Order quantity and pricing decisions in linear cost inventory systems

Abstract

The primary concern of this study is to reveal the fundamental characteristics of the linear cost inventory model where price is a decision variable in addition to procurement quantity. In this context, the optimal solution must not only strike a balance between leftovers and shortages, but also simultaneously search for the best pricing alternative within the low price high demand and high price low demand tradeoff. To some extent, this problem has been studied in the literature. However, it seems that, there is a need to improve the model in order to understand the decision process better. To this end, optimal decisions must be characterised under a more general problem setting than it has been assumed in the existing models. In this study, we employ such a general model. The overall decision problem can be formulated under a dynamic programming structure. It follows that, the single period model is the basis of this periodic decision model. For this reason, we concentrate first on this problem. Having characterised the optimal solution to this basic model we extend the decision model to account for the multi-period setting. It is established with the results of this study that the decision problem in question is understood better. It is found that the characteristics of the optimal decision under the proposed model can be substantially different from the properties of the optimal solution of the corresponding classical model where there is no pricing decision. The primary reason for this is the fact that when there is a shortage in any period, the price that is set in this period could affect the future revenue which must be accounted in the overall decision problem. That is in a general model, price is an information which has an economic value that is transferred from one period to another just like transfering inventories or backlogs to future periods.