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,
2004

[graves1993logistics]

Logistics of production and inventory

Elsevier

1993

[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