Economic and Environmental Life Cycle Optimization of Noncooperative Supply Chains and Product Systems: Modeling Framework, Mixed-Integer Bilevel Fractional Programming Algorithm, and Shale Gas Application

In this work, we propose a general modeling framework for the economic and environmental life cycle optimization of supply chains and product systems with noncooperative stakeholders. This framework is based on the functional-unit-based life cycle optimization approach and the leader follower Stackelberg game structure to capture the decentralized feature and noncooperative relationships between multiple stakeholders across the product life cycle. The leader enjoys the priority of decision-making to optimize both its own economic performance and the life cycle environmental performance of the supply chain or product system. After the observation of leader's decisions, the follower takes actions correspondingly to optimize its own economic performance. The resulting problem is formulated as a mixed-integer bilevel fractional program to account for conflicting objectives and interactions among different stakeholders. Design and decisions for both leader and follower are taken into consideration, including facility allocation, technology selection, production planning, transportation and storage scheduling, etc. To tackle the computational challenge of the resulting mixed-integer bilevel fractional programs, a tailored solution algorithm is developed based on a parametric algorithm and a projection-based reformulation and decomposition method. An application to a well-to-wire Marcellus shale gas supply chain is presented to demonstrate the applicability of the proposed life cycle optimization modeling framework and the efficiency of the solution algorithm.