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The constrained shortest path problem

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  • Y. P. Aneja
  • K. P. K. Nair

Abstract

The shortest path problem between two specified nodes in a general network possesses the unimodularity property and, therefore, can be solved by efficient labelling algorithms. However, the introduction of an additional linear constraint would, in general, destroy this property and the existing algorithms are not applicable in this case. This paper presents a parametric approach for solving this problem. The algorithm presented would require, on the average, a number of iterations which is polynomially bounded. The similarity of this approach to that of the generalized Lagrange multiplier technique is demonstrated and a numerical example is presented.

Suggested Citation

  • Y. P. Aneja & K. P. K. Nair, 1978. "The constrained shortest path problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 25(3), pages 549-555, September.
    • Handle: RePEc:wly:navlog:v:25:y:1978:i:3:p:549-555
    DOI: 10.1002/nav.3800250314
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    Cited by:

    1. Nir Halman & Mikhail Y. Kovalyov & Alain Quilliot & Dvir Shabtay & Moshe Zofi, 2019. "Bi-criteria path problem with minimum length and maximum survival probability," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(2), pages 469-489, June.

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