Abstract
We analyze a periodic review inventory system where inventory of a single item is used to serve high and low priority customers. High priority customers demand a higher service level than low priority customers and both types of customers can have quite general discrete demand distributions. The inventory is controlled by a (S, CL)-policy, where S denotes the base stock level and CL specifies the critical level, i.e., the amount of inventory reserved for high priority demand. We consider a policy, where the critical level is constant over time, which is not optimal, but makes the model analytically tractable. Unlike previous research, we clear backorders optimally and find the optimal solution. We also derive structural results.
Similar content being viewed by others
References
Arslan H, Graves S, Roemer T (2007) A single-product inventory model for multiple demand classes. Manage Sci 53: 1486–1500
Cohen M, Kleindorfer P, Lee H (1988) Service constrained (s, S) inventory systems with priority demand classes and lost sales. Manage Sci 34: 482–499
de Véricourt F, Karaesmen F, Dallery Y (2001) Assessing the benefits of different stock allocation policies for a make-to-stock production system. Manuf Serv Oper Manage 3: 105–121
de Véricourt F, Karaesman F, Dallery Y (2002) Optimal stock allocation for a capacitated supply system. Manage Sci 48: 1486–1501
Dekker R, Hill R, Kleijn M, Teunter R (2002) On the (S-1,S) lost sales inventory model with priority demand classes. Naval Res Logist 49: 593–610
Deshpande V, Cohen M, Donohue K (2003) A threshold inventory rationing policy for service-differentiated demand classes. Manage Sci 49: 683–703
Enders P, Adan I, van Houtum G, Pittsburgh PA, Eindhoven NL (2006) A mixed lost-sales backordering inventory problem with two customer classes. Carnegie Mellon University and Technische Universiteit Eindhoven, Working Paper
Evans R (1968) Sales and restocking policies in a single item inventory system. Manage Sci 14: 463–472
Fadiloglu M, Bulut O (2005) An embedded markov chain approach to the analysis of inventory systems with backordering under rationing. Working paper, Bilkent University, Ankara, Turkey
Frank K, Zhang R, Duenyas I (2003) Optimal policies for inventory systems with priority demand classes. Oper Res 51: 993–1002
Gayon J-P, de Véricourt F, Karaesman F, Dallery Y (2005) Stock rationing in a multi-class make-to-stock queue with information on the production status. Working paper, Ecole Central Paris, France, Duke University, USA, and Koc University, Turkey
Ha A (1997a) Inventory rationing in a make-to-stock production system with several demand classes and lost sales. Manage Sci 43: 1093–1103
Ha A (1997b) Inventory rationing in a make-to-stock production system with two priority classes and backordering. Naval Res Logist 44: 458–472
Ha A (2000) Stock rationing in a M/Ek/1 make-to-stock queue. Manage Sci 46: 77–87
Johnson M, Lee H, Davis T, Hall R (1995) Expressions for item fill rates in periodic inventory systems. Naval Res Logist 42(1): 57–80
Kaplan A (1968) Stock rationing. Manage Sci 15: 260–267
Kleijn M, Dekker R (1999) An overview of inventory systems with several demand classes. In: Speranza MG, Stähly P (eds) New trends in distribution logistics. Lecture Notes in Economics and Mathematical Systems. Springer, Berlin, pp 253–265
Melchiors P, Dekker R, Kleijn M (2000) Inventory rationing in an (s, Q) inventory model with lost sales and two demand classes. J Oper Res Soc 51: 111–122
Merlo A, Sericola B, Marie R (1996) A new stable algorithm for computing steady state measures for markov chains. Technical report, Institut de Recherche en Informatique et Systèmes Aléatoires, Campus de Beaulieu, Rennes Cedex, France
Nahmias S, Demmy W (1981) Operating characteristics of an inventory system with rationing. Manage Sci 27: 1236–1245
Stoyan D (1983) Comparison methods for queues and other stochastic models. Wiley, New York
Tan T, Güllü A, Erkip N (2004) Employing imperfect advance demand information in ordering and inventory rationing decisions. Technical report, Technische Universiteit Eindhoven, The Netherlands
Tempelmeier H (2006) Supply chain inventory optimization with two customer classes in discrete time. Eur J Oper Res 174: 600–621
Teunter R, Haneveld WK (1999) Reserving spare parts for critical demand. Technical report, Graduate School/Research Institute System, Organisations and Management (SOM), University of Groningen, The Netherlands
Topkis D (1968) Optimal ordering and rationing policies in a nonstationary dynamic inventory model. Manage Sci 15: 160–176
Veinott A (1965) Optimal policy in a dynamic, non-stationary inventory model with several demand classes. Oper Res 13: 761–778
Zipkin P (2000) Foundations of Inventory Management. McGraw-Hill, Boston
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Möllering, K.T., Thonemann, U.W. An optimal constant level rationing policy under service level constraints. OR Spectrum 32, 319–341 (2010). https://doi.org/10.1007/s00291-009-0167-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00291-009-0167-6