Mixed integer programming approaches to partial disassembly line balancing and sequencing problem

•A partial disassembly line balancing and sequencing problem is considered.•A mixed integer programming (MIP) model and valid inequalities are proposed.•The MIP model is able solve the problems with up to 30 disassembly tasks.•MIP-based approach is proposed to obtain good solutions for large-sized problems. Product recovery has received greater attention in recent years mainly due to increased environmental awareness of consumers and stricter environmental regulations imposed by governments. In product recovery, disassembly of the product into its constituent parts is the most significant activity and generally performed on a disassembly line. During disassembly, a complete or partial disassembly of the product may be preferred. In complete disassembly, all parts must be disassembled, while partial disassembly allows to disassemble a subset of parts (e.g., the ones with relatively high revenues). This study deals with a partial disassembly line balancing and sequencing (PDLBS) problem considering revenues of parts to be disassembled, general workstation cost, additional cost of workstation(s) with hazardous parts, and cost of direction changes. For the PDLBS problem, a generic mixed integer programming (MIP) model, with the aim of maximizing total profit, is developed. To strengthen the MIP formulation, two sets of valid inequalities are proposed. The computational results show that the MIP model with valid inequalities is able to provide optimal solutions for the PDLBS problems with up to 30 tasks. To obtain near-optimal solutions for large-sized problems, a MIP-based solution approach is proposed. The proposed approach decomposes the entire MIP model into selection and assignment (SA) and sequencing (SEQ) models. The SA model is an exact relaxation of the MIP model (with valid inequalities) obtained by removing all the sequencing variables and constraints. Hence, SA model also produces an efficient upper bound for the PDLBS problem. The SEQ model, accordingly, aims to find an optimal sequence of tasks subject to the fixed selection and assignment of tasks provided by the SA model. The computational results show that the proposed MIP-based solution approach provides efficient solutions with small optimality gaps for large-sized problems.