This study models a joint pricing, inventory, and preservation decision-making problem for deteriorating items subject to stochastic demand and promotional effort. The generalized price-dependent stochastic demand, time proportional deterioration, and partial backlogging rates are used to model the inventory system. The objective is to find the optimal pricing, replenishment, and preservation technology investment strategies while maximizing the total profit per unit time. Based on the partial backlogging and lost sale cases, we first deduce the criterion for optimal replenishment schedules for any given price and technology investment cost. Second, we show that, respectively, total profit per time unit is concave function of price and preservation technology cost. At the end, some numerical examples and the results of a sensitivity analysis are used to illustrate the features of the proposed model.

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The problem of determining the optimal selling price and lot size for an inventory system with non-instantaneous deteriorating item is considered in this chapter. In order to provide general framework, the pricing and lot sizing problem is modeled assuming a general price and time dependent demand function. The model allows for backlogging of demand which is characterized by decreasing function of waiting time. As the problem involves revenue and costs, a natural objective function for the model is profit per period. First, the sub problem in which price is fixed is solved to determine the optimal inventory policy. To broaden the problem, a procedure is developed for obtaining the optimal selling price and order size. To investigate the characteristics of the proposed model, numerical illustrations are presented.

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