Abstract
Traditionally, when optimizing base-stock levels in spare parts inventory systems, it is common to base the decisions either on a linear shortage cost or on a certain target fill rate. However, in many practical settings the shortage cost is a non-linear function of the customer waiting time. In particular, there may exist contracts between the spare parts provider and the customer, where the provider is obliged to pay a fixed penalty fee if the spare part is not delivered within a certain time window. We consider a two-echelon inventory system with one central warehouse and multiple local sites. Focusing on spare parts products, we assume continuous review base stock policies. We first consider a fixed backorder cost whenever a customer’s time in backorder exceeds a prescribed time limit, second a general non-linear backorder cost as a function of the customer waiting time, and third a time window service constraint. We show from a sustainability perspective how our model may be used for evaluating the expected hbox {CO}_2 emissions associated with not satisfying the customer demands on time. Finally, we generalize some known inventory models by deriving exact closed form expressions of inventory level distributions.
Highlights
Introduction and literature reviewIn many industries spare parts and aftersales in general are big business (Cohen et al 2006)
As mentioned in the introduction, our solution procedure can handle general non-linear backorder costs, we focus on exponentially increasing backorder costs as a function of the customer waiting time
We have presented an exact analysis of a two-echelon spare part inventory model with new types of backorder cost structures
Summary
In many industries spare parts and aftersales in general are big business (Cohen et al 2006). We extend the analysis of Graves (1985) and Axsäter (1990) by deriving closed form solutions of the probability distributions of the inventory levels and the customer waiting times. In our model we consider general non-linear backorder costs, and in particular piecewise constant backorder costs Another related stream of literature concerns lateral transshipments between warehouses, where a local warehouse with no stock on hand can request an item from another local warehouse if needed. When instead considering batch-ordering policies in multi-echelon inventory settings with time window service levels, the model complexity will increase considerably.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
