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Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand. (English) Zbl 1336.49048
Summary: 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 maximization, an optimization problem is addressed to seek for the optimal joint dynamic pricing and replenishment policy which is obtained by solving the optimization 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.

##### MSC:
 49N90 Applications of optimal control and differential games 49K15 Optimality conditions for problems involving ordinary differential equations 49M05 Numerical methods based on necessary conditions 90B05 Inventory, storage, reservoirs
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