Integrated pricing and lot-sizing decision in a two-echelon supply chain with a finite production rate

In this paper, we consider a supply chain consisting of a supplier and a retailer selling the product manufactured by the supplier in a market, in which the demand for the product is decreasing in the price set by the retailer. Previous research on coordinating the supply chain with price-sensitive demand often assumes that either the supplier purchases the product or the supplier has an infinitely large production rate. We consider explicitly the supplier’s finite production rate in the pricing and lot-sizing decision, which causes the problem much more challenging. We first investigate the optimization problem in the decentralized scenario to find the optimal order quantity and selling price for the retailer as well as the optimal wholesale price and lot size multiplier for the supplier. We then solve the joint optimization problem in the centralized supply chain to find the optimal order quantity, the selling price, and the optimal lot size multiplier. We provide two sequential algorithms to solve the joint optimization problem. Computational experiments show that the algorithms are effective (all 448 tested problems are solved optimally) and efficient (it only takes a few iterations to converge for each tested problem). The supply chain coordination mechanism is then designed through an all-unit quantity discount policy and a franchise fee.