Abstract
An arborescent distribution system is a multi-level system in which each installation receives input from a unique immediate predecessor and supplies one or more immediate successors. In this paper, it is shown that a distribution system with an arborescent structure can also be modelled using an echelon stock concept where at any instant the total echelon holding cost is accumulated at the same rate as the total conventional holding cost. The computational efficiency of the echelon model is tested on the well-known Wagner-Whitin type dynamic inventory lot-sizing problem, which is an intractable combinatorial problem from both mixed-integer programming (MIP) and constraint programming (CP) standpoints. The computational experiments show that the echelon MIP formulation is computationally very efficient compared to the conventional one, whereas the echelon CP formulation remains intractable. A CP/LP hybrid yields a substantial improvement over the pure CP approach, solving all tested instances in a reasonable time.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Afentakis, P., Gavish, B.: Bill of material processor algorithms -time and storage complexity analysis. Technical report, Graduate School of Management, University of Rochester (1983)
Afentakis, P., Gavish, B., Karmarkar, U.: Computationally efficient optimal solutions to the lot-sizing problem in assembly systems. Management Science 30, 222–239 (1984)
Axsater, S., Rosling, K.: Notes: Installation vs. echelon stock policies for multilevel inventory control. Management Science 39, 1274–1279 (1993)
Benichou, M., Gauthier, J.M., Hentges, G., Ribiere, G.: Experiments in mixed integer linear programming. Mathematical Programming 1, 76–94 (1971)
Chen, F., Zheng, Y.S.: One-warehouse multiretailer systems with centralized stock information. Operations Research 45, 275–287 (1997)
Clark, A.R., Armentano, V.A.: Echelon stock formulations for multi-stage lotsizing with lead-times. International Journal of Systems Science 24, 1759–1775 (1993)
Clark, A.R., Armentano, V.A.: A heuristic for a resource-capacitated multi-stage lot-sizing problem with lead times. Journal of the Operational Research Society 46, 1208–1222 (1995)
Clark, A.J., Scarf, H.: Optimal policies for a multi-echelon inventory problem. Management Science 6, 475–490 (1960)
Crowston, W.B., Wagner, M.H., Williams, J.F.: Economic lot size determination in multi-stage assembly systems. Management Science 19, 517–527 (1973)
Optimization, D.: Xpress-MP Essentials: An Introduction to Modeling and Optimization. Dash Associates, New Jersey (2002)
Padberg, M.W., Rinaldi, G.: A branch-and-bound algorithms for the resolution of large-scale symmetric traveling salesman problems. SIAM Review 33(1), 60–100 (1991)
Schwarz, L.B.: Multi-Level Production/Inventory Control Systems: Theory and Practice. North-Holland, Amsterdam (1981)
Schwarz, L.B.: Physical distribution: The anaylsis of inventory and location. AIIE Transactions 13, 138–150 (1981)
Schwarz, L.B., Schrage, L.: On echelon holding costs. Management Science 24, 865–866 (1978)
Silver, E.A., Pyke, D.F., Peterson, R.: Inventory Management and Production Planning and Scheduling. John-Wiley and Sons, New York (1998)
Wagner, H.M., Whitin, T.M.: Dynamic version of the economic lot size model. Management Science 5, 89–96 (1958)
Zangwill, W.I.: A backlogging model and a multi-echelon model of a dynamic economic lot size production system – a network approach. Management Science 15(9), 506–527 (1969)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tarim, S.A., Miguel, I. (2004). Echelon Stock Formulation of Arborescent Distribution Systems: An Application to the Wagner-Whitin Problem. In: Régin, JC., Rueher, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2004. Lecture Notes in Computer Science, vol 3011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24664-0_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-24664-0_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21836-4
Online ISBN: 978-3-540-24664-0
eBook Packages: Springer Book Archive