Efficient Duration-Based Workload Balancing for Interdependent Vehicle Routes

Authors Carlo S. Sartori , Pieter Smet , Greet Vanden Berghe

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Author Details

Carlo S. Sartori
  • Department of Computer Science, KU Leuven, Belgium
Pieter Smet
  • Department of Computer Science, KU Leuven, Belgium
Greet Vanden Berghe
  • Department of Computer Science, KU Leuven, Belgium


Editorial consultation provided by Luke Connolly (KU Leuven).

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Carlo S. Sartori, Pieter Smet, and Greet Vanden Berghe. Efficient Duration-Based Workload Balancing for Interdependent Vehicle Routes. In 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021). Open Access Series in Informatics (OASIcs), Volume 96, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Vehicle routing and scheduling problems with interdependent routes arise when some services must be performed by at least two vehicles and temporal synchronization is thus required between the starting times of these services. These problems are often coupled with time window constraints in order to model various real-world applications such as pickup and delivery with transfers, cross-docking and home care scheduling. Interdependent routes in these applications can lead to large idle times for some drivers, unnecessarily lengthening their working hours. To remedy this unfairness, it is necessary to balance the duration of the drivers' routes. However, quickly evaluating duration-based equity functions for interdependent vehicle routes with time windows poses a significant computational challenge, particularly when the departure time of routes is flexible. This paper introduces models and algorithms to compute two well-known equity functions in flexible departure time settings: min-max and range minimization. We explore the challenges and algorithmic complexities of evaluating these functions both from a theoretical and an experimental viewpoint. The results of this paper enable the development of new heuristic methods to balance the workload of interdependent vehicle routes with time windows.

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Computing methodologies → Temporal reasoning
  • Mathematics of computing → Graph algorithms
  • Vehicle scheduling
  • Workload balancing
  • Route duration
  • Interdependent routes
  • Time windows


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