An integrated pricing and inventory model for deteriorating products in a two-stage supply chain under replacement and shortage

In this paper, a two-stage supply chain, including a wholesaler and a retailer, is investigated, in which the retailer acts as a vendor and sells the products to the final customers. this chain only produces a single deteriorating product with constant deteriorating rate. in this chain, demand is deterministic, and lead time for replenishment and replacement of retailer's stock is considered to be zero. the objective of this study is to maximize total chain's profit by determining the optimal values of retailer's selling price (p) and order cycle length (t). since due to deterioration, a part of the initial stock is deteriorated, the retailer residuals recycle the deteriorated part and replace them with healthy product as needed instead. two scenarios with and without shortage assumptions are developed. finally, numerical examples are presented to show the applicability of the proposed models, and sensitivity analysis on some parameter's values is conducted.