Scheduling unrelated parallel machine problem with multi-mode processing times and batch delivery cost

In this study, the unrelated parallel machine scheduling problem where the processing time of jobs is controllable based on resource allocation is considered which the completed jobs are delivered in batches with unlimited batch capacity. A new mathematical model is presented for minimizing the total weighted penalties of tardiness and earliness, resource allocation, and batch delivery costs with idle time and machine elegibility constraints. Three developed metaheuristic algorithms including modified ant colony optimization (MACO) with multi-dimensional pheromone, genetic algorithm (GA) with improved operators and a hybrid algorithm based on hybridization of two the GA and MACO algorithms are proposed to solve the problem. Also, a heuristic and a dynamic programming algorithm are provided to insert idle time and to divide jobs into batches. Finally, the proposed methodologies are compared to each other, computational results shown that the hybrid algorithm could find solutions better than two other algorithms in relatively longer computation time.