Joint optimization of pricing and inventory control for dual-channel problem under stochastic demand

We consider an optimization problem for a dual-channel supply chain with one manufacturer and one retailer under stochastic demand. The manufacturer and retailer play a Stackelberg game. The manufacturer, acting as the leader, decides the total inventory capacity, wholesale price and selling price in the direct channel. The retailer, acting as the follower, decides the order quantity and retail price in the traditional channel. By solving the optimization problem, we find that given the selling price in the direct channel and wholesale price, the retailer's decisions on order quantity is similar to that for the newsvendor problem. Meanwhile, the manufacturer's decision on the inventory allocated to the direct channel also has the similar structure. Besides, we show that in our analysis framework, the retail price in the traditional channel, wholesale price and total inventory capacity can be presented in closed-forms. Finally, we numerically study the effects of the demand uncertainties and price sensitivities on the optimal solutions and performance. It is interesting to show that the retailer's expected profit may be unexpectedly increased when the demand variability in the traditional channel increases, due to the competition between two channels.