Estimating the required number of security cameras for the Afghan National Police Academy : an application of the Terrain Guarding Problem / Gerald Woodill. : D68-6/237-2013E-PDF

"In 2012, the Afghan National Police Academy (ANPA) requested of the NATO Training Mission – Afghanistan (NTM-A) the funds to provide and install security cameras for the Kabul campus. The Deputy Commander – Police (DCOM-P) had no basis on which to estimate the cost of granting such a request and a study was conducted to provide an estimate of the required number of cameras. This request was similar to a museum guarding problem or its variant the Terrain guarding problem. Seven estimates were developed using Chvàtal’s theorem, five others identified using Ghosh’s formulae, and one manually compiled from an engineer’s drawing of the compound. Two problems were identified for Chvàtal’s and Ghosh’s theorems. None of them were identified as useful for a combination of vertex, edge and point guards and they did not consider the effects of curved edges instead of straight lines and vertices. While the theorems were intended to provide an upper bound on the estimate of the minimum number of cameras required to monitor the compound, when compared to the estimate developed using a manual procedure applied to an engineer’s drawing, they were found to be overestimating by a minimum of 29% and a maximum of 196%. These were considered undesirable for the purpose of estimating the potential cost of a contract. The estimate developed using the manual method was provided to DCOM-P as insight into the decision to be made"--Abstract, p. i.

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