A total covering problem and facility dispersion with existing facility, capacitated demand, and variable transfer cost

Total covering problem is one of the most commonly used issues of locating facilities. In this context, the goal of determining the P service center is to cover at least the cost of deploying all demand points. These issues have a wide range of nature and scope, each of which is optimized by taking into account certain conditions in order to find the answer. One of these conditions can be a situation in which, in addition to full coverage of demand, the dispersion of facilities is also considered. Facility dispersion means maximizing the distance between facilities with respect to existing limits. This research seeks to provide a suitable model considering the predictable limits of the real world and the use of an appropriate method for solving the cover-dispersion model. Accordingly, the full coverage of the solution space and the choice of the optimal location of the facility with maximum dispersion, taking into account the minimum number of facilities and the lowest cost of deployment, due to the limited capacity of facilities and the minimization of transportation costs are the goals of this research. Due to the NP-HARD nature of the coating and literature models, solving these models, an algorithm is designed based on the genetic method for solving the model. In order to improve the quality of the algorithm's parameters, the parameters of the algorithm are set by the Taguchi experimental design method. The results show that the algorithm is suitable for the model.