## DYNAMIC SHORTEST PATHS MINIMIZING TRAVEL TIMES AND COSTS

##### Author(s)

Ahuja, Ravindra; Orlin, James; Pallottino, Stefano; Scutella, Maria
Download4390-02.pdf (226.0Kb)

##### Metadata

Show full item record##### 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 light

##### Date issued

2003-01-27##### Series/Report no.

MIT Sloan School of Management Working Paper;4390-02

##### Keywords

Dynamic shortest path, arc travel, FIFO networks