Non-Cooperative Games for the Optimization of Multi-Enterprise Chemical Supply Chains under Uncertainty
Kefah Hjaila1, José M. Laínez-Aguirre2,Luis Puigjaner1 and Antonio Espuña1
1Chemical Engineering Department, Universitat Politècnica de Catalunya, ETSEIB. Diagonal Avenue 647, 08028 Barcelona, Spain.
2Department of Industrial and Systems Engineering, University at Buffalo, NY, United States.
Most models currently applied to optimize the tactical decisions of chemical supply chains (SCs) are based on the optimization of the target of one organization, the “Centralized” approach (Hjaila et al., 2014). This approach does not consider the complexity that arises when different organizations participate in the SC superstructure which may bring conflictive policies and objectives into play. Typically, each organization will seek to optimize its own benefits while neglecting the risks associated with the unknown decision processes of third parties, and the uncertain reaction of the other partners as well.
Some works have been carried out to optimize the tactical decisions of decentralized SCs, through negotiations based on revenue sharing (Cao et al., 2013); multi-agent cooperation (Banaszewski et al., 2013); Scenario-Based Negotiations “SBNs” (Hjaila et al., 2015), and Game Theory (GT) based on cooperative (Zhao et al., 2013) or non-cooperative (Chu et al., 2015) situations. However, current negotiation and GT models for decentralized SC decision-making focus on the individual decisions of the participating organizations. These models rely on static scenarios without considering the interaction between the participants’ SC networks and the reaction of other partners and their third parties to the different suggested solutions. Moreover, to the best of our knowledge, the literature about GT that focus on decentralized SCs decision-making does not evaluate the negotiation outcome based on the benefits probabilities in order to support the negotiating partners in making a final decision. Most of the current non-cooperative game models tend to linearize the tactical optimization models, especially the “follower” SC model, which can lead to losing some practicality.
Stochastic programming has been widely used to tackle the different sources of uncertainty at the tactical level (Puigjaner and Laínez-Aguirre, 2008; Yeh et al., 2015) through different stages. However, most of the stochastic programming models focus on the external uncertainty sources of centralized SCs. Further efforts are needed to explore its application to model global decentralized SCs. An effective robust decision-support tool is necessary to help the tactical decision-makers to collaborate within a decentralized SC superstructure, taking into consideration the uncertain behavior of all participating partners and their third parties, so to avoid eventual disruptions in the whole system.
Accordingly, this work presents a two-stage stochastic game approach as a robust decision-support tool for the optimization of decentralized SCs by determining the best collaboration strategy between the organizations with conflicting objectives. The proposed approach takes into consideration their uncertain behavior and the uncertain nature of their third parties. At the first stage, the interactions with the different providers/clients (represented by their SCs) are modeled as non-cooperative non-zero-sum Stackelberg-games, to obtain the optimal interaction among them (along a discrete planning time horizon). They are built on expected win-to-win outcomes. Based on non-symmetric roles, and under the leading role of one of the partners, the leader designs the first game move according to its best expected benefits, estimating that the follower will respond according to its best expected benefits (assuming a dynamic game), so that the Stackelberg-expected-payoff matrix can be built. In this part, the uncertainty of the third parties is considered by generating different external risk scenarios using Monte-Carlo sampling. The Stackelberg solution will be the resource flows among the game players SCs that lead to the first win-win outcome that results from the trade-off between their expected benefits. This solution then will be set for the first stage collaboration agreement, which will be evaluated according the participating partners expected benefits probabilities. Additionally to the traditional Stackelberg strategies, which are based on the current conditions, the proposed strategy is based on the description of both leader and follower scenarios resulting from the uncertain nature of their third parties. For the second stage decision-making, the uncertain behavior of the global decentralized SC external conditions is analyzed (i.e., external market demands), and the second stage tactical-decisions are obtained.
The proposed approach results in a collection of Mixed Integer Nonlinear Programs (MINLP), as illustrated in a case study which comprises multiple vendors "follower" SCs around a client "leader" in a decentralized scenario. The results show how the tactical decisions of the leader are affected by the uncertain behavior of the followers, stressing the importance of considering this wider view of both leader and followers’ options towards higher profits expectations. The results are also compared with their standalone approach.
Acknowledgements: Financial support from the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund, both funding the Project SIGERA (DPI2012-37154-C02-01), and from the Generalitat de Catalunya (AGAUR FI program and grant 2014-SGR-1092-CEPEiMA), is fully appreciated.
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