With Newsvendor Problem (NvP) we refer to a specific class of inventory management problems, valid for a single item with stochastic demand over a single period. In the standard version, the newsvendor is allowed to issue a single order, before he or she can observe the actual demand. Since the newsvendor can face both overage and underage costs, due to lost sales or residual stock, the objective is to define the optimal order size that maximizes the expected profit. In this paper, we consider a specific version of the NvP, in which the buyer has the opportunity to make a last and single order for opportunistic reasons. Specifically, we consider discontinued, collectible items, for which demand will not vanish and whose value might appreciate. Hence, the objective is to define the optimal quantity that should be purchased, just before the item is retired from the market or sold-out, and that should be sold as soon as the price rises over a predefined target level. An optimal solution, maximizing the expected profit, is obtained both in case of negligible and non-negligible stockholding costs. In the latter case, to obtain the optimal solution in implicit form, some simplifying assumptions are needed. Hence, a thorough numerical analysis is finally performed, as a way to empirically demonstrate both the robustness and the accuracy of the model, in several scenarios differentiated in terms of costs and customers’ demand.

Trade credit is the most succeeding economic phenomenon which is used by the supplier for encouraging the retailers to buy more quantity. In this article, a mathematical model with stock dependent demand and deterioration is developed to investigate the retailer’s optimal inventory policy under the scheme of permissible delay in payment. It is assumed that defective items are produced during the production process and delay period is progressive. The objective is to minimize the total average cost of the system. To exemplify hypothesis of the proposed model numerical examples and sensitivity analysis are provided. Finally, the convexities of the cost functions and the effects of changing parameters are represented through the graphs.

Determining the optimal inventory control and selling price for deteriorating items is of great significance. In this paper, a joint pricing and inventory control model for deteriorating items with price- and time-dependent demand rate and time-dependent deteriorating rate with partial backlogging is considered. The objective is to determine the optimal price, the replenishment time, and economic order quantity such that the total profit per unit time is maximized. After modeling the problem, an algorithm is proposed to solve the resulted problem. We also prove that the problem statement is concave function and the optimal solution is indeed global.