A Mixed Integer Linear Model for the Edge Covering Problem with Finite Capacity in Facilities and Different Coverage Distances

This paper studies a covering problem on graph which is a variant of facility location problem. In this research, constraints are considered to improve the previous model. These constraints have not considered previously. The first constraint limits the capacity of the facilities and the other one considers different coverage distances. The objective is to determine the optimal subset of candidate vertices for facility location, the different coverage distances and also is to assign edges to facilities which are located on vertices. We assumed that must covered by one or both adjacent vertices. Subjecting the model to capacity constraint converts the set covering problem in to maximal covering problem. This paper applies these two types of constraints and presents a new mixed integer linear model. It is also proposed a novel heuristic algorithm for generating the initial solution of Meta heuristic methods. Key word: Facility location; Mixed integer linear model; Heuristic algorithm; Finite capacity and Different coverage distance.