In minisum multifacility location problems one has to find locations
for several new facilities such that the total interaction cost between all
the new as well as between the new and some old facilties given is minimized.
Due to its inherent nondifferentiability, this problem is considered as hard
to solve. In this thesis, a concept for reducing the complexity of the
problem is proposed. The number of unknowns and the number of terms
nondifferentiable in a minimum of the objective function can be reduced
simultaneously by considering so-called attraction conditions. These
attraction conditions are formulated for problems with attracting and
repelling facilities and in which several different distance concepts are
used simultaneously. It is shown that all other attraction conditions known
in the literature can be derived as special cases from the conditions proposed
here. Moreover, a polynomial time complexity algorithm is derived for
checking these conditions. Numerical results confirm that in this way the
computation time for solving a problem is decreased, while simultaneously
the quality of the solution computed is increased. Furthermore, a scheme
for modeling location problems in inhomogeneous spaces with or without
barriers to travel and the numerical treatment of problems of this type is
proposed.