Multi-objective Mathematical Modeling for Scheduling Machines in Parallel with Batch Processors

In this paper, the problem of scheduling the production of unrelated parallel machines to simultaneously minimize the goals of production time span, early and late fines, and the cost of purchasing machines is investigated, and a two-objective mathematical model is considered considering clearance and preparation times and limit capacity. Due to faster and cheaper operations with batch processors and increasing the efficiency of operating systems, all machines are batch processors. Initially, the model is coded and executed using the exact method in GAMS software. Due to the hard-NP nature and complex nature of the problem, a multi-objective meta-heuristic algorithm based on the coordination search method is proposed and designed. Then Taguchi method is used to find the best level for the algorithm parameters, and two examples of problems in different dimensions of tasks and machines are presented and solved by this proposed algorithm. The results of the calculations show the efficiency of this algorithm to generate more solutions at a much lower solution time.