TY - JOUR

T1 - A relationship between optimality and efficiency in multicriteria 0-1 programming problems

AU - Burkard, Rainer Ernst

AU - Keiding, H.

AU - Krarup, J.

AU - Pruznan, P.M.

PY - 1981

Y1 - 1981

N2 - An efficient or nondominated solution to a multicriteria minimization problem is a feasible solution for which a decrease in the value of any criterion can only be obtained if the value of at least one other criterion is increased. Interest in the conditions under which solutions to multicriteria programming problems can be shown to be efficient has grown enormously in recent years, not least of all due to the awareness that significant planning problems can only be meaningfully modelled if multiple measures of effectiveness are considered. However, the broad class of multicriteria 0-1 programming problems, which are of great practical importance, has received only limited attention in the literature. We establish the identity of the set of efficient solutions with respect to such multicriteria programming problems with any criteria and any constraint set and the set of optimal solutions to a parametrized unicriterion problem incorporating these criteria. Illustrative numerical examples are provided.

AB - An efficient or nondominated solution to a multicriteria minimization problem is a feasible solution for which a decrease in the value of any criterion can only be obtained if the value of at least one other criterion is increased. Interest in the conditions under which solutions to multicriteria programming problems can be shown to be efficient has grown enormously in recent years, not least of all due to the awareness that significant planning problems can only be meaningfully modelled if multiple measures of effectiveness are considered. However, the broad class of multicriteria 0-1 programming problems, which are of great practical importance, has received only limited attention in the literature. We establish the identity of the set of efficient solutions with respect to such multicriteria programming problems with any criteria and any constraint set and the set of optimal solutions to a parametrized unicriterion problem incorporating these criteria. Illustrative numerical examples are provided.

U2 - 10.1016/0305-0548(81)90011-3

DO - 10.1016/0305-0548(81)90011-3

M3 - Article

VL - 8

SP - 241

EP - 247

JO - Computers & operations research

JF - Computers & operations research

SN - 0305-0548

IS - 4

ER -