The aim of this paper is twofold: first, to extend the area of applicationsof tropical optimization by solving new constrained location problems, andsecond, to offer new closed-form solutions to general problems that are ofinterest to location analysis. We consider a constrained minimaxsingle-facility location problem with addends on the plane with rectilineardistance. The solution commences with the representation of the problem in astandard form, and then in terms of tropical mathematics, as a constrainedoptimization problem. We use a transformation technique, which can act as atemplate to handle optimization problems in other application areas, and henceis of independent interest. To solve the constrained optimization problem, weapply methods and results of tropical optimization, which provide direct,explicit solutions. The results obtained serve to derive new solutions of thelocation problem, and of its special cases with reduced sets of constraints, ina closed form, ready for practical implementation and immediate computation. Asillustrations, numerical solutions of example problems and their graphicalrepresentation are given. We conclude with an application of the results tooptimal location of the central monitoring facility in an indoor videosurveillance system in a multi-floor building environment.
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