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

Abstract

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 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.

The continuous resupply policy for deteriorating items with stock-dependent observable demand in a two-warehouse and two-echelon supply chain

“…Second, a model only based on cost will also prove difficult for accurately deriving the NPV function of the supplier since part of the costs of the retailer will translate into revenues for the supplier, and hence the need for considering the revenue stream for the supplier, too. See also Beullens [26] for a discussion on the impact that a lack of recognition of revenues shifting over time has had on inventory research.…”

Problemas de dimensionamento de lotes e planejamento de pedidos aplicados a uma indústria moveleira

“…A literatura envolvendo PDLé bastante vasta. Revisões bibliográficas de trabalhos que estudam PDL podem ser encontradas desde os trabalhos de Billington et al (1983), Bahl et al (1987), até mais recentemente, Karimi et al (2003), Glock et al (2014), Holmbom e Segerstedt (2014), Beullens (2014) e Brahimi et al (2017).…”

MIP models for production lot sizing problems with distribution costs and cargo arrangement

“…Each of these factors may have important influences on the total costs and overall performance of the production plan. Reviews of different aspects of lot sizing problems can be found, for example, in Karimi et al (2003), Brahimi et al (2006), Degraeve (2007, 2008), Robinson et al (2009), Glock et al (2014), Holmbom and Segerstedt (2014) and Beullens (2014).…”