Rj. Gallagher et Oa. Saleh, CONSTRUCTING THE SET OF EFFICIENT OBJECTIVE VALUES IN LINEAR MULTIPLE-OBJECTIVE TRANSPORTATION PROBLEMS, European journal of operational research, 73(1), 1994, pp. 150-163
Citations number
22
Categorie Soggetti
Management,"Operatione Research & Management Science
A forward dynamic programming approach is utilized to find an algebrai
c representation for a polyhedron in objective space associated with a
multiple objective transportation problem having k linear objectives.
This polyhedron has the same efficient structure as the set of all fe
asible objective values, and moreover all of its vertices are efficien
t. The algebraic representation of this polyhedron is of the form {y i
s-an-element-of R(k): Hy greater-than-or-equal-to Ua + Vd}, where the
matrices H, U and V are independent of the vector a of availabilities
and vector d of demands. The procedure is illustrated by the numerical
example of Isermann [H. Isermann, ''The enumeration of all efficient
solutions for a linear multiple-objective transportation problem'', Na
val Research Logistics Quarterly 26 (1979) 123-139].