段取費用を考慮した生産計画問題に対するラグランジュ緩和アプローチ

概要

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This paper presents an approach to solving a production planning problem formulated in a mixed integer programming problem where integer variables represent the setup of each product on each period. The production planning objective is to minimize the sum of inventory, setup, and overtime costs over the planning horizon while satisfying individual product demands within the limited production capacity. After a reformulation of the problem, we divide the original problem into a capacity planning problem and a lot size planning problem by incorporating inventory consistency relationships of the two problems into an objective function with Lagrangean multipliers. By solving the two problems iteratively, we can obtain lower and upper bounds of the original problem as well as feasible solutions. Our approach produces the best feasible solutions within a 5 % difference from the lower bounds for about 78 % of 108 test problems. Performance of the approach is enhanced under the conditions of low setup costs, many products, and low demand fluctuation.
一般社団法人日本機械学会の論文
1991-11-25