機械の種類を考慮した調理手順最適化の値範囲とbig-M法を用いた離接制約の比較

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  • Comparison of Disjunctive Constraints Using Integer Range and big-M Method for Food Preparation Scheduling Considering Machine Type

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Abstract

給食や病院食など，日々変わる献立で大量の調理をする施設では，時間内に業務をすべて終えるために，効率的な作業計画を立てることが重要である．しかし，現実の調理では様々な要素を考慮しなければならず，最適な作業計画を立てることは困難である．本研究では，調理業務効率化の支援を目標とし，調理手順最適化問題をFJSSPを応用した混合整数線形計画問題として定式化する．開発した数理モデルを利用すれば，専用ソルバーを開発することなく汎用ソルバーで容易に問題を解ける．さらに，制約と決定変数を削減するために，決定変数の値範囲を用いて離接制約を再定式化し，big-M法と比較する．

In a large food preparing facility that cooks a large amount of food with daily menus, it is important to make an efficient work plan to complete much work in time. However, because there are many factors, it is difficult to optimize food preparation in real situations. In this paper, for supporting the efficiency of work, we formulate a food preparation scheduling problem as a mixed integer linear programming problem by extension of FJSSP. By using the mathematical model, the problem can be easily solved with a general solver. We propose a method to reformulate disjunctive constraints using integer range of decision variables to reduce constraints and decision variables, and compare it with the big-M method.

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