Fair Distribution of Efficiency Gains in Supply Networks from a Cooperative Game Theory Point of View

Fair Distribution of Efficiency Gains in Supply Networks from a Cooperative Game Theory Point of View

Stephan Zelewski (University of Duisburg-Essen, Germany) and Malte L. Peters (Center for Education and Science of the Federal Finance Adminstration, Germany)
DOI: 10.4018/jisscm.2010040101
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Abstract

In this paper, the authors address the distribution of efficiency gains among partially autonomous supply network actors in a manner they will accept as fair and as an incentive to cooperation. The problem is economically significant because it requires substantiating efficiency gains in an understandable manner. Moreover, supply networks suffer from a conflict potential because the partially autonomous actors seek to maximize their own shares of the efficiency gain. The method applied appropriates a model from cooperative game theory involving the t-value. The special nature of the t-value ensures that it seems rational to the actors to cooperate in the supply network. The proposed method for the distribution problem offers a fair distribution of efficiency gains in the supply network and ensures that the distribution results can be communicated easily.
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Introduction

Over the past several years, a considerable amount of research has been carried out in the area of supply chain management (e.g., Croson & Donohue, 2006; Krol et al., 2005; Wu et al., 2007; Zokaei & Simons, 2006). One principal aim of this research is to find ways of realizing efficiency gains by coordinating the activities of all actors in a supply chain or, more precisely, in a supply network. Since this paper’s findings are not restricted to supply chains, but also apply to supply networks, the latter term will be used throughout.

Several effects must be considered as sources of efficiency gains. The most prominent effect is the so called bullwhip effect (Lee et al., 1997; see also Croson & Donohue, 2006; Krol et al., 2005; McCullen & Towill, 2002; Metters, 1997). The bullwhip effect describes especially how companies build inventory buffers based on the demand of their customers: the further the company is from the final customer the greater the “safety stock” is in times of rising demand. The cost of capital invested in oversized inventory buffers in the stocks causes inefficiency and thus efficiency gains can be realized by avoiding or reducing the bullwhip effect. Evidence of the practical relevance of the bullwhip effect to supply chain management is provided by studies of its financial consequences (McCullen & Towill, 2002; Metters, 1997). Based on available estimates of the cost of the bullwhip effect, companies should be able to increase their profits—depending on the source—by 8.4 to 20.1% (McCullen & Towill, 2002) or by 10 to 30% (Metters, 1997) by avoiding it.

When efficiency gains are realized in supply networks, a distribution problem arises. The cooperating actors know that they are realizing the efficiency gains by mutually coordinating their activities. Moreover, each actor is interested in maximizing his own gain at the expense of the other actors in the supply network. Thus, supply networks suffer from a built-in conflict between cooperation and defection. The problem lies in distributing efficiency gains among partially autonomous actors in a manner that the actors will accept as fair and advantageous to cooperation. If, on the other hand, it would be advantageous for at least one of the actors to leave the grand coalition, the supply network would collapse. With this scenario in mind, a stability requirement can be posited for the solutions of efficiency gain distribution problems. These problem solutions are regarded as desirable only, if they ensure that all actors in a supply network are willing to cooperate with each other. The fulfillment of this stability requirement is often circumscribed by the actors’ acceptance of the distribution of the efficiency gains as fair.

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