Two-stage stochastic capacitated Lot-Sizing problem by Lot-Size adaptation approach

In this paper, a two-stage stochastic capacitated lot-sizing problem with random demand, and service level constraints  under static and static-dynamic uncertainty strategies is introduced. A static strategy determines the setup period and lot sizing at the beginning of planning period, whereas a static-dynamic strategy allows the lot size to be adjusted during  the planning period. A new model formulation of the demand differential adjustment policy in a multi-stage production system is proposed. Lot-sizing adjustments depend on the difference in demand between actual and expected demand. To quantify the economics of our uncertainty strategy for multi-level lot size the problems, the number of test instances with different parameter settings is evaluated. Computational experiments show that the additional costs of semifinished products, and the lack of storage capacity in the downstream processes reduce the potential for cost savings via multi-volume reform. Also a robust model is developed and as the robust model under study is NP-hard, it solved by a hybrid heuristic using the proposed stochastic model, a robust model is developed, which is solved by a hybrid heuristic  algorithm based on Lagrangian relaxation and Bender’s decomposition algorithms. To evaluate the convergence rate and solution quality, the method is applied to some random test instances generated in the literature. The computational results indicate that the proposed method is capable of efficiently solving the model.