TY - JOUR

T1 - Some relationships between multicriteria and parametric discrete optimization problems with bottleneck objectives

AU - Burkard, Rainer Ernst

AU - Krarup, J.

AU - Pruznan, P.M.

N1 - Published online: 01 Dec 2008

PY - 1984

Y1 - 1984

N2 - Relations between efficient solutions to discrete multicriteria decision problems and optimal solutions to corresponding parametric single-criterion problems are analyzed. In particular we consider such decision problems where one criterion is a sum function while the remaining criteria are bottleneck functions. In this case the multi-criteria problem can be reduced to a linear parametric sum problem. Depending upon the nature of its feasible set, the sum problem may belong to a class of computationally tractable optimization problems, By solving it parametrically we can then generate the set of all efficient solutions to the original multicriteria problem.

AB - Relations between efficient solutions to discrete multicriteria decision problems and optimal solutions to corresponding parametric single-criterion problems are analyzed. In particular we consider such decision problems where one criterion is a sum function while the remaining criteria are bottleneck functions. In this case the multi-criteria problem can be reduced to a linear parametric sum problem. Depending upon the nature of its feasible set, the sum problem may belong to a class of computationally tractable optimization problems, By solving it parametrically we can then generate the set of all efficient solutions to the original multicriteria problem.

U2 - 10.1080/02331938408842953

DO - 10.1080/02331938408842953

M3 - Article

SN - 0323-3898

VL - 15

SP - 389

EP - 395

JO - Mathematische Operationsforschung und Statistik / Series Optimization

JF - Mathematische Operationsforschung und Statistik / Series Optimization

IS - 3

ER -