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Optimizing Service Parts Inventory in a Multiechelon, Multi-Item Supply Chain with Time-Based Customer Service-Level Agreements

School of Business, University of Wisconsin, Madison, Wisconsin 53706
School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853
School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853
School of Business, University of Wisconsin, Madison, Wisconsin 53706
kcaggiano{at}bus.wisc.edu
pj16{at}cornell.edu
muckstadt{at}orie.cornell.edu
jrappold{at}bus.wisc.edu

In the realm of service parts management, customer relationships are often established through service agreements that extend over months or years. These agreements typically apply to a piece of equipment that the customer has purchased, and they specify the type and timing of service that will be provided. If a customer operates in multiple locations, service agreements may cover several pieces of equipment at several locations. In this paper, we describe a continuous-review inventory model for a multi-item, multiechelon service parts distribution system in which time-based service-level requirements exist. Our goal is to determine base-stock levels for all items at all locations so that the service-level requirements are met at minimum investment. We derive exact time-based fill-rate expressions for each item within its distribution channel, as well as approximate expressions for the gradients of these fill-rate functions. Using these results, we develop an intelligent greedy algorithm that can be used to find near-optimal solutions to large-scale problems quickly, as well as a Lagrangian-based approach that provides both near-optimal solutions and good lower bounds with increased computational effort. We demonstrate the effectiveness and scalability of these algorithms on three example problems.

Subject classifications: inventory/production; multiechelon; multi-item; service-level constraints; heuristics.
History: Received December 2001; revision received July 2005; accepted February 2006.