Algorithms for Flows over Time with Scheduling Costs

Dario Frascaria*, Neil Olver

*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review


Flows over time have received substantial attention from both an optimization and (more recently) a game-theoretic perspective. In this model, each arc has an associated delay for traversing the arc, and a bound on the rate of flow entering the arc; flows are time-varying. We consider a setting which is very standard within the transportation economic literature, but has received little attention from an algorithmic perspective. The flow consists of users who are able to choose their route but also their departure time, and who desire to arrive at their destination at a particular time, incurring a scheduling cost if they arrive earlier or later. The total cost of a user is then a combination of the time they spend commuting, and the scheduling cost they incur. We present a combinatorial algorithm for the natural optimization problem, that of minimizing the average total cost of all users (i.e., maximizing the social welfare). Based on this, we also show how to set tolls so that this optimal flow is induced as an equilibrium of the underlying game.

Original languageEnglish
Title of host publicationInteger Programming and Combinatorial Optimization
Subtitle of host publication21st International Conference, IPCO 2020, London, UK, June 8–10, 2020, Proceedings
EditorsDaniel Bienstock, Giacomo Zambelli
Number of pages14
ISBN (Electronic)9783030457716
ISBN (Print)9783030457709
Publication statusPublished - 2020
Event21st International Conference on Integer Programming and Combinatorial Optimization, IPCO 2020 - London, United Kingdom
Duration: 8 Jun 202010 Jun 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12125 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference21st International Conference on Integer Programming and Combinatorial Optimization, IPCO 2020
Country/TerritoryUnited Kingdom


  • Flows over time
  • Tolls
  • Traffic


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