Beta-Guaranteed Joint Service Levels
31 Pages Posted: 3 Jan 2016
Date Written: January 1, 2016
Abstract
Many inventory control problems require the satisfaction of service-level criteria such as order fill rate, line-item fill rate, and dollar fill rate that are joint across random customer orders consisting of products with correlated demands. This paper introduces a multi-product, joint service-level model for setting inventory targets subject to such criteria under multivariate demand uncertainty. Unlike the extant service-constrained inventory models meeting target service levels on average, we satisfy the target joint service level with a guaranteed probability of beta in every period. We do this by combining computationally tractable approximations for service-level constraints with simulation-based procedures that are easy to implement. Numerical analysis demonstrates the effectiveness of our procedures in comparison to the widely-used heuristics, and provides new insights on managing multi-product inventory with a probabilistic guarantee on joint service-level satisfaction. In particular, as the number of products in the system increases, the beta-guaranteed solution consistently delivers the target service level with only a small percent increase in cost in comparison to the satisfaction of the target service level on average. We further consider positively correlated demands, incomplete orders, and customer segmentation, and obtain inventory targets that deliver beta-guaranteed joint service levels with reduced cost.
Keywords: Inventory, optimization, sampling, service level
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