Joint Optimization for Fleet, Staff Configuration and Operational Strategies in One-Way Mixed Fleet Carsharing Systems Considering Carbon Emission Cost: A Lagrangian Relaxation-Based Approach

Abstract

Carsharing is an emerging transportation modality aims to alleviate congestion and reduce pollution. This study explores the enhancement of carsharing services by integrating gasoline and electric vehicles in a one-way mixed fleet carsharing system (OMFCS), focusing on joint optimization for fleet, staff configurations and operational strategies (JOFSCOS) problem with consideration of carbon emission cost. Employing a space-time-electricity network modeling approach, we developed an integer linear programming model to tackle the JOFSCOS problem. To solve this model, a Lagrangian relaxation (LR)-based approach is devised. This approach incorporating the complicating coupling constraints into the objective function using Lagrangian multipliers, thereby decomposing the problem into a series of independent subproblems. These subproblems are then solved using dynamic programming to derive a relaxed solution. Subsequently, a heuristic-based algorithm is crafted to generate a feasible solution and updating the Lagrangian multipliers through the subgradient method. To further improve the solution quality, the branch-and-bound method is incorporated into the LR framework. An illustrative case and a real-world case are conducted to demonstrate the efficiency of the proposed solution method and analysis sheds light on the configurations and operation strategies of OMFCS.  The sensitive analysis results suggest that OMFCS outperforms homogenous fleet carsharing systems in terms of profitability while balancing user service quality and carbon emissions. Moreover, the study reveals that elevating carbon emission cost can effectively reduce the carbon footprint of carsharing operations.

Keywords: carsharing system, Environmental Sustainability, vehicle relocation, staff rebalancing, space-time-electricity network, Lagrangian relaxation