Logic-based Benders decomposition approaches for the distributed heterogeneous precast production scheduling problem with eligibility constraints and controllable processing times

Precast production scheduling is a critical component in the industrialized construction sector. This study addresses the Distributed Heterogeneous Precast Production Scheduling Problem with Eligibility Constraints and Controllable Processing Times (DHPPSP_ECCPT). The problem involves allocating production orders across multiple factories, adjusting processing times, and sequencing operations with the dual objectives of minimizing the makespan and the cost associated with processing time adjustments. To tackle this complex problem, we first present two Mixed-Integer Nonlinear Programming (MINLP) models. These models are subsequently linearized into Mixed-Integer Linear Programming (MILP) formulations to enhance tractability. In addition, a Constraint Programming (CP) model is proposed as an alternative modeling approach. Due to the complexity of the problem, particularly for large-scale instances, we develop a novel Logic-Based Benders Decomposition (LBBD) framework based on Manne-based models and problem structure. This framework integrates MINLP and CP to address the Assignment and Adjustment Master Problem (AAMP), and the Scheduling Subproblems (SSPs). To improve computational efficiency, we incorporate strong SSP relaxation-based inequalities into the AAMP within the LBBD framework. Furthermore, valid Benders optimality cuts are generated by solving the SSPs, thereby further strengthening the AAMP. We also propose a variant of the LBBD framework, termed Branch-and-Check (BCH), to address the DHPPSP_ECCPT. Moreover, the integration of the proposed position-based MINLP model with the LBBD framework enhances the robustness of the overall solution approach. Comprehensive computational experiments are conducted to evaluate the performance of the proposed LBBD methods. The results demonstrate their effectiveness and efficiency in solving the DHPPSP_ECCPT, offering valuable insights for prefabricated production scheduling as well as other production scheduling applications.