Solving a multi-level capacitated lot sizing problem with random demand via a fix-and-optimize heuristic

In supply chain management, the multi-level multi-product capacitated lot sizing problem (MLCLSP) plays a critical role in operational production systems, where limited resources and time phases are considered. In this paper, we present a stochastic version of MLCLSP subject to capacity constraints. In order to minimize the total expected cost of MLCLSP, a production schedule has to be determined for random demand and a new backlog-oriented δ-service-level measure should be met. We apply scenario method to approximate the stochastic MLCLSP and lead to a new MLCLSP-SCN model. For the purpose of determining production schedule efficiently, robustly and stably, a new heuristic called Fix-and-Optimize heuristic is presented handling random demand. A numerical analysis based on a set of artificial test instances is used to evaluate the relative performance of the heuristic. We further present the numerical results of dynamic programming approach and heuristic genetic algorithm as benchmarks. All the numerical study suggests that our heuristic provides high-quality solutions and the computational effort is moderate.