Emergency Service Location Problem with Ring Roads

Abstract A key purpose of a service network design is to determine the best possible location(s) for each service center. The facility services must provide a quick and easy response to callers within a reasonable distance, especially in urgent cases. It’s well known that this problem is NP-hard, non-convex and non-differentiable optimization problem. However, if we make some simplifying assumptions, the problem could be solved within a polynomial time. This article introduces an algorithm for solving the problem of determining the best possible locations of the emergency service centers, concerning the case in which these centers are located on simple closed curves (e.g., ring roads). The proposed model can be applied in designing the emergency centers on ring roads in new cities, which have become one of the most important designs in solving traffic congestion problems. The problem is mathematically formulated, an algorithm for solving the problem under simplifying assumptions is proposed, the mathematics behind the algorithm is given, and the algorithm is illustrated by a numerical example.