Revisiting foundations in lot sizing-Connections between Harris, Crowther, Monahan, and Clark

- The financial impact of lot sizing in supply chains.
- The EOQ model for uniform staircase cumulative demand with revenue considerations.
- Connects the models of Harris, Crowther, Monahan, and multi-echelon principles of Clark.
- Price discounts, joint economic lot sizing, side-payments, consignment and other payment structures.
- Derives a stochastic version of Crowther׳s model.

While many review articles exist on (deterministic) lot sizing models used in the context of price and quantity discounts, buyer-vendor coordination, supply chain management, and joint economic lot sizing problems, they do not convey the impact of important findings which date back to at least 2002, or, in hindsight, to 1984. As a result, many recent articles still model the financial implications of lot sizing decisions without having the assurance that these models would help the firm(s) involved in maximising the Net Present Value (NPV). This paper therefore reviews these findings, while adding also its own contributions, as to convey the general importance to lot sizing theory. We show that the underlying principles used in the four key articles that have led to a division in modelling approaches are in fact all in line with NPV, and argue that therefore there should not be these discrepancies that currently persist in the literature. We establish the connections between these four strands of the literature using the solution to a simple variation of Harris׳ EOQ model, deriving thereby results from Boyaci and Gallego (2002) and Beullens and Janssens (2011), but showing their general applicability to any type of supply-chain structure. The breath of implications to deterministic lot sizing theory is illustrated using practical examples. We present a stochastic version of the model of Crowther (1964), which is arguably the least understood and applied model, but on the other hand the most important one in realising how these modelling strands can be unified.