(19e) A Novel Noncooperative Modeling Framework for Economic and Environmental Life Cycle Optimization of Supply Chains and Product Systems: Miblp Model and Efficient Solution Algorithm

Sustainable design and operations of supply chains and product systems considering both economic and environmental performance have become increasingly important in industries [1-4]. Inspired by the life cycle analysis (LCA) approach and multiobjective optimization method, life cycle optimization methods are proposed for sustainability optimization from a life cycle perspective [5-7]. However, existing life cycle optimization studies rely on centralized models, assuming all the components in a supply chain or a product system operate in a cooperative way towards a universal objective [8, 9]. Supply chains and product systems normally involve multiple stakeholders, and different life cycle stages of a certain product are managed in a decentralized way. Consequently, the optimal strategies obtained from a centralized life cycle optimization model may be overly optimistic or even infeasible under a noncooperative environment [10-13]. Existing studies on optimization of noncooperative supply chains and product systems solely focus on the economic performance and fail to consider the corresponding environmental performance, especially from a life cycle perspective [14, 15]. To investigate the impact of decentralized feature on life cycle optimization and to better capture the corresponding life cycle performance, it is important to explicitly model and analyze the noncooperative feature in the life cycle optimizations of supply chains and product systems.

To fill this knowledge gap, we propose a general life cycle optimization framework for noncooperative supply chains and product systems. In this holistic model, we couple the sophisticated Stackelberg game theory model with the state-of-the-art life cycle optimization approach, which enables us to simultaneously address the trade-offs between conflicting objectives as well as the interactions between different stakeholders. Following the Stackelberg game, two types of stakeholders, namely a leader and a follower, are identified in the optimization problem [16]. The leader enjoys the priority of making decisions and has the knowledge of potential reactions of the follower. Due to the essential position and information advantage, the leader senses more responsibility of proposing sustainable strategies in terms of its economic and life cycle environmental performance. Once the leader’s decisions are made, the follower reacts rationally to optimize its own decisions. Due to the limited information, the follower is mainly driven by its economic objective. The conflicting objectives from different stakeholders will eventually lead to a Stackelberg equilibrium [17]. This modeling framework is general enough to allow for the consideration of both design and operational decisions for the leader and the follower. The resulting problem can be formulated as a mixed-integer bilevel linear fractional program (MIBLFP), which cannot be solved directly using any off-the-shelf optimization solvers [18]. We present a tailored solution strategy integrating the parametric algorithm with a projection-based reformulation and decomposition algorithm to tackle this computational challenge. To illustrate the application of proposed modeling framework and solution algorithm, a “well-to-wire” Marcellus shale gas supply chain is considered. Two major decision makers are identified as the operator of power plants and shale gas producer. Multiple decisions with respect to drilling, production, processing, transmission, and power generation are considered. The optimal levelized cost of electricity ranges from $72/MWh to $128/MWh, and the corresponding life cycle GHG emissions are 477 kg CO2-eq/MWh and 107 kg CO2-eq/MWh, respectively. Through a detailed comparison among the noncooperative models and their centralized counterparts, we conclude that noncooperative environment affects the optimal results of life cycle optimization, especially for the upstream of a shale gas supply chain. Although centralized models are easier to solve and lead to better results in most cases, the life cycle economic and environmental performance is over-optimistic, and the corresponding optimal strategy can be infeasible in a noncooperative shale gas supply chain.

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