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An inventory system for perishable items with limited replenishment capacity is introduced in this paper. The demand rate depends on the stock quantity displayed in the store as well as the sales price. With the goal to realise profit maximisation, an optimisation problem is addressed to seek for the optimal joint dynamic pricing and replenishment policy which is obtained by solving the optimisation problem with Pontryagin's maximum principle. A joint mixed policy, in which the sales price is a static decision variable and the replenishment rate remains to be a dynamic decision variable, is presented to compare with the joint dynamic policy. Numerical results demonstrate the advantages of the joint dynamic one, and further show the effects of different system parameters on the optimal joint dynamic policy and the maximal total profit.

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This paper investigates a distribution channel consisting of a manufacturer and a retailer under a cooperative program, where the manufacturer determines the national advertising and quality improving effort, while the retailer decides the local promotion effort and may undertake parts of the costs of national advertising and quality improving of the manufacturer. It is assumed that the manufacturer's national advertising and quality improving efforts positively affect the brand goodwill and reference price, whereas the retailer's local promotion effort damages them. Three scenarios of the non-cooperative and cooperative scenarios in the decentralized supply chain, and the centralized supply chain scenario, are analyzed. The corresponding equilibrium strategies and profits are obtained and compared, which shows that the cooperative program can achieve payoff-Pareto-improving, but cannot coordinate completely the supply chain. Furthermore, a revenue sharing contract combined with two-subsidy policy is designed to coordinate the decentralized supply chain. Numerical simulation and sensitivity analysis of the coordinating results on the key system parameters are provided to verify the effectiveness of the contract, and some managerial insights are provided.