A hybrid genetic algorithm to solve a lot-sizing and scheduling problem

This paper reports a lot-sizing and scheduling problem, which minimizes inventory and backlog costs of multiple products on M parallel machines with sequence-dependent set-up times over T periods. Problem solutions are represented as product subsets (ordered or unordered) for each machine m at each period t. The optimal lot sizes are then determined applying a linear program. A genetic algorithm searches either over ordered or over unordered subsets (which are implicitly ordered using a fast ATSPtype heuristic) to try to identify an optimal solution. Initial computational results are presented, comparing the speed and solution quality of the ordered and unordered genetic algorithm approaches.