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 order-up-to level S and cycle length T values that characterize optimal (S, T ) inventory policies. Using these, we characterize the order quantity, maximum backlog and fill rate in the optimal solution. We also study the sensitivity of these optimal values with respect to model parameters demand rate and opportunity cost rate. We present structural results for certain classes of ordering cost and holding-backlog cost rate functions that yield to a convex optimization problem. More general cost functions require the solution of a global optimization problem. For such cases, using our structural results, we generate lower and upper bounds on the optimal T. We illustrate how these bounds can be used to construct efficient computational algorithms to determine the optimal cycle length.