Permutation flow shop scheduling with order acceptance and weighted tardiness

In this paper we study the permutation flow shop scheduling problem with order acceptance and weighted tardiness (PFSS-OAWT) faced by firms that have a number of candidate orders to be selected and scheduled on a flow shop production line. The objective is to maximize the total net profit with weighted tardiness penalties. We formulate the PFSS-OAWT problem as an integer programming (IP) model. A heuristic algorithm named Simulated Annealing Based on Partial Optimization (SABPO) is developed for solving the IP model and obtaining near-optimal solutions. Computational studies are carried out on solving 160 problem instances with different scales (small, medium, large, and very large). The experimental results show that the SABPO algorithm exhibits good optimality for small-sized problems and robustness for medium/large-sized problems compared with benchmarks.