This work is licensed under a Creative Commons Attribution 4.0 International License. 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 [wagner1958dynamic].
Clark and Scarf introduce the echelon stock concept and give an alternative formulation for the arborescent systems [clark1960optimal].
Crowston et al. define the echelon holding cost to replace the usual holding costs and hence improve the relevance of the Clark-Scarf model [crowston1973economic].
Schwarz and Schrage give a proof for serial systems that an alternative formulation is possible by means of echelon stock and echelon holding cost [schwarz1978note].
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 [tarim2004echelon]
A literature review and many other aspects of inventory control can be found in [graves1993logistics]:
[tarim2004echelon]
Echelon stock formulation of arborescent distribution systems: An application to the Wagner-Whitin problem
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 302–318,
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[graves1993logistics]
Logistics of production and inventory
Elsevier
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[schwarz1978note]
Note-On Echelon Holding Costs
Management Science 24(8), 865–866,
1978
[crowston1973economic]
Economic lot size determination in multi-stage assembly systems
Management Science 19(5), 517–527,
1973
[clark1960optimal]
Optimal policies for a multi-echelon inventory problem
Management science 6(4), 475–490,
1960
[wagner1958dynamic]
Dynamic version of the economic lot size model
Management science 5(1), 89–96,
1958
This work is licensed under a Creative Commons Attribution 4.0 International License.