In this paper, we study an integrated logistic system where the optimal location of depots and vehicles routing are considered simultaneously. This paper presents a new mathematical model for a multi-objective capacitated location-routing problem with a new set of objectives consisting of the summation of economic costs, summation of social risks and demand satisfaction score. A new multi-objec...

Location-Routing Problem (LRP) is related to logistics system of supply chain. In LRP, aims are facility location problem and vehicle routing problem that are considered simultaneously. As shown in recent researches, the costs in distribution systems may be excessive if routes are ignored when locating depots. In this paper, a heuristic method in four phases is developed to solve Capacitated Lo...

location-allocation is a combinatorial optimization problem, and is defined as non deterministic polynomial hard (np) hard optimization. therefore, solution of such a problem should be shifted from exact to heuristic or meta heuristic due to the complexity of the problem. locating medical centers and allocating injuries of an earthquake to them has high importance in earthquake disaster managem...

In this paper we initiate the study of the heterogeneous capacitated k-center problem: given a metric space X = (F ∪C, d), and a collection of capacities. The goal is to open each capacity at a unique facility location in F , and also to assign clients to facilities so that the number of clients assigned to any facility is at most the capacity installed; the objective is then to minimize the ma...

Metric uncapacitated facility location is a well-studied problem for which linear programming methods have been used with great success in deriving approximation algorithms. Capacitated facility location (Cfl) is a generalization for which there are local-search-based constant-factor approximations, while there is no known compact relaxation with constant integrality gap. This paper produces, t...

In a surprising result, Korupolu, Plaxton, and Rajaraman [13] showed that a simple local search heuristic for the capacitated facility location problem (CFLP) in which the service costs obey the triangle inequality produces a solution in polynomial time which is within a factor of 8+ ǫ of the value of an optimal solution. By simplifying their analysis, we are able to show that the same heuristi...

We consider a generalization of the Connected Facility Location problem (ConFL), suitable to model real world network extension scenarios such as fiber-tothe-curb. In addition to choosing a set of facilities and connecting them by a Steiner tree as in ConFL, we aim to maximize the resulting profit by potentially supplying only a subset of all customers. Furthermore, capacity constraints on pote...

The Capacitated Connected Facility Location Problem (CConFL) is an NPhard combinatorial optimization problem which arises in the design of last mile communication networks (fiber-to-the-curb scenarios) [1]. Formally, we are given an undirected, weighted graph G = (V,E), with edge costs ce ≥ 0, ∀e ∈ E. The node set V = {r}∪F ∪T is the disjoint union of the root node r, potential facility locatio...

The Capacitated Facility Location Problem (CFLP) consists of locating a set of facilities with capacity constraints to satisfy the demands of a set of clients at the minimum cost. In this paper we propose a simple and effective heuristic for largescale instances of CFLP. The heuristic is based on a Lagrangean relaxation which is used to select a subset of “promising” variables forming the core ...