A flexible job shop cell scheduling with sequence-dependent family setup times and intercellular transportation times using conic scalarization method

In this paper, we propose novel mathematical models involving both single- and biobjective functions that deal with a flexible job shop scheduling problem in cellular manufacturing environment by taking into consideration exceptional parts, intercellular moves, intercellular transportation times, sequence-dependent family setup times, and recirculation. The problem has been known as NP-hard. The proposed models have been tested and solved using Lingo 11.0 with minimization of makespan for the problems involving about 4 cells, 4 part families, 15 parts, and 12 machines. The most suitable model among the proposed single-objective models is determined using the test results. Then, another objective function as total tardiness is added to this model. The obtained biobjective model is solved using the scalarization methods, the weighted sum method, e-constraint method, and conic scalarization method (CSM), in order to convert the mathematical model's objectives into a single-objective function. By utilizing these scalarization methods, the Pareto effective solutions are generated for a specific test problem. The advantages of the CSM are demonstrated by considering the Pareto effective solutions.