A Multi-Item Production Lot sizing Model with Stochastic Demand

Abstract

This paper presents a finite horizon Markov decision process model for determining the optimal production lot size (PLS) of multiple items with demand uncertainty. The model is formulated using states of a Markov chain that represent possible states of demand for items. Using weekly equal intervals, the decision of whether or not to produce additional units is made using dynamic programming over a finite period planning horizon. The proposed model demonstrates the existence of an optimal state-dependent production lot size as well as the corresponding production-inventory costs for items. A numerical example is taken to illustrate the solution procedure of the developed model.