Abstract. In this paper, we study the uniform hard capacitated k facility location problem (CkFLP) and knapsack median problem (CKM). Natural LP of both the problems have an unbounded integrality gap. Byrka et al. in [5] present an (O(1/ǫ)) for CkFLP violating cpapcities by a factor of (2 + ǫ). However, the proofs in [5] do not seem to work. In this paper, we first raise the issues in [5] and t...

Facility location-allocation models are used in a widespread variety of applications to determine the number of required facility along with the relevant allocation process. In this paper, a new mathematical model for the capacitated multi-facility location-allocation problem with probabilistic customer's locations and fuzzy customer’s demands under the Hurwicz criterion is proposed. This model...

Facility location problems are often encountered in many areas such as distribution, transportation and telecommunication. We describe a new solution approach for the capacitated facility location problem in which each customer is served by a single facility. An important class of heuristic solution methods for these problems are Lagrangian heuristics which have been shown to produce high quali...

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...