Symmetry in the Capacitated Lot Sizing Problem with Parallel Machines and Setup Carryover

Nowadays, industries have been dealing with high competitiveness and are looking for tools that allow them to be ahead of the competition. One of the tools that has been increasingly used is operational research, in the search for efficiency in the use of resources and cost minimization. The capacitated lot sizing problem with parallel machines involves determining optimal production quantities for different items to a set of parallel machines over a planning horizon, where each machine has limited capacity. Setup carryover refers to the possibility of transferring the configuration of a machine from one period to the next without additional costs, which generates greater flexibility in planning and can lead to considerable time and cost savings. Symmetry emerges as a critical aspect to be considered, as there can be several equivalent solutions due to parallel machines and setup carryover. This can cause difficulties to solving the problem, as traditional mathematical programming methods can waste time and resources by repeatedly exploring symmetric solutions. The objective of this work is to compare the benefits of adding setup carryover to the capacitated lot sizing problem with parallel machines and to introduce additional constraints that seek to reduce the symmetry present in the problem.