Optimization of Economic Production Quantity and Profits under Markovian Demand

Abstract--- In most manufacturing industries; demand uncertainty affects effective planning and control of production levels that maximize profits. In this paper, a new mathematical model is developed to optimize economic production quantity (EPQ) of a single-item, finite horizon, periodic review inventory problem with Markovian demand. In this model, sales price and inventory replenishment periods are uniformly fixed over the planning horizon. Adopting a Markov decision process approach, the states of a Markov chain represent possible states of demand for the inventory item. The production cost, holding cost, shortage cost and sales price are combined with demand and inventory positions to generate the profit for the decision problem. The objective is to determine in each period of the planning horizon an optimal economic production quantity so that the long run profits are maximized for a given state of demand. Using weekly equal intervals, the decisions of how much to produce are made using dynamic programming over a finite period planning horizon. A numerical example demonstrates the existence of an optimal state-dependent economic production quantity as well as the corresponding profits of item