Flexible job shop scheduling problem considering machine and order acceptance, transportation costs, and setup times

This paper, for the first time, studied a new extension of the flexible job shop scheduling problem by assuming the acceptance and rejection of machines and orders. The flexible job shop problem was extended to implement production without a factory in natural environments. Therefore, the mixed-integer linear programming (MILP) model was developed for this problem aiming to minimize total costs, including the fixed cost of machine selection, variable operational cost, transportation cost, and order rejection cost. Due to the high complexity of this problem, a heuristic algorithm was employed to find an acceptable solution. For algorithm performance evaluation, 40 samples were randomly generated and solved using the mathematical model and the proposed algorithm. The results of analyzing random samples showed a negligible error rate indicating algorithm efficiency.