Single-vehicle scheduling problem on a straight line with time window constraints
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.  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.
Keywordsdeadline NP-complete optimal schedule ready time vehicle scheduling problem time windows
Unable to display preview. Download preview PDF.
- 1.L. Bodin, B. Golden, A. Assad, and M. Ball. ”Routing and Scheduling of Vehicles and Crews: The State of the Art”. Computers and Operations Research, vol 10:pp. 62–212, 1983.Google Scholar
- 2.M.R. Garey and D.S. Johnson. ”Computers and Intractability: A Guide to the Theory of NP-Completeness”. Freeman, 1979.Google Scholar
- 3.Y. Karuno, H. Nagamochi, and T. Ibaraki. ”Vehicle Scheduling on a Tree with Release and Handling Times”. In ”Lecture Notes in Computer Science(762)”, pages 486–495, 1993.Google Scholar
- 4.H. Psaraftis. ”An Exact Algorithm for the Single Vehicle Dial-A-Ride Problem with Time Windows”. Transportation Science, vol 17:pp. 351–357, 1983.Google Scholar
- 5.H. Psaraftis, M. Solomon, L. Magnanti, and Tai-Up Kim. ”Routing and Scheduling on a Shoreline with Release Times”. Management Science, vol 36:pp. 212–223, February 1990.Google Scholar