The Optimal Location of GEODSS Sensors in Canada

This thesis studies the maximal coverage p-median and the set covering facility location problems as applied to the GEODSS location problem. The classical single-objective mathematical formulations of the p-median and set covering problems are converted into network-flow formulations and various sol...

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Bibliographic Details
Main Author: Forgues, Pierre J
Format: Report
Language:English
Subjects:
AREA COVERAGE
ARTIFICIAL SATELLITES
CANADA
CASE STUDIES
DETECTORS
EARTH ORBITS
FACILITIES
FORMULAS(MATHEMATICS)
FORTRAN 77
FUNCTIONS
GEODSS(GROUND BASED ELECTROOPTICAL DEEP SPACE SURVEILLANCE)
GROUND STATIONS
INTEGER PROGRAMMING
LINEAR PROGRAMMING
MATHEMATICAL PROGRAMMING
Miscellaneous Detection and Detectors
NETWORK FLOWS
Operations Research
OPTIMIZATION
POSITION(LOCATION)
RANK ORDER STATISTICS
SATELLITE TRACKING SYSTEMS
SITE SELECTION
SOLUTIONS(GENERAL)
SPACE SURVEILLANCE
THESES
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Summary:This thesis studies the maximal coverage p-median and the set covering facility location problems as applied to the GEODSS location problem. The classical single-objective mathematical formulations of the p-median and set covering problems are converted into network-flow formulations and various solution methods are developed using a scaled-down version of the GEODSS problem. The next step is the introduction of a second criterion function into the problem. This second function consists of minimizing the sum of the variance in coverage at the selected locations. Research reveals the deficiencies of MOLP (multiobjective linear programming) techniques in generating the efficient frontier of an integer problem. A 'brute-force' solution algorithm is developed and programmed in FORTRAN 77 to generate all feasible alternatives, determine which of these are non-dominated, and then provide an ordered list of alternatives using paired comparisons with the ideal. A case study is presented which shows the difficulty in finding a feasible one-site solution given the need to observe a wide segment of the geostationary belt. The example also shows that, for a given satellite population, the optimal alternative must for similar reasons include two southerly locations. The example reveals that while two-site solutions therefore exclude northerly locations, three-site solutions will usually include a northerly location.