Download bibtex

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]
S Armagan Tarim and Ian Miguel
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, 2004

[graves1993logistics]
Stephen C Graves, AHG Rinnooy Kan, and Paul Herbert Zipkin
Logistics of production and inventory
Elsevier
1993

[schwarz1978note]
Leroy B Schwarz and Linus Schrage
Note-On Echelon Holding Costs
Management Science 24(8), 1978

[crowston1973economic]
Wallace B Crowston, Michael Wagner, and Jack F Williams
Economic lot size determination in multi-stage assembly systems
Management Science 19(5), 1973

[clark1960optimal]
Andrew J Clark and Herbert Scarf
Optimal policies for a multi-echelon inventory problem
Management science 6(4), 1960

[wagner1958dynamic]
Harvey M Wagner and Thomson M Whitin
Dynamic version of the economic lot size model
Management science 5(1), 1958