Spare parts inventory routing problem with transshipment and substitutions under stochastic demands

Abstract

We study a two-level spare parts supply chain in which a manufacturer supplies a central warehouse (CW) with original equipment manufacturer (OEM) and replacement or pattern parts (PP). The CW, distantly located from the manufacturer, distributes both OEM parts and PP to a given number of depots facing stochastic demands. The demand for spare parts is intermittent, exhibiting an infrequent rate and extreme dispersal over time periods. Along with lateral transshipment, PP can be used as substitutes for the OEM parts to sidestep shortage at depots. Assuming that emergency shipments are significantly longer and more expensive, we aim at underlining the relative effectiveness of such a new spare parts inventory management policy. A mixed-integer linear programming model is proposed to solve the inventory routing problem with transshipment and substitution under stochastic demands. The objective is to minimise costs of holding inventory, transportation which includes regular shipment and transshipment, substitution and lost sales. To solve the problem, Sample Average Approximation method is used. Based on empirical goodness-of-fit tests, three demand patterns are studied: Poisson distribution, stuttering Poisson distribution and negative binomial distribution. The model is tested on well-known benchmark instances generated for multi-product multi-vehicle IRP. Computational experiments highlight the benefits of promoting transshipment and substitution on the overall supply chain performance. Results also suggest insights, which are of interest to professionals who are willing to develop new decision support models for the most efficient management of such items.