Abstract-In Multi-Retailer Inventory Control the possibility of sharing set up costs motivates communication and coordination among the retailers. We solve the problem of finding suboptimal distributed reordering policies which minimize set up, ordering, storage and shortage costs, incurred by the retailers over a finite horizon. Neuro-Dynamic Programming (NDP) reduces the computational complexity of the solution algorithm from exponential to polynomial on the number of retailers.
Consider multi-inventory systems with controlled flows and uncertain demands (disturbances) bounded within assigned compact sets. The system is modelled as a first order one integrating the discrepancy between controlled flows and demands at different sites/nodes. Thus, the buffer levels at the nodes represent the system state. Given a long-term average demand, we are interested in a control strategy that satisfies just one of the two requirements: i) meeting any possible demand at each time (worst case stability) or ii) achieving a pre-defined flow in the average (average flow constraints). Necessary and sufficient conditions * D. Bauso is with Dipartimento di Ingegneria Informatica, Universitàd iP a l e r m o ,P a l e r m o-I t a l ydario.bauso@unipa.it † F. Blanchini is with Dipartimento di Matematica e Informatica, Università di Udine, Udine -Italy blanchini@uniud.it ‡ R. Pesenti is with Dipartimento di Matematica Applicata, Università "Ca' Foscari" di Venezia -Italy pesenti@unive.it § Research supported by PRIN "Robustness optimization techniques for high performance control systems", and MURST-PRIN 2007ZMZK5T "Decisional model for the design and the management of logistics networks characterized by high interoperability and information integration".for the achievement of both goals have been proposed by the authors. In this paper we face the case in which these conditions are not satisfied. We show that if we ignore the requirement on worst case stability, we can find a control strategy driving the expected value of the state to zero. On the contrary, if we ignore the average flow constraints, we can find a control strategy that satisfies worst case stability while optimizing any linear cost on the average control. In the latter case we provide a tight bound for the cost.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.