Optimal dynamic production and price for reliability-dependent imperfect production with inventory-level-dependent demand in uncertain environment

Abstract

An inventory system for reliability-dependent imperfect production is introduced in uncertain environment. The demand rate depends on the stock quantity displayed in the store as well as the sales price. With the goal to realize profit maximization, an optimization problem is addressed to seek for the optimal joint dynamic pricing and production policy which are obtained by solving the optimization problem by Euler-Lagrange equation of optimal control theory. Here, initial selling price, holding cost, and raw material cost are taken as uncertain variables, and using uncertain expectation mathematics, the uncertain variables are converted into crisp value. The numerical results demonstrate the advantages of the joint dynamic one and further show the effects of different system parameters on the optimal dynamic policy and the maximal total profit.