Abstract
We study an inventory–transportation problem where one product has to be shipped from an origin to a destination by vehicles of given capacity over an infinite time horizon. The product is made available at the origin and consumed at the destination at the same constant rate. The intershipment time must be not lower than a given minimum value. The problem is to decide when to make the shipments and how to load the vehicles to minimize the sum of the transportation and the inventory costs at the origin and at the destination per time unit. We study the case in which the intershipment time is a multiple of the minimum value, i.e., the problem with discrete shipping times. We show that, in this case, the best double frequency policy has a tight performance bound of about 1.1603 with respect to the optimal periodic policy and of about 1.1538 with respect to the best frequency-based policy. Moreover, we show that, from the worst-case point of view, the best double frequency policy is the optimal frequency-based policy.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Blumenfeld, D.E., Burns, L.D., Daganzo, C.F., Frick, M.C., Hall, R.W.: Reducing logistics costs at General Motors. Interfaces 17, 26–47 (1987)
Campbell, A.M., Clarke, L., Kleywegt, A., Savelsbergh, M.W.P.: The inventory routing problem. In: Crainic, T.G., Laporte, G. (eds.) Fleet Management and Logistics, pp. 95–113. Kluwer, Boston (1998)
Bertazzi, L., Savelsbergh, M., Speranza, M.G.: Inventory routing. In: Golden, B., Raghavan, S., Wasil, E. (eds.) The Vehicle Routing Problem, Latest Advances and New Challenges, pp. 49–72. Springer, Berlin (2008)
Andersson, H., Hoff, A., Christiansen, M., Hasle, G., Løkketangen, A.: Industrial aspects and literature survey: combined inventory management and routing. Comput. Oper. Res. 37, 1515–1536 (2010)
Bertazzi, L., Speranza, M.G.: Inventory routing problems: an introduction. EURO J. Transp. Logist. 1, 307–326 (2012)
Bertazzi, L., Speranza, M.G.: Inventory routing problems with multiple customers. EURO J. Transp. Logist. 2, 255–275 (2013)
Coehlo, L.C., Cordeau, J.F., Laporte, G.: Thirty years of inventory-routing. CIRRELT-2012-52 (2012)
Speranza, M.G., Ukovich, W.: Minimizing transportation and inventory costs for several products on a single link. Oper. Res. 42, 879–894 (1994)
Bertazzi, L., Speranza, M.G.: Worst-case analysis of the full load policy in the single link shipping problem. Int. J. Prod. Econ. 93-94C, 217–224 (2005)
Blumenfeld, D.E., Burns, L.D., Diltz, J.D., Daganzo, C.F.: Analyzing trade-offs between transportation, inventory and production costs on freight networks. Transp. Res. 19B, 361–380 (1985)
Burns, L.D., Hall, R.W., Blumenfeld, D.E., Daganzo, C.F.: Distribution strategies that minimize transportation and inventory cost. Oper. Res. 33, 469–490 (1985)
Anily, S., Federgruen, A.: One warehouse multiple retailer systems with vehicle routing costs. Manag. Sci. 36, 92–114 (1990)
Chan, L.M.A., Federgruen, A., Simchi-Levi, D.: Probabilistic analyses and practical algorithms for inventory-routing models. Oper. Res. 46, 96–106 (1998)
Hall, R.W.: Determining vehicle dispatch frequency when shipping frequency differs among suppliers. Transp. Res. 19B, 421–431 (1985)
Maxwell, W.L., Muckstadt, J.A.: Establishing consistent and realistic reorder intervals in production–distribution systems. Oper. Res. 33, 1316–1341 (1985)
Jackson, P.L., Maxwell, W.L., Muckstadt, J.A.: Determining optimal reorder intervals in capacitated production-distribution systems. Manag. Sci. 34, 938–958 (1988)
Muckstadt, J.A., Roundy, R.O.: Analysis of multistage production systems. In: Graves, S.C., Kan Rinnooy, A.H.G., Zipkin, P.H. (eds.) Handbooks in Operations Research and Management Science, vol. 4, pp. 59–131. North-Holland, Amsterdam (1993)
Speranza, M.G., Ukovich, W.: An algorithm for optimal shipments with given frequencies. Nav. Res. Logist. 43, 655–671 (1996)
Bertazzi, L., Speranza, M.G.: Continuous and discrete shipping strategies for the single link problem. Transp. Sci. 36, 314–325 (2002)
Bertazzi, L., Speranza, M.G.: Rounding procedures for the discrete version of the capacitated economic order quantity problem. Ann. Oper. Res. 107, 33–49 (2001)
Bertazzi, L., Chan, L.M.A., Speranza, M.G.: Analysis of practical policies for the single link distribution system. Nav. Res. Logist. 54, 497–509 (2007)
Acknowledgements
The authors wish to thank the Referees, the Associate Editor and the Editor-in-Chief for useful suggestions that allowed us to improve the paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Johannes O. Royset.
Rights and permissions
About this article
Cite this article
Bertazzi, L., Chan, L.M.A. Analysis of the Best Double Frequency Policy in the Single Link Problem with Discrete Shipping Times. J Optim Theory Appl 163, 286–309 (2014). https://doi.org/10.1007/s10957-013-0476-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10957-013-0476-4