Facility Location Model Research Articles

Dynamic Model for System-Level Strategic Intermodal Facility Investment Planning

This paper proposes a scenario-based mixed-integer dynamic capacitated intermodal facility location model (IFLM) for determining the optimal strategic intermodal facility investment planning strategy that accounts for freight transportation demand uncertainty. The proposed model helps high-level policy makers with strategic investment planning for intermodal facilities at a regional or national level and fosters coordinated strategies and policies for intermodal facility development from a systems perspective. A scenario-based approach characterizes demand uncertainty induced by global trade changes and emerging infrastructure development projects. Dynamic demand is incorporated into the model to capture the impact of differences in the evolution of various scenarios on system-level strategic intermodal investment planning. The proposed IFLM captures the impact of congestion, transshipment costs, changes in capacity of intermodal facilities, economies of scale, and empty-container repositioning costs on freight transportation demand and strategic intermodal investment planning. Three numerical experiments demonstrate the applicability of the proposed model and explore the impacts of intermodal facility service-level changes of some regions on the freight transportation demand for other regions and the optimal intermodal investment planning strategy in the United States. The results show that the proposed model can help decision makers in strategic intermodal facility investment planning by prioritizing capacity expansion of ports and terminals. The results also illustrate the importance of system-level and coordinated planning in strategic intermodal investment in the decision-making process. The proposed IFLM can be integrated with operational planning models to improve investment decision making.

A Facility Location Model for MSW Management Systems Under Uncertainty: A Case Study of Nashik City, India

In India, a substantial fraction (∼0.85) of total expenditure on MSW management is spent on collection of waste. Nevertheless, the average waste collection efficiency is about 70% in Indian urban areas. Waste collection efficiency can be increased by utilising staff and collection vehicles effectively with transfer stations (TSs), though choosing best sites (in an economically optimal manner) for TSs siting is a major task. Also, many parameters (e.g., waste-generation rate, running cost of facilities, transportation cost, revenues etc.) in MSW management system are associated with uncertainties. To study the apportionment of these uncertain input parameters into the results, a comprehensive sensitivity analysis has been performed. Furthermore, the effect of interaction among most sensitive parameters is examined through design of experiment. Also, a facility location two stage stochastic model has been proposed to select the best sites for TSs siting, which is basically a framework of facility location problems involving uncertainty. The developed model is applied on the city of Nashik, Maharashtra, India. The model has 9186 constraints and 8152 variables, which has been written in AMPL (a mathematical programming language). KNITRO 5.2 (nonlinearinterior-point trust region optimizer) have been used to solve the developed model. Sensitivity analysis abduces waste generation as the most sensitive kind of parameter followed by the unit transportation cost of waste from source to TSs. Furthermore, multivariate SA identifies the importance of a facility location framework involving uncertainty.

Simulated Annealing and Direct Search based Optimization Models for Facility Location in Logistic Network Design

Finding the optimum location of facilities is an important problem related in logistics. Locations of Distribution Centers (DCs) can be at the proximity of highways and closer to populated areas in order to speedup package deliveries and minimize the overall transport cost and time. Deciding the optimum number of DCs as well as the optimum location of DCs are the most important aspects of the design of any logistics network. Deciding the number of DCs will depend upon the budget and optimum locations of DCs will reduce the overall transport cost. As operations globalize, location decisions become more complex. A powerful approach to analyzing these problems is the transportation method of linear programming. The linear programming based methods will take much time to attain a solution in such a wide problem space. But for dealing with such wide problem space, soft computing based approaches are well suited and can find a meaningful solution in finite time. This work generate the Simulated Annealing and Direct Search based model for facility location in logistics and evaluate its performance. Also, compare the performance of this model with a k-mean clustering based model.

A heterogeneous reliable location model with risk pooling under supply disruptions

This paper investigates a facility location model that considers the disruptions of facilities and the cost savings from the inventory risk-pooling effect and economies of scale. Facilities may have heterogeneous disruption probabilities. When a facility fails, its customers may be reassigned to other surviving ones to hedge against lost-sales costs. We first develop both an exact and an approximate expression for the nonlinear inventory cost, and then formulate the problem as a nonlinear integer programming model. The objective is to minimize the expected total cost across all possible facility failure scenarios. To solve this problem, we design two methods, an exact approach using special ordered sets of type two (SOS2) and a heuristic based on Lagrangian relaxation. We test the model and algorithms on data sets with up to 150 nodes. Computational results show that the proposed algorithms can solve the problem efficiently in reasonable time. Managerial insights on the optimal facility deployment, customer assignments and inventory control strategies are also drawn.

Location and reorganization problems: The Calabrian health care system case

In the last few years, the Italian healthcare system has been coping with radical changes, aimed at guaranteeing more efficiency while containing costs. Starting from the actual service network organization, we discuss the problem faced by the Italian authorities of reorganizing the healthcare service network and we propose some optimization models to support the decision-making process. In the first part of the work, we compare the existing health care service network of the northern area of Calabria (Italy) with the configurations determined by solving well-known facility location models. In the second part, taking into account the healthcare reorganization plans imposed by local governments, we consider the problem of reorganizing the public health care service network of the northern area of Calabria. Indeed, we propose two ad-hoc optimization models that consider national and regional guidelines and constraints. The behavior of the proposed models, in terms of solution quality, is evaluated on the basis of an extensive computational study on real data.

Mitigating hard capacity constraints with inventory in facility location modeling

ABSTRACTAlthough the traditional capacitated facility location model uses inflexible, limited capacities, facility managers often have many operational tools to extend capacity or to allow a facility to accept demands in excess of the capacity constraint for short periods of time. We present a mixed-integer program that captures these operational extensions. In particular, demands are not restricted by the capacity constraint, as we allow for unprocessed materials from one day to be held over in inventory and processed on a following day. We also consider demands at a daily level, which allows us to explicitly incorporate the daily variation in, and possibly correlated nature of, demands. Large problem instances, in terms of the number of demand nodes, candidate nodes, and number of days in the time horizon, are generated from United States census population data. We demonstrate that, in some instances, optimal locations identified by the new model differ from those of the traditional capacitated facility location problem and result in significant cost savings.

Optimization of reliability for a hierarchical facility location problem under disaster relief situations by a chance-constrained programming and robust optimization

Despite the frequent use of hierarchical facility location decisions for public facilities such as hospitals and schools and their important role in positioning relief facilities effectively, few studies have examined the optimized positioning of such facilities under uncertainty, which is imposed by the nature of a disaster. In this article, we present a hierarchical facility location model in a supply chain of disaster relief under uncertainty in order to schedule the customers’ services. In this model, we consider a positive probability for roadways to become closed for relief operations when a disaster occurs. In this network, a higher level relief facility offers all services provided by a minimum relief facility. Since the aim of this model is to rapidly provide the appropriate emergency supplies to the affected villages, we optimize the reliability of the network by constructing more roads and infrastructure between all villages and relief centers. For this purpose, a robust optimization and chance-constrained programming method was applied. Finally, the hybridization of the genetic algorithm, simulated annealing and an optimization technique will be introduced to solve the model efficiently.

Agility and Proximity Considerations in Supply Chain Design

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 distribution centers (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. This paper was accepted by Yossi Aviv, operations management.

A multi-objective genetic algorithm for a bi-objective facility location problem with partial coverage

In this study, we present a bi-objective facility location model that considers both partial coverage and service to uncovered demands. Due to limited number of facilities to be opened, some of the demand nodes may not be within full or partial coverage distance of a facility. However, a demand node that is not within the coverage distance of a facility should get service from the nearest facility within the shortest possible time. In this model, it is assumed that demand nodes within the predefined distance of opened facilities are fully covered, and after that distance the coverage level decreases linearly. The objectives are defined as the maximization of full and partial coverage, and the minimization of the maximum distance between uncovered demand nodes and their nearest facilities. We develop a new multi-objective genetic algorithm (MOGA) called modified SPEA-II (mSPEA-II). In this method, the fitness function of SPEA-II is modified and the crowding distance of NSGA-II is used. The performance of mSPEA-II is tested on randomly generated problems of different sizes. The results are compared with the solutions of the most well-known MOGAs, NSGA-II and SPEA-II. Computational experiments show that mSPEA-II outperforms both NSGA-II and SPEA-II.

The wisdom of voters: evaluating the Weber objective in the plane at the Condorcet solution

We investigate the quality of Condorcet solutions when compared to a central decision maker solution in the context of a facility location model in the plane. We perform an extensive set of experiments and conclude that if each population member votes according to his/her own self interest, then the Weber objective at the Condorcet solution point is very close to the optimal Weber objective value. Reducing the set of voters has little impact on the quality of the Condorcet solution. Being short of a good candidate has some impact but the final decision is still a good one. The distance metric seems to be of little relevance as well. As long as candidates are diverse, the Condorcet solution results in a good decision when compared to the decision by a benevolent dictator.

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

Many traditional facility location models have sought optimal solutions in two-dimensional space. However, certain locations in reality need to be modeled in three-dimensional space. This paper addresses a location problem in three-dimensional space from the application perspective. Specifically, we introduce a 3D coverage location model of Wi-Fi access points (APs) in an indoor environment. To do this, we first incorporate a generic radio propagation assuming typical obstructions of a building into the standard coverage model, using 3D Euclidean distance characterizing radio signal penetration. The suggested model is then applied for an efficient AP placement plan in a multi-story building at a university campus. The empirical results present 3D representations of the solutions for multi-floor deployment of Wi-Fi APs. This research is expected to provide a useful modeling framework for combining facility location model with wireless network design in a 3D environment.

A leader–follower model for discrete competitive facility location

In this paper we investigate a leader–follower (Stackelberg equilibrium) competitive location model. The competitive model is based on the concept of cover. Each facility attracts consumers within a “sphere of influence” defined by a “radius of influence.” The leader and the follower, each has a budget to be spent on the expansion of their chains either by improving their existing facilities or constructing new ones. We find the best strategy for the leader assuming that the follower, knowing the action taken by the leader, will react by investing his budget to maximize his market share. The objective of the leader is to maximize his market share following the follower׳s reaction.

Dynamic Access Network Reorganization for the Depopulation Age

The populations of industrialized countries will decline over the coming decades. To ensure that we have efficient access networks in the coming age of depopulation, it is important to consider the reorganization of central offices over time. The cost for operating and maintaining central offices can be reduced by efficiently closing central offices. However, dynamic facility location models that have been developed largely focused on the problem of optimally expanding a network over time to meet increasing demand. The practical relevance of the dynamic models is limited because the complexity and the required amount of data are much greater than with static models. This paper proposes a dynamic access network reorganization model for the depopulation age. Although the proposed model is a dynamic model, it is simple because it assumes that the only option will be to close central offices. The model first searches for a set of optimal solutions for each planning period as a capacitated facility location problem. Then, it selects the optimal combination of optimal solutions that can minimize the total number of open offices with the limitation of network reorganization. The validity of the proposed model was evaluated with computer simulations. It was confirmed that although the proposed model is a dynamic model it is simple and practical.

The reliable p-median problem with at-facility service

This paper deals with a discrete facility location model where service is provided at the facility sites. It is assumed that facilities can fail and customers do not have information on failures before reaching them. As a consequence, they may need to visit more than one facility, following an optimized search scheme, in order to get service. The goal of the problem is to locate p facilities in order to minimize the expected total travel cost. The paper presents two alternative mathematical programming formulations for this problem and proposes a matheuristic based on a network flow model to provide solutions to it. The computational burden of the presented formulations is tested and compared on a test-bed of instances.

Facility location models to locate data in information networks: a literature review

The usage of the Internet has grown substantially in recent times. This has resulted in high volumes of data traffic. There is a concomitant rise in bandwidth demands that could result in excessive download delays (or latency). Thus, a single-server system is no more a prudent choice for data storage. Replication of content and placing them on multiple servers is a method that is used to reduce latency. However, this solution comes at a huge cost. Moreover, replicating objects randomly does not necessarily improve system performance. It is possible to arrive at a solution to the problem of placing content so as to achieve better cost performance. Other performance measures include latency, load balancing and data availability. We refer to the problem of locating content as data location problem in information networks, or DLPIN. The choice of server locations, query routing strategy and user assignment are some of the important problems that require attention along with the location of the data/content. Resource constraints and the nature of traffic (static/dynamic) are two important parameters in the problem environment, and therefore are key distinguishing features in the models. The main contribution of this paper is a novel classification and study of DLPIN on the basis of problem features. The research in this area started with files, the smallest units of allocation. Gradually, files and programs, database segments and entire databases (or mirrors) have been studied. We design examples from these use cases to elaborate a variety of problems in a comprehensive review. Facility location models from physical logistics are extensively used to model these problems. Our paper presents a literature survey of such mathematical models for data location problems. We present a gap analysis that provides pointers to possible future research in this area. This paper also serves to document the success in the use of mathematical programming approaches for data location in information networks.

Determining the timing of project control points using a facility location model and simulation

Projects are usually performed in relatively unstable environments. As such, changes to the baseline schedules of projects are inevitable. Therefore, project progress needs to be monitored and controlled. The control process can be assumed as a continuum in which one side is continuous control and the other side is no-control. Continuous control and no-control strategies are cost-wise prohibited. Hence, project progress should be controlled at some discrete points in time during the project׳s duration. The optimal number and timing of control points are the main issues that should be addressed. In this paper, taking a dynamic view to the project control, for the first time we use an adapted version of the facility location model (FLM) to find the optimal timing of project control points. Initially, the adapted FLM determines the optimum timing of the control points in the project׳s duration. A simulation model is then used to predict the possible disruptions in the time period between the beginning of the project and the first control point (monitoring phase). If no disruptions are observed, the project׳s progress is monitored in the second control point, otherwise possible corrective actions are taken using an activity compression model. Whenever due to disruptions, the baseline schedule is to be updated, the FLM is run again to determine the new timing of the control points for the rest of the project׳s duration. In an iterative manner, this process continues until the timing of the last control point is determined.

Effects of Disruption Risks on Biorefinery Location Design

While ever-growing bio-ethanol production poses considerable challenges to the bioenergy supply chain, the risk of refinery operation disruptions further compromises the efficiency and reliability of the energy supply system. This paper applies discrete and continuous reliable facility location models to the design of reliable bio-ethanol supply chains so that the system can hedge against potential operational disruptions. The discrete model is shown to be suitable for obtaining the exact optimality for small or moderate instances, while the continuous model has superior computational tractability for large-scale applications. The impacts of both site-independent and dependent disruptions (i.e., due to flooding) are analyzed in empirical case study for the State of Illinois (one of the main biomass supply states in the U.S.). The reliable solution is compared with a deterministic solution under the same setting. It is found that refinery disruptions, especially those site-dependent ones, affect both optimal refinery deployment and the supply chain cost. Sensitivity analysis is also conducted to show how refinery failure probability and fixed cost (for building biorefineries) affect optimal supply chain configuration and the total expected system cost.

A Capacitated Facility Location Model with Bidirectional Flows

Supply chains with returned products are receiving increasing attention in the operations management community. The present paper studies a capacitated facility location model with bidirectional flows and a marginal value of time for returned products. The distribution system consists of a single supplier that provides one new product to a set of distribution centers (DCs), which then ships to the final retailers. While at the retailers' site, products can be shipped back to the supplier for reprocessing. Each DC is capacitated and handles stocks of new and/or returned products. The model is a nonlinear mixed-integer program that optimizes DC location and allocation between retailers and DCs. We show that it can be converted to a conic quadratic program that can be efficiently solved. Some valid inequalities are added to the program to improve computational efficiency. We conclude by reporting numerical experiments that reveal some interesting properties of the model.

Planning charging infrastructure for plug-in electric vehicles in city centers

ABSTRACTInstalling charging facilities in existing parking lots in city centers is considered an effective measure to encourage the adoption of plug-in electric vehicles (PEV). This article is concerned with the problem of locating these facilities so as to minimize the total system cost. The problem is formulated as a fixed charge facility location model with charging capacity constraints. The proposed model extends the existing work by allowing unserved demands and considering drivers’ preference for familiar parking lots. Accordingly, inconvenience costs are introduced for unserved demands and for those who have to change their parking lots in order to charge at work. The proposed model is not only always feasible, but also introduces a pricing mechanism so that the level of service (measured by the cost of unserved demands) can be traded off with the infrastructure cost. In addition, a stochastic version of the proposed model is developed to address the effects of uncertain PEV market penetration rate on the planning of charging facilities. A case study is conducted to analyze the sensitivity of the models to different cost components, and to compare the results of the stochastic and deterministic models.

On models for continuous facility location with partial coverage

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.