Coordinating ordering, pricing and advertising policies for a supply chain with random demand and two production modes

This paper discusses production and order as well as advertising coordination issues for a single-manufacturer single-buyer supply chain. In the two-echelon system, the manufacturer sells a newsvendor-type product through the buyer who faces a random demand depending on advertising expenditure and selling price. Before the start of the selling period, the buyer needs to determine how much she should invest in advertising, how many units of products she should order from the manufacturer and at what price she should sell the ordered products. At the end of the selling period, when the revealed demand exceeds stock on hand, all the superfluous demand is met by a second order from the manufacturer, if unfilled customers are offered a discount in selling price. Based on the buyer's first order, the manufacturer needs to select his initial production quantity under a relatively cheap but long lead-time production mode, and responds to the buyer's second order with an expensive but quick-response production mode (if necessary). Under both the centralized and decentralized setting, we formulate mathematical models of how two members make their decisions, respectively, and provide the closed-form solution to each model. In order to achieve perfect coordination of the supply chain, we propose an improved sales rebate contract, which can arbitrarily allocate the profit between two parties. Finally, we implement a numerical study to illustrate the models.