An iterated greedy algorithm for distributed flowshops with tardiness and rejection costs to maximize total profit

Distributed permutation flowshop scheduling problems (DPFSP) have become research hotspots. However, a DPFSP with tardiness and rejection costs (DPTR), which has important practical significance, has not yet been addressed. As manufacturers are most concerned about the maximization of the total profit, this study addresses the DPFSP to maximize the total profit. A mixed-integer linear programming model is used to describe the DPTR. An iterated greedy algorithm named IG_TR is proposed. IG_TR generates initial solutions using an improved NEH heuristic using four rules based on the deadline, due date, tardiness and rejection costs. For IG_TR, a dynamic number of jobs are removed from factories in the destruction phase. In the reconstruction phase, the removed jobs and those waiting to be processed are selected to be inserted into appropriate positions in the factories. Two local search methods are designed to improve the quality of solutions generated in the reconstruction phase. During the acceptance phase, a restart mechanism is proposed to avoid falling into local optimal. The experimental results of the component analysis demonstrate the effectiveness of IG_TR. Several comprehensive experiments show that IG_TR outperforms five related algorithms.