Optimal pricing and replenishment policies when consumer demand depends on the in-store inventory level

The paper studies an optimal control problem of pricing and inventory replenishment in a system with sequential inventories. Consumer demand for a specific product depends on price as well as the in-store stock of the product. The hypothesis is that for some consumer products, a large volume of displayed goods leads consumers to buy more than if the stock is small. In addition to the displayed stock, there is an inventory of the product in a central warehouse. We consider a setup in which management of the two stocks is decentralized such that pricing decisions are made by the store manager who also decides on the level of in-store inventory. The manager of the warehouse makes replenishment decisions about the stock in the warehouse. We also study the problem where decisions are centralized and investigate the policy impacts of having a stock-dependent demand. Phase diagrams and a synthesizing procedure are used to derive optimal inventory, replenishment, and retail price policies.