Robust battery swapping for e-bike sharing with uncertain covariates and partial outsourcing

Abstract

We consider the dynamic battery swapping problem in an e-bike sharing system, where both the swapping demands and covariates (e.g., weather) are random. In this problem, the firm first makes constant insourcing decisions for each shift in a two-shift system, followed by hourly outsourcing decisions based on observed information, including covariates and past demand realizations. Motivated by the identified correlation between covariates and demands, we propose a distributionally robust optimization model with a scenario-wise ambiguity set to address these uncertainties and their interdependencies. We begin by analyzing the value of covariate information in a one-period special case, demonstrating its potential to reduce the over-conservatism of robust solutions. To solve for the multiperiod system, an approximation approach is introduced using the linear decision rule. Exact solution approaches for multiperiod adaptive robust optimization problems are scarce in the literature. To fill this research gap, we introduce a vertex enumeration approach—derived from convex optimization theory—to identify the optimal solution. To address the exponential number of constraints and variables, we design a column-and-constraint generation approach that converges to an optimal solution within a finite number of iterations. Finally, we assess the effectiveness of our proposed solution by comparing its performance to several widely recognized benchmark models through a case study using real-world operational data provided by our industry partner. The findings offer valuable managerial insights for e-bike sharing firms by demonstrating how the integration of covariate information and a combination of insourcing and outsourcing strategies can optimize battery swapping operations.