Dynamic Shortest Paths Minimizing Travel Times and Costs

16 Pages Posted: 26 Oct 2002

See all articles by Ravindra K. Ahuja

Ravindra K. Ahuja

University of Florida - Department of Industrial and Systems Engineering

James B. Orlin

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Stefano Pallottino

University of Pisa - Department of Information Science

Maria G. Scutella

University of Pisa - Department of Information Science

Date Written: August 2002

Abstract

In this paper, we study dynamic shortest path problems that determine a shortest path from a specified source node to every other node in the network where arc travel times change dynamically. We consider two problems: the minimum time walk problem and the minimum cost walk problem. The minimum time walk problem is to find a walk with the minimum travel time. The minimum cost walk problem is to find a walk with the minimum weighted sum of the travel time and the excess travel time (over the minimum possible travel time). The minimum time walk problem is known to be polynomially solvable for a class of networks called FIFO networks. In this paper: (i) we show that the minimum cost walk problem is an NP-hard problem; (ii) we develop a pseudopolynomial-time algorithm to solve the minimum cost walk problem (for integer travel times); and (iii) we develop a polynomial-time algorithm for the minimum time walk problem arising in road networks with traffic lights.

Keywords: Node, Minimum Cost Walk Problem, Polynomially, FIFO Networks, NP-hard Problem

Suggested Citation

Ahuja, Ravindra K. and Orlin, James B. and Pallottino, Stefano and Scutella, Maria G., Dynamic Shortest Paths Minimizing Travel Times and Costs (August 2002). Available at SSRN: https://ssrn.com/abstract=344442 or http://dx.doi.org/10.2139/ssrn.344442

Ravindra K. Ahuja

University of Florida - Department of Industrial and Systems Engineering ( email )

303 Weil Hall
Gainesville, FL 32611-6595
United States

James B. Orlin (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

E53-357
Cambridge, MA 02142
United States
617-253-6606 (Phone)
617-258-7579 (Fax)

Stefano Pallottino

University of Pisa - Department of Information Science ( email )

Pisa
Italy

Maria G. Scutella

University of Pisa - Department of Information Science ( email )

Pisa
Italy

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