A variant SDDP approach for periodic-review approximately optimal pricing of a slow-moving a item in a duopoly under price protection with end-of-life return and retail fixed markdown policy

Abstract

In this paper, we examine a selling environment where a manufacturer-controlled retailer and an independent retailer sell a slow-moving A item. The manufacturer offers the independent retailer a price protection contract stipulating that the manufacturer reimburses the independent retailer in case of a reduction in the wholesale price. The price set by the independent retailer is assumed to be determined by Retail Fixed Markdown (RFM) policy. The manufacturer also offers the independent retailer a special discount rate for the replenishment orders and the retailers are assumed to follow (R, S) inventory replenishment policy. The manufacturer adopts a periodic-review pricing strategy and the mean demand observed by each retailer in a given period depends on the prices. We also take the customers choosing no-purchase option into account. We employ multinomial logit (MNL) models to forecast customers’ preferences based on retail prices. The retailers’ market shares are estimated by customized choice probability functions. We propose stochastic programming models to determine the manufacturer’s pricing strategy. Then, we propose a variant Stochastic Dual Dynamic Programming (SDDP) algorithm to determine the manufacturer’s approximately optimal pricing strategy by getting around three curses of dimensionality. Then, we move on to the observations on the impact of four critically important contractual parameters on the price, the market shares and the expected total net profits and finally discuss some possible approaches for the selection of the best compromise values of those contractual parameters.