Note on supply chain integration in vendor-managed inventory

doi:10.1016/j.dss.2007.03.003

Decision Support Systems

Volume 44, Issue 1, November 2007, Pages 360-365

https://doi.org/10.1016/j.dss.2007.03.003 Get rights and content

Abstract

In a recent paper Yao et al. present a single-buyer-single-supplier model to explore the effects of collaborative supply-chain initiatives such as vendor managed inventory (VMI). Several conclusions drawn from their model are arguable as (i) the model ignores the costs of shipments from the supplier to the buyer and (ii) the model times the incoming and outgoing flows at the supplier in a manner that overstates the inventory needed at the supplier.

Introduction

The model developed in Yao et al. [2] explores the cost savings to be realized from collaborative initiatives such as vendor-managed inventory (VMI). The system modeled is that of a supply chain for a single item with two parties, where the downstream party (the buyer) faces demand at a constant rate r. The buyer is replenished by the upstream party (the supplier). Two situations are modeled: no-VMI and VMI. These two situations differ in the way the item flow is managed. In the no-VMI situation each of the parties optimizes his own ordering strategy ignoring costs borne by the partner. In the VMI situation the supplier, as an omnipotent manager, optimizes the ordering process at both the supplier and the buyer so as to minimize the total costs of the supply chain.

We find the outcomes of their model, which will be referred to as the Yao-model, arguable for two reasons.

(1)
The model ignores costs borne by the supplier for shipping goods to the buyer.
(2)
The model manages the incoming and outgoing flows at the supplier in the worst-case manner, thus overstating the inventory kept at the supplier.

Either one of these criticisms contests main conclusions in [2]. In particular, this note shows that under VMI:

(1)
Shipment sizes from supplier to buyer increase.
(2)
Inventory at the supplier goes down.
(3)
Inventory at the buyer goes up.

This note follows [2] in notation. Uppercase characters represent variables and parameters that affect the supplier and lowercase characters are used to denote quantities that affect the buyer. Symbols are primed in the VMI situation, whenever their value differs from that in the no-VMI situation. See Fig. 1.

Section snippets

Extending the Yao-model with delivery cost

In the models of Yao et al. the delivery costs T and t are overlooked. Because delivery costs to the customers of the buyer cannot be impacted by the buyer's ordering pattern and therefore in the model represent sunk costs, t indeed can be ignored. The costs T of the outgoing shipments at the supplier however cannot be disregarded, as they are impacted by the buyer's ordering decisions. These costs, comprising of costs for order picking, shipping and transportation can be considerable; they can

Case descriptions

This section gives an overview of 5 possible cases; two cases in the no-VMI situation and three cases in the VMI situation. The two cases in the no-VMI situation differ in the way the buyer is charged by the supplier and the three cases for the VMI situation differ in the timing of replenishment orders at the supplier. Values pertinent to a certain case are subscripted with the case's number.

Analyses

Minimizing the total cost functions and relaxing the requirement that k be an integer, leads for the various cases, to the values as listed in Table 1.

Note that for all cases $Q^{⁎} = \sqrt{2 Cr / H}$

To juxtapose the various cases, we have to further detail the relationship between parameter values in the no-VMI situation and the VMI situation.

•
Consider, as in [2], $c ≫ c'$
The values c and c′ represent the buyer's ordering costs in the no-VMI situation and in the VMI situation, respectively. As already remarked by [2]

Comparisons

Comparisons will be made now for the cost rate, the shipment size from supplier to buyer, the inventory at the buyer and the inventory at the supplier while considering parameter values in no-VMI and VMI situations as considered in the foregoing subsection.

Conclusion

Table 2 lists the difference in conclusions in our analysis with those in [2] when comparing VMI with No-VMI (Fup).

Our conclusions challenge the conclusions made in [2].

We hasten to add that the VMI analysis presented is limited in that it only considers and models effects that are a consequence of considering total costs in the optimization or that are a consequence of the coordinated inventory management at the supplier. Effects of VMI that are produced by considering

•
the redistribution of

Piet van der Vlist is adjunct professor of Supply Chain Management at the Erasmus University's Rotterdam School of Management. He holds an MSC in Electronic engineering from Delft University of Technology and an MBA from the University of Twente.

References (2)

Yuliang Yao et al.
Supply chain integration in vendor-managed inventory
Decision Support Systems
(2007)
Edward A. Silver et al.
Decision Systems for Inventory Management and Production Planning
(1985)

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Roelof Kuik is associate professor of Logistics and Simulation at RSM Erasmus University. He holds an Msc and a PhD in Physics from the University of Groningen.

Bas Verheijen is a PhD candidate in the department of Decision Sciences and Information Technology at RSM Erasmus University in Rotterdam. He holds an MSc in Applied Physics from Eindhoven University of Technology.

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