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Revenue Maximization in Transportation Networks

Authors Kshipra Bhawalkar, Kostas Kollias, Manish Purohit

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Kshipra Bhawalkar
  • Google Research, Mountain View, CA, USA
Kostas Kollias
  • Google Research, Mountain View, CA, USA
Manish Purohit
  • Google Research, Mountain View, CA, USA

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Kshipra Bhawalkar, Kostas Kollias, and Manish Purohit. Revenue Maximization in Transportation Networks. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 26:1-26:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


We study the joint optimization problem of pricing trips in a transportation network and serving the induced demands by routing a fleet of available service vehicles to maximize revenue. Our framework encompasses applications that include traditional transportation networks (e.g., airplanes, buses) and their more modern counterparts (e.g., ride-sharing systems). We describe a simple combinatorial model, in which each edge in the network is endowed with a curve that gives the demand for traveling between its endpoints at any given price. We are supplied with a number of vehicles and a time budget to serve the demands induced by the prices that we set, seeking to maximize revenue. We first focus on a (preliminary) special case of our model with unit distances and unit time horizon. We show that this version of the problem can be solved optimally in polynomial time. Switching to the general case of our model, we first present a two-stage approach that separately optimizes for prices and routes, achieving a logarithmic approximation to revenue in the process. Next, using the insights gathered in the first two results, we present a constant factor approximation algorithm that jointly optimizes for prices and routes for the supply vehicles. Finally, we discuss how our algorithms can handle capacitated vehicles, impatient demands, and selfish (wage-maximizing) drivers.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Pricing
  • networks
  • approximation algorithms


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  1. Reza Alijani, Siddhartha Banerjee, Sreenivas Gollapudi, Kostas Kollias, and Kamesh Munagala. The segmentation-thickness tradeoff in online marketplaces. POMACS, 3(1):18:1-18:26, 2019. Google Scholar
  2. Siddhartha Banerjee, Daniel Freund, and Thodoris Lykouris. Pricing and optimization in shared vehicle systems: An approximation framework. In Proceedings of the 2017 ACM Conference on Economics and Computation, EC '17, Cambridge, MA, USA, June 26-30, 2017, page 517, 2017. Google Scholar
  3. Siddhartha Banerjee, Sreenivas Gollapudi, Kostas Kollias, and Kamesh Munagala. Segmenting two-sided markets. In Proceedings of the 26th International Conference on World Wide Web, WWW 2017, Perth, Australia, April 3-7, 2017, pages 63-72, 2017. Google Scholar
  4. Siddhartha Banerjee, Ramesh Johari, and Carlos Riquelme. Pricing in ride-sharing platforms: A queueing-theoretic approach. In Proceedings of the Sixteenth ACM Conference on Economics and Computation, EC '15, Portland, OR, USA, June 15-19, 2015, page 639, 2015. Google Scholar
  5. Nikhil Bansal, Avrim Blum, Shuchi Chawla, and Adam Meyerson. Approximation algorithms for deadline-tsp and vehicle routing with time-windows. In Proceedings of the 36th Annual ACM Symposium on Theory of Computing, Chicago, IL, USA, June 13-16, 2004, pages 166-174, 2004. Google Scholar
  6. Kostas Bimpikis, Ozan Candogan, and Daniela Sabán. Spatial pricing in ride-sharing networks. Operations Research, 67(3):744-769, 2019. Google Scholar
  7. Avrim Blum, Shuchi Chawla, David R. Karger, Terran Lane, Adam Meyerson, and Maria Minkoff. Approximation algorithms for orienteering and discounted-reward TSP. SIAM J. Comput., 37(2):653-670, 2007. Google Scholar
  8. Juan-Camilo Castillo, Dan Knoepfle, and Glen Weyl. Surge pricing solves the wild goose chase. In Proceedings of the 2017 ACM Conference on Economics and Computation, EC '17, Cambridge, MA, USA, June 26-30, 2017, pages 241-242, 2017. Google Scholar
  9. Chandra Chekuri, Nitish Korula, and Martin Pál. Improved algorithms for orienteering and related problems. ACM Trans. Algorithms, 8(3):23:1-23:27, 2012. Google Scholar
  10. George B. Dantzig and J. H. Ramser. The truck dispatching problem. Management Science, 6(1):80-91, 1959. Google Scholar
  11. Gilbert Laporte. The vehicle routing problem: An overview of exact and approximate algorithms. European Journal of Operational Research, 59:345-358, 1992. Google Scholar
  12. Hongyao Ma, Fei Fang, and David C. Parkes. Spatio-temporal pricing for ridesharing platforms. In Proceedings of the 2019 ACM Conference on Economics and Computation, EC 2019, Phoenix, AZ, USA, June 24-28, 2019., page 583, 2019. Google Scholar
  13. Viswanath Nagarajan and R. Ravi. The directed orienteering problem. Algorithmica, 60(4):1017-1030, 2011. Google Scholar
  14. Michael Ostrovsky and Michael Schwarz. Carpooling and the economics of self-driving cars. In Proceedings of the 2019 ACM Conference on Economics and Computation, EC 2019, Phoenix, AZ, USA, June 24-28, 2019., pages 581-582, 2019. Google Scholar
  15. Alice Paul, Daniel Freund, Aaron Ferber, David B. Shmoys, and David P. Williamson. Prize-collecting TSP with a budget constraint. In 25th Annual European Symposium on Algorithms, ESA 2017, September 4-6, 2017, Vienna, Austria, pages 62:1-62:14, 2017. Google Scholar
  16. Duncan Rheingans-Yoo, Scott Duke Kominers, Hongyao Ma, and David C. Parkes. Ridesharing with driver location preferences. In Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, IJCAI 2019, Macao, China, August 10-16, 2019, pages 557-564, 2019. Google Scholar
  17. Ola Svensson, Jakub Tarnawski, and László A. Végh. A constant-factor approximation algorithm for the asymmetric traveling salesman problem. J. ACM, 67(6):37:1-37:53, 2020. Google Scholar
  18. Adrian Vetta. Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions. In 43rd Symposium on Foundations of Computer Science (FOCS 2002), 16-19 November 2002, Vancouver, BC, Canada, Proceedings, page 416, 2002. Google Scholar
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