A Multi-objective continuous covering location model

This paper presents a multi-objective continuous covering location problem in fuzzy environment. Because the covering radius is assumed to be uncertain, this paper uses the possibility concept. Since uncertainty may cause risk of uncovering customers, the problem is formulated as a risk management model. The presented model is an extension of the discrete covering location model to continuous space. Two variables, namely selecting zone variable and covering variable are introduced for extending the discrete model to the continuous one. In the model, a facility is located in a zone with a predetermined radius from its center and is determined by the selecting zone variable. Allocating a customer to a facility is shown by a covering variable. Also, the paper introduces the possibility of covering, based on distance between the customers and the facilities. Two objectives are considered in the model; the first is the possibility of covering by each facility and the second is the risk cost of the uncovered customers. Fuzzy programming is applied for converting the model to a single objective one. Finally, a numerical example with sensitivity analysis is expressed to illustrate the presented model.