A column generation heuristic for simultaneous lot-sizing and scheduling problems with secondary resources and setup carryovers

This study introduces an innovative approach to address the Capacitated Lot-Sizing and Scheduling Problem with Sequence-Dependent Setups (CLSD), considering both the sequence-dependent setups and costs. Facing the challenge of large-scale instances, a Column Generation-based Neighbourhood Search (CGNS) algorithm is proposed, efficiently handling real-life CLSD scenarios with extensions like secondary resources and setup carryover and crossovers. The algorithm demonstrates superior performance compared to commercial solvers and fix and relax-based benchmark algorithms, producing high-quality solutions within specified time limits on large data sets. The study's contributions include a distinctive pattern and column structure in the proposed formulation, effectively managing the exponential increase in decision variables. Test instances and a real- life case study validate the algorithm's applicability to production systems under the CLSD and Capacitated Lot-Sizing Problem (CLSP) frameworks, making it a valuable tool for optimising simultaneous lot-sizing and scheduling challenges in practical settings.