The achievements of this study can be extended to other emergency service facility location applications such as ambulance and/or fire stations, in the presence of barriers as in the case of overground trains that move on predetermined tram lines. Street collisions on bicycle routes and at tramline intersections are common examples of the proposed problem with barriers. Since the position of the overground train on the tramline is not deterministic, but moving, a probability distribution function is devoted to the barrier location on the route.
The research work we developed is motivated by an application of locating a number of departments in the Metropolitan police as new facilities in Kingston Upon Thames, a royal borough located in South West London, England. Kingston Upon Thames includes 16 local areas called wards that are considered as demand points in this research. We were primarily concerned with the current situation where all offences and committed crimes are reported to the Metropolitan police, when each kind of offence should be processed by a specialised inspection department. In the city, there is an overground route (connecting Surbiton-Beverley) in Kingston Upon Thames that is a barrier on its route. We intended to investigate a decentralized approach that focuses on new police departments whom are dependent on the frequency of offences occurred in each ward. That leads to the conclusion that, while we consider the barrier, the police cabins are widely dispersed in the region from one month to the next to decrease the maximum travelled distance. However, while ignoring the barrier, new cabins are positioned close to each other to reduce the relocation cost, and therefore minimize the maximum travelling distance. In other words, ignoring the barrier may mislead the urban decision makers and managers in their location and relocation decisions. Thus, formulating a mathematical model and proposing a solution procedure for such a practical problem seems to be worthwhile. The results of this modelling approach show a significant improvement in travelled distances in case of emergencies.
Urban development, industrial unit design, and war strategic planning are some examples of fields of applications for such kind of problems. Locating a set of maintenance departments or tool rooms that respond to the existing requirements in an industrial plant when a moving wagon travels on a rail may be another application. An overground train or a wagon with a negligible width compared to its length that occurs on its route can be considered as the line barrier. Accidents, unplanned road constructions, and hazards on a city street may cause detours and delays on the transportation networks. The design and implementation of robots to avoid collisions with random obstacles while being on a least-cost path is another example.
Amiri-Aref M., Zanjirani Farahani R., Javadian N., Klibi W. (2016). A rectilinear distance location–relocation problem with a probabilistic restriction: mathematical modelling and solution approaches. International Journal of Production Research, 54(3), 629-646.