Parametric Analysis of Fixed Costs in Uncapacitated Facility Location
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Solving facility location problems does not only require to compute optimal or nearby optimal solutions, but also to perform a sensitivity and parametric analysis. It is necessary to provide insight into the behaviour of the total cost in dependence on the number of facilities to locate and into the possible variations of the data, which do not affect the optimality of a solution. Such an information is needed because locational decisions have a long-term planning horizon and the cost and demand data are subject to unforeseeable changes. Furthermore, only the information of the cost curve in the neighborhood of the optimum allows the decision maker to assess the consequences of a deviation from the optimal solution, which may be desirable for certain reasons.
Regarding the Uncapacitated Facility Location Problem (UFLP), such a sensitivity and parametric analysis of the fixed costs can be done by means of Lagrangean relaxation. In this paper, we will describe this approach theoretically and demonstrate its use on two real depot location problems.
KeywordsVariable Cost Lagrangean Relaxation Cost Curve Perturbation Function Open Depot
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