A Markov decision model for optimising economic production lot size under stochastic demand

Abstract

Traditional approaches towards determining the economic production lot (EPL) size in manufacturing applications assume deterministic demand, often at a constant rate. In this paper, an optimisation model is developed for determining the EPL size that minimises production and inventory costs of a periodic review production-inventory system under stochastic demand. Adopting such a Markov decision process approach, the states of a Markov chain represent possible states of demand. The decision of whether or not to produce additional inventory units is made using dynamic programming. This approach demonstrates the existence of an optimal state-dependent EPL size, and produces an optimal lot sizing policy, as well as the corresponding total production and inventory costs.