### Description

The projekt deals with efficiently solvable variants of location problems. The project splits up into three subareas: semi-obnoxious location problems, inverse location problems and location problems with budget constraints. In all areas our main focus lies on the development of efficient algorithms for the solution of the considered location problems.

In classical location problems, each client wishes to have its closest facility as near to itself as possible. In semi-obnoxious facility location problems, we treat the case of facilities for which closeness is desirable only for some clients while other clients prefer the facilities to be as far away as possible.

Inverse location problems deal with modifying a set of input parameters at minimum cost such that a given feasible solution of the underlying location problem becomes optimal.

The third subarea is concerned with three classes of location problems with budget constraints. Given a limited budget and a set of input parameters of the location problem that can be changed, the goal in improvement problems is to change the parameters within the given budget in such a way so as to improve the quality of an already given solution or of a new optimal solution of the location problem under investigation as much as possible. There also exist variants where the aim is to degrade the quality instead of improving it.

In classical location problems, each client wishes to have its closest facility as near to itself as possible. In semi-obnoxious facility location problems, we treat the case of facilities for which closeness is desirable only for some clients while other clients prefer the facilities to be as far away as possible.

Inverse location problems deal with modifying a set of input parameters at minimum cost such that a given feasible solution of the underlying location problem becomes optimal.

The third subarea is concerned with three classes of location problems with budget constraints. Given a limited budget and a set of input parameters of the location problem that can be changed, the goal in improvement problems is to change the parameters within the given budget in such a way so as to improve the quality of an already given solution or of a new optimal solution of the location problem under investigation as much as possible. There also exist variants where the aim is to degrade the quality instead of improving it.

Status | Finished |
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Effective start/end date | 1/07/06 → 1/07/09 |