The bi-objective multimodal car-sharing problem

TL;DR

This paper introduces a bi-objective optimization model for multimodal car-sharing that balances cost and user satisfaction, incorporating user preferences, time-dependent factors, and routing decisions, solved with advanced algorithms.

Contribution

It develops a novel branch-and-cut algorithm for the complex BiO-MMCP, addressing multiple variants and integrating user preferences and routing in a bi-objective framework.

Findings

Branch-and-cut outperforms MIP formulation in computational tests.

User preferences significantly influence optimal mode assignment.

Time-dependent travel times affect solution strategies.

Abstract

The aim of the bi-objective multimodal car-sharing problem (BiO-MMCP) is to determine the optimal mode of transport assignment for trips and to schedule the routes of available cars and users whilst minimizing cost and maximizing user satisfaction. We investigate the BiO-MMCP from a user-centred point of view. As user satisfaction is a crucial aspect in shared mobility systems, we consider user preferences in a second objective. Users may choose and rank their preferred modes of transport for different times of the day. In this way we account for, e.g., different traffic conditions throughout the planning horizon. We study different variants of the problem. In the base problem, the sequence of tasks a user has to fulfill is fixed in advance and travel times as well as preferences are constant over the planning horizon. In variant 2, time-dependent travel times and preferences are introduced. In variant 3, we examine the challenges when allowing additional routing decisions. Variant 4 integrates variants 2 and 3. For this last variant, we develop a branch-and-cut algorithm which is embedded in two bi-objective frameworks, namely the $\epsilon$-constraint method and a weighting binary search method. Computational experiments show that the branch-and cut algorithm outperforms the MIP formulation and we discuss changing solutions along the Pareto frontier.