Mathematical model proposals for multi-product double row facility layout problem with identical machines

Purpose: In this study, double row facility layout problem (DRFLP), which is a frequently used layout type in flexible manufacturing systems, is discussed. It is aimed to model and solve the DRFLP that takes into account the processing routes of products and the use of identical machines in a multi-product production environment. Theory and Methods: Firstly, a mixed-integer mathematical model that allows only forward movement of products was proposed for DRFLP in a multi-product production environment with different processing routes. Secondly, the problem was expanded with identical machines capable of performing the same operation. With the proposed model, the products choose the alternative route that will enable them to move a shorter distance during their forward movement. Results: Randomly generated test problems were used to evaluate the proposed mathematical models and solved using GUROBI 8.1 solver with MATLAB R2018b. Optimal solutions were obtained for instances up to the size of 8 products and 25 machines in the first problem. For the second problem with identical machines, instances up to the size of 3 products, 20 machines, and 2 identical machine groups were solved optimally. The optimality gaps reached within a time limit were reported for larger problems. Conclusion: This study discusses the effect of multiple processing routes and using identical machines on the arrangement of machines in DRFLP. It can be said that adding identical machines to the problem increases the complexity of the model. On the other hand, the large number of identical machines provides route flexibility in a multi-product environment with multiple flow-lines. However, a trade-off arises due to the high initial investment costs of the machines.