عنوان مقاله [English]
Set covering problems have attracted a great deal of attention by researchers in recent years, especially in emergency systems. One of the most important objectives in set covering problems is for emergency vehicles to be on time at accident locations in order to provide services. Based on real observations, service facilities (i.e., emergency vehicles) are not always available, and are provided in an uncertainty condition. Regarding these problems, after defining customer location, facility centers are selected from candidate points to present services to customers efficiently. Hence, an appropriate method is investigated to localize emergency centers, so that accident locations receive appropriate services.
In this paper, a new approach, based on queuing systems, is presented for developing set covering problems, in which the arrival rate of the emergency services and service rate vary at different time intervals, as shown by
$lambda(t)$ and $mu(t)$, respectively. These are categorized as non-stationary queuing systems
with time-varying rates, which is a probability variable, depending on the traffic conditions, accidents, weather conditions, failure of vehicles, and condition of routes, and so on. To approximate arrival and service rates in
non-stationary M(t) /M(t) /1 queuing systems, their average rates can be considered to determine the probability of available facilities.
Since exact solutions of the set covering problems that belong to the category of NP-hard problems are not practical on a large scale, two meta-heuristic algorithms, namely; Improved Particle Swarm Optimization (IPSO) and Simulated Annealing (SA), are presented, and the results are compared with the branch and bound algorithm in small size problems. At the end, a number of test problems in large scale are solved, and the efficiency of the foregoing algorithms is evaluated. The results have shown that IPSO obtained high quality solutions with a reasonable computational time and accuracy, rather than the SA algorithm.