Single-vehicle scheduling problem on a straight line with time window constraints

  • Chi-lok Chan
  • Gilbert H. Young
Session 11A: Scheduling
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)


The problem of single-vehicle scheduling with ready time and deadline constraints can be applicable to many practical transportation problems. But the general case is a generalization of classical Traveling Salesman Problem and it is NP-hard. Psaraftis et al. [5] presented an O(n2) algorithm for vehicle scheduling problems where the topological structure of sites are restricted to straight line and there is no deadline for each site. They conjectured that this problem is NP-hard if each site has an arbitrary ready time and deadline (called time window). In this paper, we prove the conjecture and show that the decision versions of vehicle scheduling problems on a straight line topology with time window are NP-complete for both path and tour versions. We also give an O(n2) algorithm to solve a special case of this problem in which all sites have a common ready time. This algorithm is applicable to both path and tour versions.


deadline NP-complete optimal schedule ready time vehicle scheduling problem time windows 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Chi-lok Chan
    • 1
  • Gilbert H. Young
    • 1
  1. 1.High Performance Computing Laboratory Department of Computer ScienceThe Chinese University of Hong KongShatin, N.T.Hong Kong

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