Note—On the Maximal Covering Location Problem and the Generalized Assignment Problem

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Abstract
In many public sector location problems, it is often desirable to locate facilities in such a way to minimize the number (or cost) of facilities while insuring tint all demand centers are within a stated maximal service time front any facility. However, when insufficient resources exist to allow die construction of enough facilities to serve all demand centers within the alloted time, the location problem is frequently restated in order to locate the budgeted facilities to serve the serviced population. Problems of the latter type are generally known as maximal covering location problems, which may have a number of extensions, including mandatory closeness constraints which place an upper bound on the maximal service time requirement for the entire population. This note demonstrates how this class of frequently encountered problems can be formulated as generalized assignment problems within the conceptual framework presented by Ross and Soland (Ross, G. T., R. Soland. 1977. Modeling facility location problems as generalized assignment problems. Management Sci. 24 (3, November) 345–357.) for other discrete public and private location problems.

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