow him/her to in°uence the policiesrnat other levels and in this manner improve his/her own objective function.rnTherefore a multilevel programming problem approach is developed for mod-rnelling such type of decentralized planning problems.rnA multilevel programming problem is a nested optimization problem over arnsingle feasible region. This approach partitions control of the decision vari-rnables among several decision makers,in the hierarchy. Each decision-maker inrnthe hierarchy acting in a sequence to maximize his/her own objective func-rntion. These decision-makers interact through a set of corporate" constraintsrninvolving the decision variables of all divisions. The general structure of thernmultilevel programming problem method will be discussed in detail and wernwill focus on three level linear programming problems.

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Linear Three-level Programming Problem With The Application To Hierarchical Organizations

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