(331f) The Potential of Cooperative Game Theory for the Design of Chemical Supply Chain Networks Under the Carbon Trading Scheme

Abstract

         Nowadays,
business decisions are dominated by the globalization of markets and increased competitiveness
among firms. In particular, decision problems in supply chain management can be
enhanced by taking into account that they are not only influenced by a single
decision maker but for several. Here is where cooperation strategies come into
play. In the literature, several types of cooperation are distinguished. Interorganizational
cooperation (cooperation of economically and legally independent units) versus intra-organizational
cooperation (cooperating business units belonging all to the same company). Another
classification differentiates between vertical (buyer-seller) and horizontal
(buyer-buyer, seller-seller) cooperation. In the latter case, companies that
belong to the same supply chain stage jointly work to produce or trade the same
product (they are competing and are part of the same industry). The most
prominent reasons for horizontal cooperation are the synergistic effects
(economies of scale, scope, and speed) and strengthening the competitiveness¹. Nevertheless, horizontal
cooperation is not exempt from drawbacks, such as the creasing complexity of
the purchasing process; the loss of flexibility and control².

         As the
interactions among single companies in a supply network directly lead to a
multi-decision maker framework, game theory ‑predicts the rational
strategic behavior of individuals in conflicting or cooperating situations‑
seems to provide an adequate modeling basis for problems in supply chain
management. The field of game theory may be divided roughly in two parts,
namely non-cooperative game theory and cooperative game theory. Models in
non-cooperative game theory assume that each player in the game (e.g., a company
in a supply chain) optimizes its own objective and does not care for the effect
of its decisions on others. The focus is on finding optimal strategies for each
player. Binding agreements among the players are not allowed. One of the main points of concern is whether the
proposed mechanism provides a solution that maximizes the total supply chain
profit under Nash equilibrium. Alternatively, cooperative game theory assumes
that players can make binding agreements. One of the main questions when
applying cooperative game theory to supply chains is whether cooperation is
stable, that is, whether there exists an allocation of the joint profit among
all the parties in the supply chain such that no group of them can do better on
its own.

         As
well as other topics related to chemical engineering, supply chain networks demand
the application of the sustainability principles during their process design. One major motivation for this trend is the pressure placed on
governments and regulatory agencies to tighten environmental regulations (e.g.
on reducing greenhouse gas, GHG). In particular, capping GHG emissions and establishing a price through trading on
them is an essential foundation for climate change policy³. The idea
behind this cap-and-trading scheme is to set a price tag on carbon emissions
and in consequence, a financial incentive to decrease them. After a cap is fixed
on emissions, companies are allowed to buy or sell from each other the
allowances to emit GHGs. Firms exceeding their emissions cap must buy extra
credits to cover the excess. Meanwhile, those that do not use all their
allowances can sell them, providing the least-polluting firms with an extra
revenue ⁴. There are already active carbon markets for GHG emissions
such as the European Union Emissions Trading Scheme (EU ETS), the New Zeland
Emissions Trading Scheme (NZ ETS), the Chicago Climate Exchange, and the
Montreal Climate Exchange ⁵. Applying this carbon trading scheme, governments
seek for reducing the overall GHG emissions in an industry sector, and here is
where the cooperation among companies (i.e., players) fits perfectly. Models
based on cooperative game theory can not only improve the economic performance
of the whole set of companies but also the overall environmental impact for all
the firms, which is the aim of the governments.

The aim of this work is to show the applicability of Cooperative
Game Theory as a methodology for analyzing sustainable supply chains. The
success and sustainability of cooperation depends on the stability as
constituting element. In this way, the solution concept based on this theory
provides us under what allocation of the costs would the players want to form
the grand coalition (i.e., all the players cooperate in unique coalition). Under
the perspective of the game theory, the supply chain design problem we pose, is
a transferable utility game, which is a pair consisting of
a finite set of players (i.e., plants in the supply chain) and a characteristic
function, which measures the cost of every coalition of players (i.e., any subset
of all the players) through a real valued mapping. We applied our
methodology to a three-echelon petrochemical supply chain
(production-storage-market), which satisfies the game property of being
subadditive (i.e., it is always beneficial for two disjoint coalitions to
cooperate and form a larger coalition). The environmental performance of each
company in the SC is assessed according to the principles of Life Cycle
Assessment (LCA) using the global warming potential (GWP) indicator. CO₂ emissions trading is modeled by
introducing a balance equation that relates the total equivalent CO₂
emission for each company in the SC to be equal to the free allowance emissions
cap plus the extra rights bought to emit minus the sold rights⁶. First,
we illustrate the main concepts of cooperative game theory with a small motivation
example with only 3 companies. To this purpose we introduce the concept of the
non-emptiness of the core, that means that there exists at least one stable
allocation of the total cost such that no group of players has an incentive to
leave. This first case study can be solved geometrically (see Figure 1). Then,
we extend the proposed framework to a case study with 8 companies cooperating. As
the number of coalitions rises exponentially with an increasing number of
players, here we use an algorithm that finds an element in the core without
testing the constraints for all possible coalitions. This solution strategy is based
on a row generation procedure, whose key idea is to start with a relaxed
version of the original problem and add missing relaxed constraints over
several iterations. The solution to these case studies shows that the
Cooperative Game Theory provides a holistic solution for the design of
sustainable supply chains with environmental concerns and, can be included as
another useful mathematical tool for Chemical Engineers.

Figure 1. Geometric interpretation of the core in a cooperative game
with 3 players.

References

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(2)          Schotanus, F. Horizontal Cooperative Purchasing (Ph.D.
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(3)          Stern, N. Stern review on the economics of climate
change. London,UK: HM Treasury. http://www.sternreview.org.uk/

(4)          Young, T. The beginners’ guide to the UK’s carbon
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(5)          Chaabane, A.; Ramudhin, A.; Paquet, M., Design of
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(6)          Ruiz-Femenia, R.;
Salcedo-Díaz, R.; Guillén-Gosálbez, G.; Caballero, J. A.; Jiménez, L.,
Incorporating CO 2 emission trading in the optimal design and planning of
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