Handbook of EOQ Inventory Problems pp 79-119 | Cite as

# Generalizing the Ordering Cost and Holding-Backlog Cost Rate Functions in EOQ-Type Inventory Models

## Abstract

In this chapter, we discuss generalizations of the ordering, inventory holding, and backlog costs in EOQ-type models. We solve nested optimization problems to determine the optimal \((S,T)\) inventory policy with \(S\) denoting the order-up-to level and \(T\) the cycle length. In addition, we characterize the order quantity, maximum backlog, and fill rate for the optimal policy and study the sensitivity of these optimal values with respect to model parameters such as demand rate and opportunity cost rate. We also identify the classes of ordering cost and holding-backlog cost rate functions for which the considered optimization problem reduces to a convex minimization problem. For more general cost functions, this optimization problem is related to a global optimization problem. For such cases, using our structural results for convex problems, we generate lower and upper bounds on the optimal cycle length \(T\), and illustrate how this can be used to construct efficient computational algorithms to determine the optimal \((S,T)\) policy.

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