Nested-Solution Facility Location Models.

Facility location methods play a crucial role in specifying the optimum location options for various types of facilities. A question that arises is what makes a facility location decision a sustainable one? Facility location, also known as location analysis, is a known concept in the literature, but sustainable facility location is not. This requires appropriately defining the concept and framing the problem in order to address the relevant issues. Facility location models in the existing literature do not effectively include all the requirements of sustainable development. This paper serves as a discussion of the current literature concerning the sustainability aspects of the location problem. The aim is to conduct a comprehensive literature review to identify the characteristics of the sustainable facility location problem and propose a framework for classification of sustainability characteristics. The study shows that the location literature has steadily progressed toward considering not only economic but also social and environmental criteria in location decisions; but that many steps remain to be taken toward developing location models that integrate all three aspects of sustainability into decision making. The main motivation for the current study is to provide a foundation from which issues of sustainable development can be built into facility location and siting models.

α-Reliable p-minimax regret: A new model for strategic facility location modeling

Distributionally robust facility location with bimodal random demand

In this research, facility location problem-network design under uncertainty robust mode has been discussed. In this regard a model will be developed, so that the uncertainty in parameters such as demand and problem’s various costs considered. Facility location-network design, unlike classical facility location models, which are assumed that network structure is pre-defined and pre-specified, will also decide on the structure of the network.

Transportation is one of the main contributing factors of global carbon emissions, and thus, when dealing with facility location models in a distribution context, transportation emissions may be substantially higher than the emissions due to production or storage. Because facility location models define the configuration of deliveries, green location models become an important alternative to reduce CO2 emissions in logistics.

Applied p-median and p-center algorithms for facility location problems

In this chapter, we consider models for facility sizing and location under oligopolistic market equilibrium conditions on a spatial network. As in Chapter 6, we employ the paradigm of a large firm locating facilities on a defined network. To solve facility sizing/location models in oligopolistic competition, sensitivity based bilevel algorithms are developed. We will observe that there exist both significant similarities and differences between the algorithms developed in this chapter and those presented in Chapter 6 where a spatial price equilibrium characterized the economic conditions under which the firm of interest made its locational decisions.

This paper presents a new concept of partial coverage distance, where demand points within a given threshold distance of a new facility are covered in the traditional sense, while non-covered demand points are penalized an amount proportional to their distance to the covered region. Two single facility location models, based on the minisum and minimax criteria, are formulated with the new distance function, and the structure of the models is analysed.

Facility Location embodies a class of problems concerned with locating a set of facilities to serve a geographically distributed population of customers at minimum cost. We address the classical Capacitated Facility Location Problem (CFLP) in which the assignment of facilities to customers must ensure enough facility capacity and all the customers must be served. This is a well-known NP-hard problem in combinatorial optimization that has been extensively studied in the literature. Due to the difficulty of the problem, significant research efforts have been devoted to developing advanced heuristic methods aimed at finding high-quality solutions in reasonable computational times. We propose a Relaxation Adaptive Memory Programming (RAMP) approach for the CFLP. Our method combines lagrangean subgradient search with an improvement method to explore primal-dual relationships to create advanced memory structures that integrate information from both primal and dual solution spaces. The algorithm was tested on the standard ORLIB dataset and on other very large-scale instances for the CFLP. Our approach efficiently found the optimal solution for all ORLIB instances and very competitive results for the large-scale ones. Comparisons with current best-performing algorithms for the CFLP show that our RAMP algorithm exhibits excellent results.

In classical uncapacitated facility location problems (UFLP) the goal is to satisfy requirements of some demand points by setting up some servers, among potential facility locations, such that the total cost including service costs and fixed costs are minimized. In this paper a generalization of UFLP is considered in which some demand points, called self-serving, could be served exclusively by a new server at that point. Numerical experiments show that near optimal solutions are achieved by the proposed method.

3D coverage location modeling of Wi-Fi access point placement in indoor environment

We study the classic facility location setting, where we are given n clients and m possible facility locations in some arbitrary metric space, and want to choose a location to build a facility. The exact same setting also arises in spatial social choice, where voters are the clients and the goal is to choose a candidate or outcome, with the distance from a voter to an outcome representing the cost of this outcome for the voter (e.g., based on their ideological differences). Unlike most previous work, we do not focus on a single objective to optimize (e.g., the total distance from clients to the facility, or the maximum distance, etc.), but instead attempt to optimize several different objectives simultaneously. More specifically, we consider the l-centrum family of objectives, which includes the total distance, max distance, and many others. We present tight bounds on how well any pair of such objectives (e.g., max and sum) can be simultaneously approximated compared to their optimum outcomes. In particular, we show that for any such pair of objectives, it is always possible to choose an outcome which simultaneously approximates both objectives within a factor of 1 plus square root of 2, and give a precise characterization of how this factor improves as the two objectives being optimized become more similar. For q>2 different centrum objectives, we show that it is always possible to approximate all q of these objectives within a small constant, and that this constant approaches 3 as q increases. Our results show that when optimizing only a few simultaneous objectives, it is always possible to form an outcome which is a significantly better than 3 approximation for all of these objectives.

The purpose of this chapter is to succinctly review certain classical models for locating production activities on networks. By classical model, we mean one for which the locating firm is either a price taker or a monopolist, so that the analysis of competition is especially simple. Although these classical models are non-equilibrium models, an understanding of their assumptions and mathematical formulations is essential to understanding the equilibrium network facility location models presented in subsequent chapters.

Uncertainties and errors associated with aggregation have long been recognized in the study of spatial problems. In facility location modeling, while much has been done to examine the aggregation of large datasets of discrete points, errors and uncertainties involved in aggregating continuous spatial units are not well understood. This study focuses on the effects of aggregating continuous spatial units into discrete points within the context of the location set covering problem. We propose new measures to understand and quantify errors associated with a continuous aggregation scheme. In a real-world application, the proposed methods can be used to suggest an appropriate aggregation scheme before the application of the location model. We demonstrate the concepts developed here with an empirical study of siting emergency warning sirens in the city of Dublin, OH.

Risk management in uncapacitated facility location models with random demands