Facility location problem

About: Facility location problem is a research topic. Over the lifetime, 5338 publications have been published within this topic receiving 142908 citations.

The Design of Approximation Algorithms

Abstract: Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.

Optimization models in emergency logistics: A literature review

Abstract: Optimization modeling has become a powerful tool to tackle emergency logistics problems since its first adoption in maritime disaster situations in the 1970s. Using techniques of content analysis, this paper reviews optimization models utilized in emergency logistics. Disaster operations can be performed before or after disaster occurrence. Short-notice evacuation, facility location, and stock pre-positioning are drafted as the main pre-disaster operations, while relief distribution and casualty transportation are categorized as post-disaster operations. According to these operations, works in the literature are broken down into three parts: facility location, relief distribution and casualty transportation, and other operations. For the first two parts, the literature is structured and analyzed based on the model types, decisions, objectives, and constraints. Finally, through the content analysis framework, several research gaps are identified and future research directions are proposed.

On the Complexity of Some Common Geometric Location Problems

Abstract: Given n demand points in the plane, the p-center problem is to find p supply points (anywhere in the plane) so as to minimize the maximum distance from a demand point to its respective nearest supply point. The p-median problem is to minimize the sum of distances from demand points to their respective nearest supply points. We prove that the p-center and the p-median problems relative to both the Euclidean and the rectilinear metrics are NP-hard. In fact, we prove that it is NP-hard even to approximate the p-center problems sufficiently closely. The reductions are from 3-satisfiability.

Reliability Models for Facility Location: The Expected Failure Cost Case

Abstract: Classical facility location models like the P-median problem (PMP) and the uncapacitated fixed-charge location problem (UFLP) implicitly assume that, once constructed, the facilities chosen will always operate as planned. In reality, however, facilities "fail" from time to time due to poor weather, labor actions, changes of ownership, or other factors. Such failures may lead to excessive transportation costs as customers must be served from facilities much farther than their regularly assigned facilities. In this paper, we present models for choosing facility locations to minimize cost, while also taking into account the expected transportation cost after failures of facilities. The goal is to choose facility locations that are both inexpensive under traditional objective functions and also reliable. This reliability approach is new in the facility location literature. We formulate reliability models based on both the PMP and the UFLP and present an optimal Lagrangian relaxation algorithm to solve them. We discuss how to use these models to generate a trade-off curve between the day-to-day operating cost and the expected cost, taking failures into account, and we use these trade-off curves to demonstrate empirically that substantial improvements in reliability are often possible with minimal increases in operating cost.

Greedy strikes back: improved facility location algorithms

Abstract: A fundamental facility location problem is to choose the location of facilities, such as industrial plants and warehouses, to minimize the cost of satisfying the demand for some commodity. There are associated costs for locating the facilities, as well as transportation costs for distributing the commodities. We assume that the transportation costs form a metric. This problem is commonly referred to as theuncapacitated facility locationproblem. Application to bank account location and clustering, as well as many related pieces of work, are discussed by Cornuejols, Nemhauser, and Wolsey. Recently, the first constant factor approximation algorithm for this problem was obtained by Shmoys, Tardos, and Aardal. We show that a simple greedy heuristic combined with the algorithm by Shmoys, Tardos, and Aardal, can be used to obtain an approximation guarantee of 2.408. We discuss a few variants of the problem, demonstrating better approximation factors for restricted versions of the problem. We also show that the problem is max SNP-hard. However, the inapproximability constants derived from the max SNP hardness are very close to one. By relating this problem to Set Cover, we prove a lower bound of 1.463 on the best possible approximation ratio, assumingNP?DTIMEnO(loglogn)].