The Competitive Pickup and Delivery Orienteering Problem for Balancing Car-Sharing Systems

Abstract

Competition between one-way car-sharing operators is currently increasing. Fleet relocation as a means to compensate demand imbalances constitutes a major cost factor in a business with low profit margins. Existing decision support models have so far ignored the aspect of a competitor when the fleet is rebalanced for better availability. We present mixed-integer linear programming formulations for a pickup and delivery orienteering problem under different business models with multiple (competing) operators. Structural solution properties, including existence of equilibria and bounds on losses as a result of competition, of the competitive pickup and delivery problem under the restrictions of unit-demand stations, homogeneous payoffs, and indifferent customers based on results for congestion games are derived. Two algorithms to find a Nash equilibrium for real-life instances are proposed. One can find equilibria in the most general case; the other can only be applied if the game can be represented as a congestion game, that is, under the restrictions of homogeneous payoffs, unit-demand stations, and indifferent customers. In a numerical study, we compare different business models for car-sharing operations, including a merger between operators and outsourcing relocation operations to a common service provider (coopetition). Gross profit improvements achieved by explicitly incorporating competitor decisions are substantial, and the presence of competition decreases gross profits for all operators (compared with a merger). Using a Munich, Germany, case study, we quantify the gross profit gains resulting from considering competition as approximately 35% (over assuming absence of competition) and 12% (over assuming that the competitor is omnipresence) and the losses because of the presence of competition to be approximately 10%.

Rebalancing in Shared Mobility Systems – Competition, Feature-Based Mode Selection and Technology Choice

“…We further observe that market segmentation (two or more operators who consider competition) is substantially less profitable than a single operator, since rebalancing operations cannot be pooled as easily. Chapter 3 is based on Martin et al (2020b).…”

Joint Optimization of Allocations and Relocations in One-Way Carsharing Systems with Two Operators

“…The studies above all focused on the allocation problem in single-operator carsharing systems. While the carsharing market develops continuously, it is common for multiple operators to coexist in a carsharing system, and Martin et al [3] also pointed out that considering other operators has a huge impact on the profitability of all operators. Unlike studies on single-operator carsharing systems, there are interactions among operators in multiple-operator systems, specifically in allocations and demands.…”

“…Most research focuses on one-way carsharing systems with a single operator. While multiple operators coexist in the same city or zone, the performance of this kind of system is worth exploring [3].…”