Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state-space-time network representations

Monirehalsadat Mahmoudi, Xuesong Zhou

Research output: Contribution to journalArticle

89 Scopus citations

Abstract

Optimization of on-demand transportation systems and ride-sharing services involves solving a class of complex vehicle routing problems with pickup and delivery with time windows (VRPPDTW). This paper first proposes a new time-discretized multi-commodity network flow model for the VRPPDTW based on the integration of vehicles' carrying states within space-time transportation networks, so as to allow a joint optimization of passenger-to-vehicle assignment and turn-by-turn routing in congested transportation networks. Our three-dimensional state-space-time network construct is able to comprehensively enumerate possible transportation states at any given time along vehicle space-time paths, and further allows a forward dynamic programming solution algorithm to solve the single vehicle VRPPDTW problem. By utilizing a Lagrangian relaxation approach, the primal multi-vehicle routing problem is decomposed to a sequence of single vehicle routing sub-problems, with Lagrangian multipliers for individual passengers' requests being updated by sub-gradient-based algorithms. We further discuss a number of search space reduction strategies and test our algorithms, implemented through a specialized program in C++, on medium-scale and large-scale transportation networks, namely the Chicago sketch and Phoenix regional networks.

Original languageEnglish (US)
Pages (from-to)19-42
Number of pages24
JournalTransportation Research Part B: Methodological
Volume89
DOIs
StatePublished - Jul 1 2016

Keywords

  • Forward dynamic programming
  • Lagrangian relaxation
  • Ride-sharing service optimization
  • Time-dependent least-cost path problem
  • Vehicle routing problem with pickup and delivery with time windows

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Transportation

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