The models we present in this chapter are related to two classical inventory models: The EOQ model of Harris (1913) and the dynamic lot size model of Wagner and Whitin (1958). In relation to the EOQ model, our models depart in three different ways: (1) the EOQ model assumes that the problem...

Inventory control is among the most important topics in operations research because of large investments in inventory and their effect on the profitability of the firms. A systematic analysis of inventory problems began with the development of the classical EOQ formula of Ford W. Harris in 1913,...

This paper considers an optimal control problem with two state variables for the dynamics of the Nerlove-Arrow advertising model. The optimal control is the rate of advertising expenditure required to maximize the present value of net profit streams over an infinite horizon subject to a...

We study infinite-horizon stochastic inventory problems with general demand distributions and piecewise linear concave ordering costs. Such costs arise in the important cases of quantity discounts or multiple suppliers. We consider the case of concave cost involving two linear segments. This...

We consider a stochastic multi-product inventory model with a ware-housing constraint with the objective of minimizing the expected long-run average cost. Using the vanishing discount approach, a dynamic programming equation and the corresponding verification result are established. The...

We propose a model where customers are classified into two groups: short lead-time customers who require the product immediately and long lead-time customers to whom the supplier may deliver either immediately or in the next cycle. Unmet orders are backlogged with associated costs. Specifically,...

We study a firm's optimal transshipment problem considering the impacts of setup costs for transshipment and demand distribution shapes. We assume that the demand follows a three-point distribution, which changes from a degenerate distribution, to a unimodal distribution, and to a bimodal...

This article analyzes a discrete time lost sales inventory system with partially observed demand and unobserved shrinkages which happen both before and after the demand realization. When the demand exceeds the remaining inventory, the unmet demand is lost and unobserved. This problem in general...

This entry is a brief survey of classical inventory models and their extensions in several directions such as world-driven demands, presence of forecast updates, multi-delivery modes and advanced demand information, incomplete inventory information, and decentralized inventory control in the...

This paper investigates a decentralized assembly system that consists of one manufacturer and multiple suppliers who produce the complementary components. In a single selling season, the manufacturer initially sets a vendor inventory liability period (VILP) to control the suppliers' delivery...