TY - JOUR

T1 - The shortest path problem with two objective functions

AU - Henig, Mordechai I.

PY - 1986/5

Y1 - 1986/5

N2 - We present methods to find the shortest path in a network where each path is associated with two objectives. We describe how to obtain the nondominated paths and the extreme nondominated paths, and compare the expected complexity of the methods. An improvement in efficiency can be obtained when quasiconcave or quasiconvex utility functions are assumed. In the first case, we describe how to find the optimal extreme nondominated path and bounds for the optimal path value. Then the optimal path can be located by calculating the k-th shortest path. In the second case we suggest a branch and bound method to solve the problem.

AB - We present methods to find the shortest path in a network where each path is associated with two objectives. We describe how to obtain the nondominated paths and the extreme nondominated paths, and compare the expected complexity of the methods. An improvement in efficiency can be obtained when quasiconcave or quasiconvex utility functions are assumed. In the first case, we describe how to find the optimal extreme nondominated path and bounds for the optimal path value. Then the optimal path can be located by calculating the k-th shortest path. In the second case we suggest a branch and bound method to solve the problem.

KW - Dynamic programming

KW - multiattribute utility

KW - networks

UR - http://www.scopus.com/inward/record.url?scp=0022711421&partnerID=8YFLogxK

U2 - 10.1016/0377-2217(86)90092-5

DO - 10.1016/0377-2217(86)90092-5

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AN - SCOPUS:0022711421

SN - 0377-2217

VL - 25

SP - 281

EP - 291

JO - European Journal of Operational Research

JF - European Journal of Operational Research

IS - 2

ER -