A reply to Mueller (2018) Supply chain collaboration: Further insights into incentive alignment in the Beer Game scenario
Journal of Industrial Engineering and Management
JIEM
2013-0953
A Reply to Mueller (2018) Supply Chain Collaboration: Further Insights into Incentive Alignment in the Beer Game Scenario
Borja Ponte 1
Isabel Fernández 0
Rafael Rosillo 0
José Parreño 0
Nazario García 0
0 University of Oviedo , Spain
1 The Open University , United Kingdom
Purpose: We expand a previous discussion in this journal by proposing a new solution concept, based on game theory, for profit allocation with the aim of aligning incentives in collaborative supply chains. Design/methodology/approach: Through the Gately's notion of propensity to disrupt, we minimize the desire of the nodes to leave the grand coalition in the search of a self-enforcing allocation mechanism. Findings: We discuss the benefits and limitations of this solution in comparison with more established alternatives (e.g. nucleolus and Shapley value). We show that it considers the bargaining power of the nodes, but it may not belong to the core. Originality/value: Finding a fair and self-enforcing scheme for incentive alignment, and specifically profit allocation, is essential to ensure the long-term sustainability of collaborative supply chains.
beer game; game theory; Gately point; incentive alignment; profit allocation; supply chain collaboration
1. Introduction
In 2016, we (Ponte, Fernández, Rosillo, Parreño & García, 2016) investigated in this journal how game-theoretical
concepts and ideas suggest an appropriate framework to align incentives in supply chains through the design of a
fair and self-enforcing mechanism for allocating the net profit derived from collaborative solutions. From this
perspective, we defined three conditions (efficiency, individual rationality, and coalition rationality) to be verified in
viable profit allocations, and proposed a mechanism for profit allocation based on the notion of the nucleolus
(Schmeidler, 1969). This mechanism allocates the profit among the different supply chain partners by maximizing
the satisfaction of the unhappiest coalition. We think that this solution concept fits very well with the essence of the
incentive alignment problem in collaborative supply chains (see e.g. Simatupang & Sridharan, 2005). To illustrate our
proposal, we developed a numerical example based on the widely-used Beer Game scenario (Goodwin & Franklin,
1994). We showed that it clearly outperforms traditional methods for profit allocation, which despite their simplicity
are often used in practice (see e.g. Liu, Wu & Xu, 2010), in terms of compensation fairness.
Recently, Mueller (2018) extended the discussion initiated by our previous paper from different perspectives. First,
they presented and discussed additional game-theoretic properties that can be useful for ensuring the robustness of
the profit allocation in collaborative supply chains. Second, they clarified the mathematical definition of the
nucleolus through the concept of lexicographic order of a specific allocation. In this sense, the solution they
suggested not only maximizes the satisfaction of the unhappiest coalition but, when several possible allocations
verify this aim, it also looks at (maximizing the satisfaction of) the second unhappiest coalition, the third one, and so
on. It should be noted that the computation of this solution would require solving a sequence of nested
optimization problems. Finally, they presented a new solution concept for this problem, i.e. the Lorenz set (see e.g.
Hougaard, Peleg & Thorlund-Petersen, 2001), based on the concept of Lorenz dominance
(Bishop, Formby &
Smith, 1991)
, which looks at the concentration of wealth in the coalition. Mueller (2018) employed the same
numerical example to illustrate their proposal and discussed the different solutions.
We truly appreciate the authors’ efforts in continuing the avenue that we opened in our prior work. Through the
previously highlighted lines of contribution, we believe that they provide relevant insights into the analysis of the
value of game theory concepts in the field of supply chain collaboration. In this new article we would like to
continue the discussion by proposing a new solution concept for the problem of profit allocation in collaborative
supply chains. This is based on the Gately point
(Gately, 1974; Straffin, 1993)
, which aims to minimize the maximum
propensity to deviate from the collaborative behavior in the supply chain. We present this new mechanism for
incentive alignment, discuss why it fits with the essence of the profit allocation problem, and illustrate its application
to the same numerical example in the Beer Game scenario. Through the comparison with the previous benchmark
alternatives, we aim to gain insight into the usefulness and limitations of the different solution concepts.
2. Characterization of the Gately solution
Gately (1974)
introduced the concept of propensity to disrupt a coalition to explore the distribution of the gains
among three partners in a p (...truncated)