Optimizing Ride-Matching in Urban Transportation: A Rank Maximal Matching Approach for Cab Allocation

In this project, "Optimizing Ride-Matching in Urban Transportation: A Rank-Maximal Matching Approach for Cab Allocation", we show that matching algorithms can enhance efficiency and fairness in cab allocation systems. The system employs the Rank-Maximal Matching (RMM) algorithm in which passenger preferences are prioritized while ensuring drivers have roughly equal overall utilization. Therefore, the RMM algorithm matches the highest number of passengers possible to their preferred available driver, maximizing rider comfort and quality of service.   The modeling of the problem uses bipartite graph theory to represent two distinct groups: passengers and drivers, with edges that represent the passenger’s preferences. RMM leverages lexicographic optimization to efficiently obtain the maximal matches first of all possible matches at rank one, then rank two, etc. The resulting system maximizes matches and is preference-driven and fair, while still being efficient in dynamic conditions and new ride requests or driver cancellations. Experimental data and simulation results suggest that the new approach will result in improvements in matching accuracy, user satisfaction, and overall system responsiveness compared to traditional distance-based and random matching methods. The feedback cycle may also increase service standards among drivers, creating an overall sense of accountability and trust in the ride-hailing platform.   However, the project identifies issues associated with the computational cost of processing large amounts of data, as well as the need for real-time optimization for high-density urban environments. Future work could involve incorporating machine learning models for predictive matching, reinforcement learning for adapting the model, and multi- objective optimization to make the system more efficient, fair, and profitable at once.     In closing, the project shows Rank-Maximal Matching provides a scalable, fair, and user-oriented approach to the new challenges that are present in ride-hailing and urban transport. The project can also serve as a baseline for future smart mobility systems that have a priority on operational efficiency and human user satisfaction.

[1]    P. Ghosal, A. Kunysz, and K. Paluch, “The Dynamics of Rank-Maximal   and         Popular       Matchings,”   Theoretical Computer Science, 2023. https://www.sciencedirect.com/science/article/pii/S030439752 3003961   [2]    E. Magsino, C.-C. Huang, and J. Garg, “Evaluating Stable Matching Methods and Ridesharing Techniques in Optimizing Passenger Transportation Cost and Companionship,” 2022. https://www.researchgate.net/publication/365261356_Evaluati ng_Stable_Matching_Methods_and_Ridesharing_Techniques _in_Optimizing_Passenger_Transportation_Cost_and_Compa nionship [3]   J. Peters, “Online Elicitation of Necessarily Optimal Matchings,” 2022.https://cdn.aaai.org/ojs/20451/20451-13-24464-1-2- 20220628.pdf [4]   H. Hosseini, R. Vaish, and P. Chaudhury, “Necessarily Optimal One-Sided Matchings,” 2021. https://www.researchgate.net/publication/363391183_Necessa rily_Optimal_One-Sided_Matchings [5]   O. F. Aydin, M. Kandemir, and A. Magdy, “Matching Algorithm for Improving Ridesharing by Incorporating Route Splits and Social Factor,” 2020. https://www.researchgate.net/publication/339710215_Matchin g_algorithm_for_improving_ride- sharing_by_incorporating_route_splits_and_social_factors   [6]   M. Nasre, P. Nimbhorkar, and B. R. Chaudhury, “Dichotomy Results for Classified Rank-Maximal Matchings and Popular Matchings,” 2018. https://www.researchgate.net/publication/325034230_Dichoto my_Results_for_Classified_Rank-Maximal_Matchings_and_Popular_Matchings   [7]   D. Zhao, D. Zhang, M. Khan, and L. Perrussel, “Maximal Matching for Double Auction,” 2010. https://www.researchgate.net/publication/220935855_Maxima l_Matching_for_Double_Auction   [8]    R. W. Irving, T. Kavitha, K. Mehlhorn, D. Michail, and K. Paluch, “Rank-Maximal Matchings,” ACM Transactions on Algorithms, vol. 2, no. 4, pp. 602–610, 2006. https://www.researchgate.net/publication/220390476_Rank- Maximal_Matchings?_sg=0lNuvZF5PfMZevrl9WMljk6g71v 0mQvztpOrUUmHi3KsmugSjwY7b8ZUlwWP4FxOI27ICUy cbiyb2ds&_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InB1 YmxpY2F0aW9uIiwicGFnZSI6Il9kaXJlY3QifX0