Logic-based Benders decomposition for integrated order acceptance, distributed heterogeneous factories, inventory, and hub-spoke delivery scheduling under make-to-order products

This article investigates an integrated production and distribution scheduling problem considering order acceptance (OA-IPDS) with committed delivery dates. It integrates order acceptance, distributed heterogeneous factories, inventory, and a hub-spoke delivery network within a complex system for producing customised orders, aiming to minimize total operating costs, including rejection, production, transportation, inventory, and overdue costs. Accepted orders are split into jobs and then enter the production system. Completed jobs are transported from factories to service centers, and then orders with all their jobs arrive and are delivered from service centers to customers. A mixed integer programming model is formulated and further enhanced by a proposed dominance rule, for which a logic-based Benders decomposition (LBBD) method and a branch-and-check search framework are also developed. The proposed LBBD method divides the problem into the master problem of order acceptance and job assignment and the subproblem of production and distribution scheduling. A hybrid algorithm, TS_LBBD, integrating tabu search and the LBBD method, is also proposed to further enhance computational performance. Extensive computational experiments demonstrate that the proposed algorithm can generate optimal or near-optimal solutions efficiently and validate the OA-IPDS model, analyze the sensitivity of key cost factors, and provide valuable managerial insights for practitioners.