Optimizing service parts inventory in a multiechelon, multi-item supply chain with time-based customer service-level agreements

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.