Emergency orders in the periodic-review inventory system with fixed ordering costs and stochastic lead times for normal orders

Abstract

This paper presents various periodic review policies for inventory control of a single item facing compound Poisson demand. Emergency orders are controlled by a reorder point policy with a target stock level, whereas normal orders are issued according to a reorder point policy with a fixed order quantity. We assume that emergency orders have a short constant lead time and are more expensive than normal orders for which the extra lead time is specified as a stochastic multiple of the review period. In addition to variable and fixed costs for emergency orders and fixed costs for normal orders, our model includes linear holding and backlogging costs.Pure policies issuing either emergency orders or normal orders are used for benchmarking and initialization purposes of two combined policies, OPT and SIMP, which allow at most one normal order with remaining lead time longer than the lead time for emergency orders. The combined policies are computed by applying Markov decision models and, for some model-exogenous control variables, neighborhood search. The numerical study shows a large potential for cost improvement from using normal orders and emergency orders in combination. The relative cost increase of the new SIMP compared with the previously studied OPT is often about 1%. Because SIMP is easier than OPT to administer and explain, it is more appropriate than OPT for practical applications.