prob040: A Distribution Problem with Wagner-Whitin Costs

proposed by

References

The original paper on the control of single stocking points with linear holding and fixed ordering costs, and dynamic deterministic demand is due to Wagner and Whitin.

H. M. Wagner, T. M. Whitin, "Dynamic version of the economic lot size model", Management Science, 5, 89-96, 1958.

Clark and Scarf introduce the "echelon stock" concept and give an alternative formulation for the arborescent systems.

A. J. Clark, H. Scarf, "Optimal policies for a multi-echelon inventory problem," Management Science, 6, 475-490, 1960.

Crowston et al. define the "echelon holding cost" to replace the usual holding costs and hence improve the relevance of the Clark-Scarf model.

W. B. Crowston, H. M. Wagner, J. F. Williams, "Economic lot size determination in multi-stage assembly systems", Management Science, 19, 517-527, 1973.

Schwarz and Schrage give a proof for serial systems that an alternative formulation is possible by means of "echelon stock" and "echelon holding cost".

L. B. Schwarz, L. Schrage, "On echelon holding costs", Management Science, 24, 865-866, 1978.

Tarim and Miguel extend Schwarz and Schrage's proof for serial systems to arborescent systems and examine the computational efficiency of introducing various implied constraints into MIP (mixed-integer programming) and constraint programming/linear programming (CP/LP) hybrid models:

S. A. Tarim, I. Miguel, "Echelon stock formulation of arborescent distribution systems: an application to the Wagner-Whitin problem", in Proceedings of the International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR), 2004.

A relatively recent literature review and many other aspects of inventory control can be found in:

S. C. Graves, A. H. G. Rinnooy Kan, P. H. Zipkin (eds), Logistics of Production and Inventory, Handbooks in Operations Research and Management Science, Vol.4, North-Holland, 1993.

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