Abstract

We offer a variant of the maximal covering location problem to locate up to p signal-receiving stations. The “demands,” called geolocations, to be covered by these stations are distress signals and/or transmissions from any targets. The problem is complicated by several factors. First, to find a signal location, the signal must be received by at least three stations—two lines of bearing for triangulation and a third for accuracy. Second, signal frequencies vary by source and the included stations do not necessarily receive all frequencies. One must decide which listening frequencies are allocated to which stations. Finally, the range or coverage area of a station varies stochastically because of meteorological conditions. This problem is modeled using a multiobjective (or multicriteria) linear integer program (MOLIP), which is an approximation of a highly nonlinear integer program. As a solution algorithm, the MOLIP is converted to a two-stage network-flow formulation that reduces the number of explicitly enumerated integer variables. Non-inferior solutions of the MOLIP are evaluated by a value function, which identifies solutions that are similar to the more accurate nonlinear model. In all case studies, the “best” non-inferior solutions were about one to four standard deviations better than the sample mean of thousands of randomly located receivers with heuristic frequency assignments. We also show that a two-stage network-flow algorithm is a practical solution to an intractable nonlinear integer model. Most importantly, the procedure has been implemented in the field.

Keywords: Maximal-coverage facility-location; Location–allocation; Primary vs. backup coverage; Assignment; Mutiobjective optimization; Network flow; Enhanced 911

Article Outline

1. Introduction

2. The GSAR problem as a location problem

3. Mathematical description of the problem

4. Solution via a multicriteria linear integer program

4.1. MOLIP criterion functions

4.2. MOLIP constraints

4.3. MOLIP validation

4.4. Two-stage network-flow formulation

4.5. Evaluating non-inferior solutions

5. GSAR case studies using two-stage MOLIP

5.1. Case I results

5.2. Case II results

5.3. Observations from the case studies

5.4. Calibrating a value function

6. Summary, conclusion and recommendations

6.1. Conclusion

6.2. Recommendations

Acknowledgements

Appendix A. Properties of the models

A.1. Similarities

A.2. Differences

Appendix B. Acronyms

References