Facility Location Model Research Articles

Robust mean absolute deviation problems on networks with linear vertex weights

AbstractThis article deals with incorporating the mean absolute deviation objective function in several robust single facility location models on networks with dynamic evolution of node weights, which are modeled by means of linear functions of a parameter. Specifically, we have considered two robustness criteria applied to the mean absolute deviation problem: the MinMax criterion, and the MinMax regret criterion. For solving the corresponding optimization problems, exact algorithms have been proposed and their complexities have been also analyzed. © 2012 Wiley Periodicals, Inc. NETWORKS, 2013

Aggregation in continuous space coverage modeling

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.

GIS Exploitation for New Facility Location Decisions- A Logistics Perspective

Logistical facility location decisions can make a crucial difference in the success or failure of a company. Geographical Information Systems (GIS) have recently become a very popular decision support system to help deal with facility location problems. However, until recently, GIS methodologies have not been fully embraced as a way to deal with new facility location problems in business logistics. This research makes a framework for categorizing empirical facility location problems based on the intensity of the involvement of GIS methodologies in decision making. This framework was built by analyzing facility location models and GIS methodologies. The research results revealed the depth of the embracement of GIS methodologies in logistics for determining new facility location decisions. In the new facility location decisions, spatial data inputs are almost always coupled with the visualization of the problems and solutions. However, the usage of GIS capability solely (i.e. suitability analysis) for problem solving has not been embraced at the same level. In most cases, the suitability analysis is used together with special optimization models for choosing among the multiple alternatives.

GIS Exploitation for New Facility Location Decisions- A Logistics Perspective

Logistical facility location decisions can make a crucial difference in the success or failure of a company. Geographical Information Systems (GIS) have recently become a very popular decision support system to help deal with facility location problems. However, until recently, GIS methodologies have not been fully embraced as a way to deal with new facility location problems in business logistics. This research makes a framework for categorizing empirical facility location problems based on the intensity of the involvement of GIS methodologies in decision making. This framework was built by analyzing facility location models and GIS methodologies. The research results revealed the depth of the embracement of GIS methodologies in logistics for determining new facility location decisions. In the new facility location decisions, spatial data inputs are almost always coupled with the visualization of the problems and solutions. However, the usage of GIS capability solely (i.e. suitability analysis) for problem solving has not been embraced at the same level. In most cases, the suitability analysis is used together with special optimization models for choosing among the multiple alternatives.

A study on the budget constrained facility location model considering inventory management cost

One of the important issues on the distribution network design is to incorporate inventory management cost into the facility location model. This paper deals with a network model making the decisions on the facility location such as the number of DCs and their locations as well as the decisions on the inventory management such as the ordering quantity and the level of safety stock at each DC. The considered model differs from the previous works by classifying the related costs into the operating cost and the investment cost. For this model, a solution procedure based on the Lagrangian relaxation method was proposed and tested for its effectiveness with various numerical examples.

Making Location Decision Based on Regional Industrial Capabilities: A Case of a Distributor

This article presents a structured process to make facility location decisions based on regional industrial capabilities. It presents a framework for collecting business intelligence on major cities of the region of interest. In the next step, the collected business intelligence is incorporated into a quantitative decision analysis model for facility location. While the proposed framework is generic and builds on the existing international business and supply chain management literature, the article mainly focuses on the facility location problem of a distribution firm that is not well represented in the literature. Two cases—one each for new and established distributors who are trying to sell to the Mexican market—are presented in the article.

Spatio-temporal location modeling in a 3D indoor environment: the case of AEDs as emergency medical devices

This research innovatively extends optimal emergency facility location models to the interior space of multistory buildings with an integrated spatial-temporal framework. We present the case of deployed emergency medical devices known as automated external defibrillators (AEDs), which serve to treat sudden cardiac arrest on-site within the first few critical minutes of the event. AEDs have become a critical element of basic life support services in many public buildings. The proposed framework is based on the concept of discrete time windows to capture the time-dependence of potential demand and stochastically model the detection time component of impedance as a function of space–time distribution of demand. Different optimization objectives minimizing sudden cardiac arrest outcome consequences (e.g., brain damage or death) as a function of suffering time are formulated and solved. The first model is the multiple-time-window maximal covering location problem model which optimizes the placement of AEDs by maximizing the covered demand over all time periods. The second is the multiple-time-window p-Median model which places AEDs to maximize the expected value of prevented death or permanent brain impairment in case of defibrillation treatment over multiple time windows. Both models are implemented through tight coupling of commercial geographic information system software and a linear programming solver. The models are novel in two primary respects, namely location modeling in 3D microscale spaces and the integration of spatial and temporal considerations. Innovative visualization techniques for AED indoor location and coverage are also presented.

Multi-criteria multi-facility location in Niwai block, Rajasthan

Rural regions often suffer disproportionately when compared to urban areas in the access to basic healthcare and educational opportunities. The provision of these facilities to the populace has been identified as one of the means of stimulating development in a region.A problem-structuring method with multi-criteria decision analysis was used for the selection of different facilities based on the needs of the rural area under consideration. A facility location model was created and algorithms were developed in order to provide a solution for locating facilities in 45 villages of Niwai block in Tonk district, Rajasthan.Sixteen different facilities were chosen for consideration, each falling into one of five broad groups: healthcare, education, connectivity, agriculture and drinking water. Alternative scenarios for locating facilities were generated and explored, providing a base for the micro-level planning process at the block level in a district.

Capacitated two-stage facility location problem with fuzzy costs and demands

In this study, we develop a two-stage capacitated facility location model with fuzzy costs and demands. The proposed model is a task of 0–1 integer two-stage fuzzy programming problem. In order to solve the problem, we first apply an approximation approach to estimate the objective function (with fuzzy random parameters) and prove the convergence of the approach. Then, we design a hybrid algorithm which integrates the approximation approach, neural network and particle swarm optimization, to solve the proposed facility location problem. Finally, a numerical example is provided to test the hybrid algorithm.

Modelling lost demand in competitive facility location

In this paper, we propose a simple new approach to model lost demand (also referred to as elastic demand) in competitive facility location. A ‘dummy’ competing facility that attracts the lost demand is added to the list of competing facilities. All competitive facility location models, regardless of their complexity or assumptions, can be modified to include lost demand and be solved by the same algorithms designed for standard models once the dummy facility is added to the data as an additional competitor.

Centralized Router Election for IP-WSN Based on Facility Location Model

It is a good alternative that uses reduced IPv6 as network layer protocol of wireless sensor network (WSN). This will generate a new problem: how to choose some nodes as router for homogenous, dense deployment WSN. This paper proposed a centralized router election method, which is based on facility location model, for IP-WSN. This method creates a 0-1 integer programming model by regarding router election as uncapacitated facility location problem firstly. Then genetic algorithm is used for solving the created model. The simulation results show that this method can elect small number of nodes as router with high efficiency.

Agility and Proximity Considerations in Supply Chain Design - An Analytical Approach

Strategic supply chain design decisions are critical to the long-term success of a business. Traditional facility location models for supply chain design focus on the trade-offs between the costs and benefits of proximity, i.e., the distance between facilities and customers. These strategic-focused models do not consider the supply chain's agility, i.e., its ability to quickly respond to unexpected fluctuations in customer needs. In this paper, we study the problem of designing a supply chain distribution network under demand uncertainty and analyze how the optimal design characteristics of proximity and agility depend on various input parameters. We are able to draw managerial insights on how agility considerations may invalidate well-established and widely-accepted qualitative results derived from traditional models. In particular, we show that it is optimal to increase the density of DCs when the shortage penalty cost increases, and to decrease the density of DCs when a certain unit transportation cost parameter increases. Through these findings, our work conveys the message that traditional, proximity-based facility location models can be inadequate for designing modern responsive supply chains, and calls for the need to develop a new class of models for the task.

A two-echelon stochastic facility location model for humanitarian relief logistics

We develop a two-stage stochastic programming model for a humanitarian relief logistics problem where decisions are made for pre- and post-disaster rescue centers, the amount of relief items to be stocked at the pre-disaster rescue centers, the amount of relief item flows at each echelon, and the amount of relief item shortage. The objective is to minimize the total cost of facility location, inventory holding, transportation and shortage. The deterministic equivalent of the model is formulated as a mixed-integer linear programming model and solved by a heuristic method based on Lagrangean relaxation. Results on randomly generated test instances show that the proposed solution method exhibits good performance up to 25 scenarios. We also validate our model by calculating the value of the stochastic solution and the expected value of perfect information.

Incorporating recycling into post-disaster debris disposal

Although large amounts of disaster-generated debris significantly strain landfill capacities, until recently existing policy provided no financial incentive to consider other disposal alternatives such as recycling. In 2007, the U.S. Federal Emergency Management Agency (FEMA) released a new pilot program that provides incentives for communities to recycle by allowing them to retain revenue from the sale of disaster debris. This first-ever policy offers significant financial benefits for communities seeking to cleanup in an environmentally responsible way but requires reexamining existing assumptions and decision processes that are based on prior reimbursement programs. This paper presents a decision model with recycling incentives for locating temporary disposal and storage reduction (TDSR) facilities in support of disaster debris cleanup operations. A facility location model is proposed to incorporate the unique assumptions, objectives, and constraints of disaster recovery in light of FEMA’s new policy.

Scaling and entropy inp-median facility location along a line

The p-median problem is a common model for optimal facility location. The task is to place p facilities (e.g., warehouses or schools) in a heterogeneously populated space such that the average distance from a person's home to the nearest facility is minimized. Here we study the special case where the population lives along a line (e.g., a road or a river). If facilities are optimally placed, the length of the line segment served by a facility is inversely proportional to the square root of the population density. This scaling law is derived analytically and confirmed for concrete numerical examples of three US interstate highways and the Mississippi River. If facility locations are permitted to deviate from the optimum, the number of possible solutions increases dramatically. Using Monte Carlo simulations, we compute how scaling is affected by an increase in the average distance to the nearest facility. We find that the scaling exponents change and are most sensitive near the optimum facility distribution.

A multi-objective facility location model with batch arrivals: two parameter-tuned meta-heuristic algorithms

Many research works in mathematical modeling of the facility location problem have been carried out in discrete and continuous optimization area to obtain the optimum number of required facilities along with the relevant allocation processes. This paper proposes a new multi-objective facility-location problem within the batch arrival queuing framework. Three objective functions are considered: (I) minimizing the weighted sum of the waiting and the traveling times, (II) minimizing the maximum idle time pertinent to each facility, and (III) minimizing the total cost associated with the opened facilities. In this way, the best combination of the facilities is determined in the sense of economical, equilibrium, and enhancing service quality viewpoints. As the model is shown strongly NP-hard, two meta-heuristic algorithms, namely genetic algorithm (GA) and simulated annealing (SA) are proposed to solve the model. Not only new coding is developed in these solution algorithms, but also a random search algorithm is proposed to justify the efficiency of both algorithms. Since the solution-quality of all meta-heuristic algorithms severely depends on their parameters, design of experiments and response surface methodologies have been utilized to calibrate the parameters of both algorithms. Finally, computational results obtained by implementing both algorithms on several problems of different sizes demonstrate the performances of the proposed methodology.

A facility location model with safety stock costs: analysis of the cost of single-sourcing requirements

We consider a supply chain setting where multiple uncapacitated facilities serve a set of customers with a single product. The majority of literature on such problems requires assigning all of any given customer's demand to a single facility. While this single-sourcing strategy is optimal under linear (or concave) cost structures, it will often be suboptimal under the nonlinear costs that arise in the presence of safety stock costs. Our primary goal is to characterize the incremental costs that result from a single-sourcing strategy. We propose a general model that uses a cardinality constraint on the number of supply facilities that may serve a customer. The result is a complex mixed-integer nonlinear programming problem. We provide a generalized Benders decomposition algorithm for the case in which a customer's demand may be split among an arbitrary number of supply facilities. The Benders subproblem takes the form of an uncapacitated, nonlinear transportation problem, a relevant and interesting problem in its own right. We provide analysis and insight on this subproblem, which allows us to devise a hybrid algorithm based on an outer approximation of this subproblem to accelerate the generalized Benders decomposition algorithm. We also provide computational results for the general model that permit characterizing the costs that arise from a single-sourcing strategy.

A discrete competitive facility location model with variable attractiveness

We consider the discrete version of the competitive facility location problem in which new facilities have to be located by a new market entrant firm to compete against already existing facilities that may belong to one or more competitors. The demand is assumed to be aggregated at certain points in the plane and the new facilities can be located at predetermined candidate sites. We employ Huff's gravity-based rule in modelling the behaviour of the customers where the probability that customers at a demand point patronize a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. The objective of the firm is to determine the locations of the new facilities and their attractiveness levels so as to maximize the profit, which is calculated as the revenue from the customers less the fixed cost of opening the facilities and variable cost of setting their attractiveness levels. We formulate a mixed-integer nonlinear programming model for this problem and propose three methods for its solution: a Lagrangean heuristic, a branch-and-bound method with Lagrangean relaxation, and another branch-and-bound method with nonlinear programming relaxation. Computational results obtained on a set of randomly generated instances show that the last method outperforms the others in terms of accuracy and efficiency and can provide an optimal solution in a reasonable amount of time.

Cooperative location games based on the minimum diameter spanning Steiner subgraph problem

In this paper we introduce and analyze new classes of cooperative games related to facility location models. The players are the customers (demand points) in the location problem and the characteristic value of a coalition is the cost of serving its members. Specifically, the cost in our games is the service diameter of the coalition.We study the existence of core allocations for these games, focusing on network spaces, i.e., finite metric spaces induced by undirected graphs and positive edge lengths.

Analysis of facility location model using Bayesian Networks

In this study, we propose an integrated approach that combines Bayesian Networks and Total Cost of Ownership (TCO) to address complexities involved in selecting an international facility for a manufacturing plant. Our goal is to efficiently represent uncertain data and ambiguous information, and to unite them to improve the quality of the decisions. Bayesian Networks provide a framework to elicit information from experts, and provide a structure guide to efficient reasoning, even with incomplete knowledge. Our method is presented in a hierarchical structure so that it can be decomposed into the forms of more manageable units. We consider many tangible and intangible facility location criteria, then these criteria are grouped into few numbers of factors. These factors are then combined to form a cost perspective using the essentials of TCO.