Optimal policy and stability regions for the single product periodic review inventory problem, with stationary demands

In this paper we present rules concerning the optimal policy and stability regions for the single product periodic review inventory problem with stationary demands, over a finite horizon. The key parameter to the whole study is the Lot-Sizing Index (LSI) introduced by Blackburn and Millen. Two algorithms are presented. The first one constructs stability regions which are expressed as intervals of the LSI parameter, covering the whole range of its values. The proposed algorithm is very simple to understand and implement, and most importantly, it provides a solution table which can be used by the decision maker to easily determine the optimal policy for any problem with a given horizon and any possible combination of its cost parameters, namely any LSI value. The second proposed algorithm determines the optimal policy for any given LSI value; it constitutes a completely different approach to that of the Wagner–Whitin algorithm and requires very little computational effort.