The quickest path problem with interval lead times

In this paper, a version of the quickest path problem is considered in which arc capacities are fixed but lead times are expressed as intervals on real line. By considering order relations that represent the decision maker's preference between interval transmission times, we show that the problem can be solved by transforming it into a sequence of bicriteria shortest path problems in properly defined networks.

[1]  Pierre Hansen,et al.  Bicriterion Path Problems , 1980 .

[2]  Johannes Jahn,et al.  Recent Advances and Historical Development of Vector Optimization , 1987 .

[3]  Michael H. Moore.  On the Fastest Route for Convoy-Type Traffic in Flowrate-Constrained Networks , 1976 .

[4]  S. Chanas,et al.  Multiobjective programming in optimization of interval objective functions -- A generalized approach , 1996 .

[5]  D. Shier,et al.  An empirical investigation of some bicriterion shortest path algorithms , 1989 .

[6]  G. Alefeld,et al.  Introduction to Interval Computation , 1983 .

[7]  Yen-Liang Chen,et al.  An algorithm for finding the k quickest paths in a network , 1993, Comput. Oper. Res..

[8]  Kim Allan Andersen,et al.  A label correcting approach for solving bicriterion shortest-path problems , 2000, Comput. Oper. Res..

[9]  John W. Chinneck,et al.  Linear programming with interval coefficients , 2000, J. Oper. Res. Soc..

[10]  Ralph E. Steuer.  Algorithms for Linear Programming Problems with Interval Objective Function Coefficients , 1981, Math. Oper. Res..

[11]  Gen-Huey Chen,et al.  Distributed algorithms for the quickest path problem , 1992, Parallel Comput..

[12]  Paolo Serafini,et al.  Some Considerations about Computational Complexity for Multi Objective Combinatorial Problems , 1987 .

[13]  Arthur Warburton,et al.  Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems , 1987, Oper. Res..

[14]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[15]  Gen-Huey Chen,et al.  Algorithms for the constrained quickest path problem and the enumeration of quickest paths , 1994, Comput. Oper. Res..

[16]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[17]  Y. H. Chin,et al.  The quickest path problem , 1990, Comput. Oper. Res..

[18]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[19]  J. Ben Rosen,et al.  Algorithms for the quickest path problem and the enumeration of quickest paths , 1991, Comput. Oper. Res..

[20]  C. Zaroliagis,et al.  Transmissions in a Network with Capacities and Delays , 1999 .

[21]  James E. Falk.  Technical Note - Exact Solutions of Inexact Linear Programs , 1976, Oper. Res..