The Security Assignment Problem and Its Solution

In this paper we derived a new method for finding the optimal solution to security assignment problems using projection onto a convex set. This study will help communities find the optimal number of assigned and reserved personnels in designating security officers to an area. This study is applicable as well to CCTV assignment problems. The main goal of this study is to give a new method that can be applied in solving security assignment problems. We used some of the known properties of the convex optimization in proving the properties of the optimal solution, such as the concept of proximity operator, projection onto the convex set, and primal and dual problem. In addition to that, we used some basic knowledge in graph theory to answer our real-life application of this study. The main results of this paper showed that we found instances when the optimal solution to a security problem exists and when the solutions exist, we can determine the answer to the problem explicitly. Also, we proved that there always exists a Pseudo-solution in security assignment problems, and if the solution exists, then the Pseudo-solution will coincide with it. The most important aspect of this paper is the introduction of the application of convex optimization in the security problem.