Makespan minimization in flowshop batch processing problem with different batch compositions on machines

In this research, we consider the flowshop batch processing problem (FBPP) with minimization of makespan, in which the composition of batches can change on different machines. A batch capacity of a machine restricts not only the maximum number of jobs, but also the total attribute size of jobs assigned to the batch processed on the machine. This is the first time that the FBPP is considered for different batch compositions on machines with respect to both the total size and the number of jobs assigned to batches. We propose a mixed-integer linear programming model for the research problem. Since this problem is shown to be NP-hard, several meta-heuristic algorithms based on particle swarm optimization (PSO), enhanced with local search structures, are proposed to solve the research problem heuristically. To have more diversity, different rules are implemented to generate the initial population of the PSO algorithms. Two lower bounding mechanisms are also proposed to generate good quality lower bounds for special cases of the research problem and, consequently, evaluate the performance of the proposed PSO algorithms. A data generation mechanism has been developed in a way that it fairly reflects the real industry requirements. The proposed PSO algorithms are examined by different numerical experiments and the results affirm the efficiency of the proposed algorithms.