A cost-based set-covering location-allocation problem with unknown covering radius

This paper proposes a covering problem in a discrete space where the covering radius is unknown and will be determined according to the distances among existing facilities and candidate points. On the other hand, cost of servicing is considered in our formulation as an important factor for allocating each demand point to the service point which is covered by. The problem is to find coverage radius, minimum number of service points, their locations in such a way that each customer shouldn´t travel so far for servicing and the optimal allocation of demand points to service points to minimize the total cost of allocation or transportation. A multi-objective formulation is proposed for this problem and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) for MODM (Multi Objective Decision Making) will be used for optimizing the problem. Finally a numerical example illustrates the results of proposed model.