Dissertation > Mathematical sciences and chemical > Mathematics > Operations Research > Planning Theory ( mathematical programming)

The Research on Uncertain Optimization Method of Production Planning Problem

Author ZhangFeng
Tutor WanZhong
School Central South University
Course Operational Research and Cybernetics
Keywords production planning uncertainty interval possibility degree credibility measure aggregate production planning problem generalizedproduction planning problem
CLC O221
Type Master's thesis
Year 2013
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Production planning problems have become a cross-disciplina--iy research field of operation research and applied mathematics, which have found an extensive application in economic management sciences, system engineering and energy market. Since there are some uncertainties in the actual production process, many scholars have begun to study the uncertain production planning problems and proposed a series of uncertain models and solution methods of production planning problems. In this thesis, based on the existent research achievements, it is intended to be studied that two types of uncertain production planning model and the derivation of their deterministic equivalent, and numerical examples show that the proposed model and method are validity and effective. The main contribution in this thesis is as follows:In the beginning, the thesis gives an introduction of some basic knowledge about production planning problems and analyzes the uncertainties in the process of production plan. Advancement and future research trends of the uncertain production planning problems are also summarized.In Chapter2, we introduce the theories and methods of uncertain optimization. In particular, the possibility degree method for the order of interval numbers and credibility measure methods for the order of fuzzy numbers. The two methods lay a solid theoretical foundation for the two types of uncertain optimization model of production planning problems and derivation method of deterministic equivalent.In Chapter3, we propose a new fuzzy programming model of aggregate production planning based on the theory of credibility measure, and gives a derivation of its deterministic equivalent. The case study shows the feasibility and necessity of the proposed model and method.In Chapter4, we consider the polymorphic uncertainty of the practical problems. Taking interval and fuzzy uncertainties into account, we construct a polymorphic uncertain linear programming model of a generalized production planning problem. A deterministic equivalent formulation for this model is derived based on the theory of fuzzy interval program and the modified possibility degree for the order of interval numbers and a robust optimal solution is obtained for the original problem by the standard smooth optimization techniques. The case study shows that the proposed polymorphic uncertain programming model is more realistic and significant.

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