Abstract
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.
Highlights
In classical inventory models, the demand whether deterministic or stochastic was often treated as an exogenous variable, without considering the effect of operating strategy
Marketing practitioners and researchers have noticed that in many practical cases the demand rate depends on the stock quantity displayed in the store as well as the sales price
Demand rate decreases with sales price yet increases with the stock quantity on display
Summary
The demand whether deterministic or stochastic was often treated as an exogenous variable, without considering the effect of operating strategy. Marketing practitioners and researchers have noticed that in many practical cases the demand rate depends on the stock quantity displayed in the store as well as the sales price. Demand rate decreases with sales price yet increases with the stock quantity on display. Extensive literature has focused on this phenomenon that demand rate depends on the stock quantity displayed in the store. Gupta and Vrat [2] first set up a model to look into this phenomenon where it was assumed that the demand rate was a function of initial stock level. Baker and Urban [3] developed an economic order quantity (EOQ) model with a power-form inventory-level-dependent demand rate, decreasing with the inventory level throughout the sales period. Datta and Pal [4] extended the model developed by Baker and
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