Turnpike policies for periodic review inventory model with emergency orders

This paper presents a periodic review capacitated lot sizing model with limited backlogging and a possibility of emergency orders. The main intention of placing emergency orders is to satisfy the demand as soon as a shortage occurs. It is assumed that the demands are independently distributed in successive periods. There are two resupply modes available: a regular mode and an emergency mode. Hence, no lead-time of emergence orders is assumed, the purchase price could be high. The measure of effectiveness is the total (or average per period) expected cost, which includes holding cost, shortage cost and both types of order costs. The minimum cost is obtained by considering this system as a discrete-time Markov decision process. We use this model to describe a simple and efficient value function algorithm for finding optimal policies. We find propositions on specially structured optimal policies generalizing classical results on (s,S) policies. Some connections of the turnpike policies and optimal infinite policies are presented. Computational results are given through numerical examples.