In this survey, we examine an important class of facility location problems known as the multisource Weber problem (also referred to as the continuous location-allocation problem). We also show how recent advances in the use of metaheuristic rules have significantly improved the ability to solve problems of this type. The new solution methods are discussed for both the well known multisource W...

In this paper, we present one generalization of the famous capacitated p-median location problem, called budget constraint multi-capacitated location problem (MCLP). This generalization is characterized by allowing each facility to be used with different capacity levels. We consider n customers, m facilities and l capacity levels, we note that the solution shape of MCLP can be represented as a ...

In this paper, we establish a novel duality relationship between node-capacitated multiflows and tree-shaped facility locations. We prove that the maximum value of a tree-distance-weighted maximum node-capacitated multiflow problem is equal to the minimum value of the problem of locating subtrees in a tree, and the maximum is attained by a half-integral multiflow. Utilizing this duality, we sho...

In the Universal Facility Location problem we are given a set of demand points and a set of facilities. The goal is to assign the demands to facilities in such a way that the sum of service and facility costs is minimized. The service cost is proportional to the distance each unit of demand has to travel to its assigned facility, whereas the facility cost of each facility i depends on the amoun...

In this paper several dynamic multi-level location problems are formulated as mixed-integer linear programs. Both uncapacitated and capacitated versions of the problem are studied. The models presented are more complete than the ones known from the literature: they are dynamic and consider the possibility of a facility being open, closed and reopen more than once during the planning horizon. Th...

This paper investigates a capacitated planar location-allocation problem with facility fixed cost. A zonebased fixed cost which consists of production and installation costs is considered. A nonlinear and mixed integer formulation is first presented. A powerful three stage Cross Entropy meta-heuristic with novel density functions is proposed. In the first stage a covering location problem provi...