Mathematical formulation and a hybrid evolution algorithm for solving an extended row facility layout problem of a dynamic manufacturing system

Abstract

• An extended row facility layout problem is investigated considering dynamic manufacturing environment. • Specific row layout changes over multiple periods and a mixed integer linear programming model is built for it. • A hybrid evolution approach combining linear programming and evolutionary operations is developed. • A special decoding approach for the extended row facility layout problem is designed. • Comparison with other methods indicates that the proposed algorithm achieves highly preferable results. In this study, a dynamic extended row facility layout problem is investigated where the dynamic manufacturing process is considered. This problem involves the rearrangement cost when the location of the department changes over adjacent periods and it is aimed at minimising the sum of total material handling and rearrangement costs. The specific number of rows in each period is not predetermined in this study. Based on the product processing in practice, the essential clearance between departments and floor boundaries is also considered when calculating relative positions and exact locations of departments. A mixed-integer linear programming model is established for this problem. A hybrid evolution algorithm (HEA) that combines the exhaustive pairwise swap and variation operations is proposed to resolve this problem. First, a decoding strategy is designed to represent the department sequence and the optimal exact locations are solved using the linear programming method. Second, an exhaustive pairwise swap operation is addressed to search for the neighbourhood space without repeated calculations. This operation terminates when all swap pairs run out or preferable solution is found. Therefore, the variation operation starts immediately to switch to a new neighbourhood space. The HEA is tested with many instances and its good performance has been proven by comparing its results with existing solutions of fixed-row, flexible-row facility layout problems, and results of exact approach (CPLEX).