Coordination of pricing and inventory replenishment decisions in a supply chain with multiple geographically dispersed retailers

We study the efficiency of a multi-stage supply chain controlled by a single decision-maker with the goal of maximizing the total profit per time unit for a single product by coordinating the purchasing of raw materials from an external supplier, manufacturing and shipping the product between consecutive stages, and determining the selling price and final demand for the product sold by multiple retailers. Retailers are geographically dispersed, control their own market areas, and differ in terms of operating costs and marketing strategies. Each retailer has a different price-sensitive demand function. In this study, we propose a mixed integer nonlinear programming model that maximizes the total profit per time unit, which includes the revenue of the final product, echelon holding costs, and fixed costs for ordering and shipping items at each stage and at each retailer location. Using a numerical example, we show that the model with varying selling prices at the retailers yields higher profits than the model with the same selling price across all the retailers. We also perform an analysis comparing the coordinated approach versus the sequential approach for pricing and inventory replenishment decisions by varying the market size and demand function parameters. The results show that, as the market size parameter decreases, the coordinated approach yields a higher profit than the sequential approach does. Additionally, given a constant market size setting, the results show that pricing and inventory replenishment decisions are very sensitive to the demand function parameters. The analysis also shows that the coordinated approach yields an average profit gain of 24.18% compared to the profit of 3.53% yielded by the sequential approach. Similarly, it is shown that the coordinated approach always yields a better profit than the sequential approach across all scenarios generated by varying the demand parameters. Moreover, we propose a Simulated Annealing (SA) algorithm to obtain near-optimal solutions in a timely manner. A computational comparison shows that the average solution reached by the proposed SA algorithm is at 0.04% from the optimal solution.