Capacitated Multi-Item Multi-Echelon Lot Sizing with Setup Carry-Over Under Uncertain Demand

This study focuses on the lot sizing problem with setup carry-over in multi-item multi-echelon capacitated production systems under uncertain customer demand. We investigate budget-uncertainty robust optimization and scenario-based stochastic programming, to address the uncertainty in customer demand. Three modeling strategies are proposed within the stochastic programming framework, exploring different decision stages for setup carry-over and production quantities. In our examination of the robust model, we explore different robustness parameters, specifically the uncertainty budget and the variation interval. Extensive numerical experiments are conducted to compare the average and worst case performance of the models on out-of-sample scenarios. We fit conditional inference trees to the evaluation results and predict the suitability of robust and stochastic approaches for the test instances based on their problem characteristics. The findings provide valuable managerial insights, enabling decision makers to estimate the most appropriate modeling approach for their lot sizing problem at hand. Moreover they highlight the importance of choosing appropriate robustness parameters for robust optimization models and emphasize the value of flexibility in carry-over and quantity decisions. Lastly, we analyze the production plans obtained by lot sizing models with different levels of flexibility according to their solution structures and investigate the resulting changes in setup patterns