A local search enhanced logic-based Benders decomposition approach for order acceptance and scheduling problem with preemption

This paper addresses an order acceptance and scheduling problem (OAS) that incorporates the allowance for preemption. We introduce a novel continuous-time mixed-integer linear programming (MILP) formulation for the problem. Allowing preemption greatly increases the complexity of the MILP model by requiring a larger number of variables and constraints to sequence order parts, rather than merely orders. Consequently, the performance of the MILP formulation rapidly deteriorates as the problem size grows. To efficiently solve the problem, we propose an approach based on the logic-based Benders decomposition (LBBD). The preemptive Earliest Due Date (EDD) rule is utilized to efficiently solve the subproblem in LBBD. Additionally, a local search heuristic is developed to construct high-quality solutions based on the LBBD master problem solutions. This local search-enhanced LBBD approach (LS-LBBD) is capable of solving instances with up to 200 orders to optimality within 3600 s, achieving an average optimality gap of only 3.02% across 200-order instances with various parameters. The effectiveness of the local search heuristic has been validated by comparative experiments. For instances where the optimal solution was not obtained, the solutions from LS-LBBD were on average 6.57% better than those from the original LBBD.