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A periodic optimization approach to dynamic pickup and delivery problems with time windows

Abstract

In dynamic pickup and delivery problems with time windows (PDPTWs), potentially urgent request information is released over time. This gradual data availability means the decision-making process must be continuously repeated. These decisions are therefore likely to deteriorate in quality as new information becomes available. It is still believed that the state of the art for this problem remains far from reaching maturity due to the distinct absence of algorithms and tools for obtaining high-quality solutions within reasonable computational runtimes. This paper proposes a periodic approach to the dynamic PDPTW based on buffering, more specifically a two-step scheduling heuristic which consists of the cheapest insertion followed by a local search. The heuristic’s performance is assessed by comparing its results against those obtained by a mixed integer linear programming model which operates under the assumption that all information is available in advance. Results illustrate how the performance is impacted by urgency levels, the degree of dynamism associated with request arrivals and re-optimization frequency. The findings indicate that increases in dynamism improve solution quality, whereas increases in urgency have the opposite effect. In addition, the proposed approach’s performance is only slightly affected by re-optimization frequency when changing these two characteristics.

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Acknowledgements

Wim Vancroonenburg is a postdoctoral research fellow at Research Foundation Flanders - FWO Vlaanderen. This research is funded by FWO as part of ORDinL (Operational Research and Data science in Logistics) project under the Strategic Basic Research (SBO) programme. Editorial consultation is provided by Luke Connolly (KU Leuven).

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Appendix: Terminology

Appendix: Terminology

List of notations

\(\theta _i\) Input element i S Set of feasible solutions
ET Execution time, re-optimization step length \(\Theta \) Set of the PDPTW’s instances
\(p_i\) A task i’s service time \(\theta \) The PDPTW instance
\([st_i,dt_i)\) Time window of task i R Set of all requests
UW Urgency window \(T^p\) Set of all pickup tasks
\([st_{k},dt_{k})\) Vehicle k ’s availability time window \(T^d\) Set of all delivery tasks
\(\tau \) Scheduling horizon length T Set of all tasks (\(T=T^p \cup T^d\))
V Fleet of vehicles V Set of all vehicles
\(\varepsilon \) All request arrival events VK Set of all undispatched vehicles
\(Ct_i\) Task i’s completion time RL Set of all eligible requests
\(ot_{k}\) Vehicle k’s overtime \(UR_t\) Set of unprocessed requests at time t
\(d_{ij}\) Travel time from location i to j \(CP_t\), Set of currently processing requests at time t
\(l_{i}\) Tardiness of task i \(CE_t\) Set of currently executing requests at time t
\(ot_{k}\) Overtime of vehicle k. \(FR_t\) Set of finished requests

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Karami, F., Vancroonenburg, W. & Vanden Berghe, G. A periodic optimization approach to dynamic pickup and delivery problems with time windows. J Sched 23, 711–731 (2020). https://doi.org/10.1007/s10951-020-00650-x

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  • DOI: https://doi.org/10.1007/s10951-020-00650-x

Keywords

  • Buffering
  • Dynamic pickup and delivery problems
  • Dynamism
  • Logistics
  • Urgency