Pricing and lot-sizing policies for deteriorating items with partial backlogging under inflation

In this paper, we develop an inventory lot-size model for deteriorating items under inflation using a discounted cash flow (DCF) approach over a finite planning horizon. We allow not only a multivariate demand function of price and time but also partial backlogging. In addition, selling price is allowed for periodical upward and downward adjustments. The objective is to find the optimal lot size and periodic pricing strategies so that the net present value of total profit could be maximized. By using the properties derived from this paper and the Nelder–Mead algorithm, we provide a complete search procedure to find the optimal selling price, replenishment number and replenishment timing for the proposed model. At last, numerical examples are used to illustrate the algorithm.