Summary
Consider a two-echelon inventory system consisting of a central depot (CD) supplying a number of retailers. Only the retailers face customer demand. Both the CD and every retailer adopt a periodic review echelon order-up-to policy, i.e., periodically an order is placed to raise the echelon inventory position to the order-up-to-level. At the CD incoming stock is allocated by using the Balanced Stock (BS) rationing policy. When the orders arrive at the retailers, an instantaneous rebalancing of the total echelon stock of the retailers takes place. This rebalancing is realized by lateral transshipments, assuming zero transshipment lead times. The used rebalancing policy is also a BS rationing policy.
The objective of this paper is to determine all the control parameters, such that the target customer service levels are attained at minimal expected total costs. Exact expressions are developed to determine these parameters. The order-up-to-levels are computed by a heuristic, since the exact expressions are intractable. A numerical study reveals that the performance of this heuristic is good. Furthermore, this model is compared with the same model without lateral transshipments, which yields insight into the conditions under which transshipment could be useful.z
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References
Burgin, T. (1975): The gamma distribution and inventory control. Operational Research Quarterly 26, 507–525.
Clark, A.J., Scarf, Η. (1960): Optimal policies for a multi-echelon inventory problem. Management Science 6, 475–490.
Cohen, M.A., P.R. Kleindorfer, P.R., Lee, H.L. (1986): Optimal stocking policies for low usage items in multi-echelon inventory systems. Naval Research Logistics Quarterly 33, 17–38.
Diks, E.В., Kok, A.G. de (1996): Controlling a divergent two-echelon network with transshipments using the consistent appropriate share rationing policy. International Journal of Production Economics 45, 369–379.
Diks, E.Ð’., Kok, A.G. (1998a): Computational results for the control of a divergent N-echelon inventory system. International Journal of Production Economics, In press.
Diks, E.B., Kok, A.G. de (1998b): Optimal control of a divergent N-echelon inventory system. European Journal of Operational Research, To appear.
Diks, E.B., Kok, A.G. de, Lagodimos, A.G. (1996): Multi-echelon systems: A service measure perspective. European Journal of Operational Research 95, 241–263.
Donselaar, K. van, Wijngaard, J. (1987): Commonality and safety stocks. Engineering Costs and Production Economics 12, 197–204.
Eppen, G., Schrage, L. (1981): Centralized ordering policies in a multiwarehouse system with lead times and random demand, in: L.B. Schwarz (ed.), Multi-level Production/Inventory Control Systems: Theory and Practice, North-Holland Publishing Company, 51–67.
Federgruen, A. (1993): Centralized planning models for multi-echelon inventory systems under uncertainty. in: Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, P.H. (eds.), Logistics of production and inventory, Handbooks in Operations Research and Management Science 4, Elsevier Science Publishers B.V., Amsterdam, North-Holland, Chapter 3, 133–173.
Hadley, G., Whitin, T.M. (1963): Analysis of Inventory Systems. Prentice-Hall Inc., Englewood Cliffs, New Jersey.
Heijden, M.C. van der (1997): Supply rationing in multi-echelon divergent systems. European Journal of Operational Research, To appear.
Heijden, M.C. van der, Diks, E.B., Kok, A.G. de and A.G. de Kok (1997): Stock allocation in general multi-echelon distribution systems with (R, S) order-up-to-policies. International Journal of Production Economics 49, 157–174.
Hoadley, H., Heyman, D.P. (1977): A two-echelon inventory model with purchases dispositions shipments, returns and transshipments. Naval Research Logistics Quarterly 24, 1–19.
Houtum, G.J. van, Inderfurth, K., Zijm, W.H.M. (1996): Materials coordination in stochastic multi-echelon systems. European Journal of Operational Research 95, 1–23.
Houtum, G.J. van, Zijm, W.H.M. (1991): Computational procedures for stochastic multi-echelon production systems. International Journal of Production Economics 23, 223–237.
Jönsson, H., Silver, E.A. (1987): Analysis of a two-echelon inventory control system with complete redistribution. Management Science 33, 215–227.
Karmarkar, U.S., Patel, N.R. (1977): The one-period, N-location distribution problem. Naval Research Logistics Quarterly 24, 559–575.
Kok, A.G. de (1990): Hierarchical production planning for consumer goods. European Journal of Operational Research 45, 55–69.
Kok, A.G. de, Lagodimos, A.G., Seidel, H.P. (1994): Stock allocation in a two-echelon distribution network under service-constraints. EUT 94–03, Department of Industrial Engineering and Management Science, Eindhoven University of Technology.
Klein, M., Dekker, R. (1997): Using break quantities for tactical optimisation in multistage distribution systems. in: Fleischmann, В., Nunen, J. van, Speranza, G., Stähly, P. (eds.), Advances in Distribution Logistics, series Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Chapter 17.
Lagodimos, A.G. (1992): Multi-echelon service models for inventory systems under different rationing policies. International Journal of Production Research 30, 939–958.
Langenhoff, L.J.G., Zijm, W.H.M. (1990): An analytical theory of multiechelon production/ distribution systems, Statistica Neerlandica 44, 149–174.
Lee, H.L. (1987): A multi-echelon inventory model for repairable items with emergency lateral transshipments, Management Science 33, 1302–1316.
Seidel, H.P., Kok, A.G. de (1990): Analysis of stock allocation in a 2-echelon distribution system. Technical Report 098, CQM, Eindhoven.
Silver, Ε.Α., Peterson, R. (1985): Decision Systems for Inventory Management and Production Planning, John Wiley and Sons, New York.
Tagaras, G. (1989): Effects of pooling on the optimization and service levels of two-location inventory systems, IIE Transactions 21, 250–257.
Tagaras, G., Cohen, M.A. (1992): Pooling in two-location inventory systems with non-negligible replenishment lead times. Management Science 38, 1067–1083.
Tijms, H.C. (1994): Stochastic Models: an Algorithmic Approach, John Wiley and Sons, Chichester.
Tüshaus, U., Wahl, С. (1997): Inventory Positioning in a Two-stage Distribution System with service Level Constraints. in: Fleischmann, В., Nunen, J. van, Speranza, G., Stähly, P. (eds.), Advances in Distribution Logistics, series Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Chapter 20.
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Diks, E.B., de Kok, A.G. (1998). Transshipments in a divergent 2-echelon system. In: Fleischmann, B., van Nunen, J.A.E.E., Speranza, M.G., Stähly, P. (eds) Advances in Distribution Logistics. Lecture Notes in Economics and Mathematical Systems, vol 460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46865-0_18
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