Robust design and pricing of electric vehicle battery reuse network by tailored branch-and-cut algorithm

The rapid proliferation of electric vehicles (EVs) has led to a significant increase in the quantity of used electric vehicle batteries (EVBs). This necessitates the design of a waste reverse supply chain to reuse and recycle EVBs and protect the environment. This paper examines an integrated reuse network design and pricing problem for EVBs, which involves two stakeholders: an echelon utilization enterprise (leader) and a recycling company (follower). Two stakeholders interact through a hierarchical decision-making process under the uncertainty of return quantity. To tackle this problem, we present two bilevel globalized distributionally robust (GDR) design and pricing models. The leader optimizes the locations of collection and echelon utilization centers, the transportation of used EVBs, and pricing strategies to maximize profit. The follower determines the quantity of used EVBs to purchase for dismantling and recycling in order to maximize profit. We derive computationally tractable reformulations of GDR expectation and chance constraints using Lagrangian duality and conjugate function. To efficiently solve the resulting joint chance-constrained model, we propose a tailored branch-and-cut (B&C) algorithm incorporating a strengthened formulation. A real-world case study is conducted to validate the superiority of the proposed methods. Results demonstrate that the globalized distributionally robust optimization models exhibit greater robustness than stochastic optimization models. The computational performance of the tailored B&C algorithm incorporating a strengthened formulation is assessed compared to the standard solver. We also analyze the impact of globalized sensitivity parameter, Wasserstein radius, norm choice, and tolerance level on profitability and provide decision-makers with insights for choosing parameters.