Sensitivity analysis in continuous location models via interval analysis (Q2708110)

Review: The paper is focused on processing of uncertain parameter values. Difficulty of parameter determination emerges whenever model of strategical decision is formed and some costs or weights must be estimated to describe an impact of the decisions to objective function. The exact determination of the costs or weights is usually difficult or impossible task, but in many cases it is possible to obtain an interval within which they are known to vary. The authors devoted their attention to a general continuous location problem and assumed that each parameter of the model is known to lie in a given interval. They employed interval analysis and presented new way for dealing with the uncertainty of the parameters which occur in the model formulation. They constituted so called perturbed problem by means of interval analysis and covered the set of feasible solutions by \(n\)-dimensional intervals -- boxes. Then they suggested an algorithm, which finds upper bound of the optimal solution and specifies set of points which are near to optimal solutions for particular values of the parameters. The algorithm is based on processing of the boxes. During the process a box may be discarded in accordance to several rules, which prove that the box does not contain good solution. In the case, when a box can not be discarded, splitting of the box is performed and the both resulting boxes are processed separately in the next steps. The algorithm was verified using a set of generated location problems and the results were reported in the end of the paper together with some suggestion on precision and computation time reduction.