Facility Location Model Research Articles

Fuzzy Multi-Objective Programming Model for Facility Location in an Integrated Supply Chain Network

Traditional supply chain network design problems are often taken as a single objective. However, supply chains are complex networks formed by organizations having conflicting objectives with each other in real life. In this study, a multi-product, multi-stage and multi-period planning model is proposed to achieve multiple incommensurable goals in an integrated supply chain network with uncertain market demands. The supply chain planning model is constructed as a mixed-integer nonlinear programming problem to satisfy several conflicting objectives with each other. The proposed model consists of two objective functions. The first one is minimizing the fixed opening and operating costs with transportation costs determined depending on distances. Second one is minimizing the purchasing, ordering, inventory and backlogging costs according to Economic Production Quantity (EPQ) model. Fuzzy goal programming approach is used in order to include decision maker's imprecise goal values in proposed model. The model is solved using GAMS optimization program. The application results presented in this study, demonstrates that fuzzy modeling and solution approaches could be used in the creation of more realistic models of the supply chain.

Research on Location-Inventory Model in Grain Emergency Network

Once the disaster occurred, a huge amount of grain supply is needed from disaster area. Because of the short shelf life, grain is very strict with reserve environment and needed to rotate on a regular basis in the process of reserves. Considering the limitations of existing related research, this paper presented a facility location model for grain emergency network that incorporates inventory factors and rotation mechanism, and then designed genetic algorithm based on Matlab to solve the model. Finally we verified the feasibility and effectiveness of the algorithm by computational examples and presented the directions for future work.

A bi-objective stochastic single facility location model for a supermarket

Selecting a new location is vital for retail stores such as chain supermarkets and can be considered as a huge competitive advantage which may result in their failure or success. Location models are hard to implement in the real world, firstly because of the uncertainties of the input parameters and secondly, due to the intensive computations involved when the solution space is large such as a city. In this study, a stochastic bi-objective model is developed for point and area destinations with the purpose of finding a single new location for a chain supermarket that aims to be close to more customers and have the minimum number of competitors near to the new location. Customer locations are considered to be regional with a uniform probability distribution. A reduced gradient solution procedure is used as an algorithm for solving the model. The problem is solved with the help of the MATLAB software due to the high computations involved.

Hierarchical facility location problem: Models, classifications, techniques, and applications

The primary objective in a typical hierarchical facility location problem is to determine the location of facilities in a multi-level network in a way to serve the customers at the lowest level of hierarchy both efficiently (cost minimization objective) and effectively (service availability maximization objective). This paper presents a comprehensive review of over 40years of hierarchical facility location modeling efforts. Published models are classified based on multiple characteristics including the type of flow pattern, service availability, spatial configuration, objective function, coverage, network levels, time element, parameters, facilities, capacity, and real world application. A second classification is also presented on the basis of solution methods adopted to solve various hierarchical facility location problems. The paper finally identifies the gaps in the current literature and suggests directions for future modeling efforts.

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

Facility location problems with the objective to minimize the sum of the setup cost and transportation cost are studied in this paper. The setup and transportation costs are considered as a function of the number of opened facilities. Three methods are introduced to solve the problem. The facility location model with bounds for the number of opened facility is constructed in this work. The relationship between setup cost and transportation cost is studied and used to build these methods based on greedy algorithm, p-median algorithm and p-center algorithm. The performance of the constructed methods is tested using 100 random data sets. In addition, the networks representing the road transportation system of Chiang Mai city and 5 provinces in Northern Thailand are illustrated and tested using all presented methods. Simulation results show that the method developed from greedy algorithm is suitable for solving problems when the setup cost is higher than transportation cost while the opposite cases are more efficiently solved with the method developed by the p-median problem.

An Efficient Approach for Solving Reliable Facility Location Models

We consider reliable facility location models in which facilities are subject to unexpected failures, and customers may be reassigned to facilities other than their regular facilities. The objective is to minimize the total expected costs in normal and failure scenarios. We allow facilities to have different failure rates and do not limit the number of facilities that might be assigned to a customer. Lower bounds for reliable uncapacitated fixed-charge location problem (RUFLP) are derived and used to introduce a class of efficient algorithms for solving the RUFLP problem.

Network modelling of palm biodiesel plants to supply the isolated electric power systems of Pará state

Despite the great advance brought by the National Interconnected System (NIS), which is able to provide clean hydroelectric power to almost all Brazilian customers, there are still cities supplied by power generated from fossil fuel, which are subsidized by taxes, they are called Isolated Electric Power Systems (IEPS). Para State, that has 34 cities with IEPS, also has potential to crop raw material (palm and sugar cane) to produce biodiesel for power generation. Our study analyzes the supply and distribution network of biodiesel under some scenarios of waterways availability, considering that they are also source of power to the NIS by the construction of hydroelectric dams. We develop specific demand and facility location models and apply them to the scenarios. Our results point to the efficiency of the generated models, the importance of three cities for the network, and to the little impact of some waterways in the total transportation costs.

An approach for the optimal planning of electric vehicle infrastructure for highway corridors

An approach is presented for the estimation of minimum PEV charging infrastructure needs, and the optimization of infrastructure deployment for highway corridors. We utilize continuous facility location models, which is distinguished from previous research that uses graph theory methods. We aim to obtain the optimal locations of publicly-funded infrastructure, to complement infrastructure provided by private industry, while carefully dealing with demand uncertainty. A case study is presented for highway corridors in the Texas Triangle megaregion. A discussion is provided on demand uncertainty and implementation considerations as well.

Park and Ride Facility Location Research of Rail Transit Based on Bi-Level Programming Model

This paper seeks to build new park and ride facilities (including the location and size) as well as expand the old ones based on the super road network composed of the road network and mass rapid transit (MRT) network. Park and ride facility location model of the outskirts of the city is established grounded infusing path-based user equilibrium assignment model and multi-assignment method, which is based on minimal investments. The calculation results of the model show that park and ride facilities on the outskirts of the city can greatly reduce the road traffic in central area.

A comparison of linear reformulations for multinomial logit choice probabilities in facility location models

In the last decade several papers appeared on facility location problems that incorporate customer demand by the multinomial logit model. Three linear reformulations of the original non-linear model have been proposed so far. In this paper, we discuss these models in terms of solvability. We present empirical findings based on synthetic data.

Developing Network Location Model in Uncertainty Mode (Robust Mode)

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.

Optimization Model for Fire Station Location Based on GIS and Python: A Case Study in North Cyprus

In this paper, the location selection process related to fire stations in Famagusta city is enhanced by applying Quantum Geographic Information Systems (QGIS) and Python programming language. This procedure leads to obtaining the optimum emergency service location based on the minimization of response time. This study aims to commence service coverage modeling in a consistent demand region, with road availability considerations. In addition, this study focuses on the capability of GIS to create service areas by means of the travel time regions in a facility location model. Another purpose of this research is to maximize the overall service area of the determined number of facilities and to state the capability of GIS for establishing the suitable service areas of fire stations in Famagusta city so as to achievie a maximal overall service area from a specific fire station facility to other locations. The best location for only one fire station is determined which is placed around the signalized intersection joining Mustafa Kemal Boulevard and Topçular Boulevard in Famagusta (node 230).

Robust sustainable bi-directional logistics network design under uncertainty

Abstract Reverse logistics networks are often implemented to ensure a sustainable product or material recovery and to improve a company's sustainability footprint. The most common approach for designing bi-directional networks is the independent design of reverse and forward networks. The joint integration of both networks is rarely considered. Here we study a strategic capacitated facility location problem with integrated bi-directional product flows through a network of multiple supply stages, including production allocations, uncertain data development, facility locations and flexible capacity adjustments. We extend the location and capacity problem by including the decision on the type of depot to install. Forwarding or collecting depots only process one designated direction. Hybrid sites process products of both flow directions. We first introduce a detailed deterministic model assessing the impact of incorporating reverse logistics into a forward-oriented supply chain. This is then extended to a robust capacitated facility location model, which minimizes the expectations of relative regrets for a set of scenarios over a multi-period planning horizon, while considering uncertainty regarding supplying and collecting goods. Example settings show the superior performance of the robust model compared to the deterministic model. The resulting network design mitigates the risks of higher costs and of not being able to fully satisfy demand. This is achieved at costs not significantly higher than the individual optimal solution and with solution times that are promising for applications in practice. The approach supports practitioners in assessing the flexibility of their supply chain, independent of its product flow direction, when operating under uncertainty.

Location planning for transit-based evacuation under the risk of service disruptions

The effectiveness of transit-based emergency evacuation highly depends on the location of pick-up facilities, resource allocation, and management. These facilities themselves are often subject to service disruptions during or after the emergency. This paper proposes a reliable emergency facility location model that determines both pre-emergency facility location planning and the evacuation operations afterwards, while facilities are subject to the risk of disruptions. We analyze how evacuation resource availability leverages individual evacuees’ response to service disruptions, and show how equilibrium of the evacuee arrival process could be reached at a functioning pick-up facility. Based on this equilibrium, an optimal resource allocation strategy is found to balance the tradeoff between the evacuees’ risks and the evacuation agency’s operation costs. This leads to the development of a compact polynomial-size linear integer programming formulation that minimizes the total expected system cost from both pre-emergency planning (e.g., facility set-up) and the evacuation operations (e.g., fleet management, transportation, and exposure to hazardous surroundings) across an exponential number of possible disruption scenarios. We also show how the model can be flexibly used to plan not only pre-disaster evacuation but also post-disaster rescue actions. Numerical experiments and an empirical case study for three coastal cities in the State of Mississippi (Biloxi, Gulfport, and D’lberville) are conducted to study the performance of the proposed models and to draw managerial insights.

A facility location model for socio-environmentally responsible decision-making

The consideration of external costs is becoming more important in supply network design, as companies are under increasing pressure to reduce the environmental and social impacts of their operations. This paper presents a single time period, single-product mixed integer linear programming formulation, which considers such external costs, as well as the impact of waste disposal. The model presented considers a network of suppliers, manufacturing facilities, customers, scrap recyclers, general recycling facilities and landfill sites and makes facility location and allocation decisions so as to minimise both the economic and external costs of all network operations. The model was formulated using the What’s Best Excel add-in and tested on a commercial case study concerning the supply network operations of Hydram, a leading sheet metal fabrication company, considering three different scenarios. Details of how the external and economic costs were determined are included, with reference to the literature. By analysis of the experimental results, commercial recommendations for facility location are made, and the managerial uses of the model for socio-environmentally responsible decision-making are discussed. The benefits and limitations of the proposed model are also discussed.

A Novel Facility Location Model in Content Distribution Networks

A Novel Facility Location Model in Content Distribution Networks

A multi-objective optimization model for sustainable logistics facility location

This paper offers an exploratory study of sustainable facility location. The methodology, based on the classical uncapacitated facility location problem, provides decision makers with a multi-objective optimization model to determine the trade-off among economic, service and environmental considerations. Our results indicate that it may be desirable to open more facilities than optimal from a narrow economic perspective to reduce the carbon dioxide emissions of transport and to improve service reliability.

Cone contraction and reference point methods for multi-criteria mixed integer optimization

Interactive approaches employing cone contraction for multi-criteria mixed integer optimization are introduced. In each iteration, the decision maker (DM) is asked to give a reference point (new aspiration levels). The subsequent Pareto optimal point is the reference point projected on the set of admissible objective vectors using a suitable scalarizing function. Thereby, the procedures solve a sequence of optimization problems with integer variables. In such a process, the DM provides additional preference information via pair-wise comparisons of Pareto optimal points identified. Using such preference information and assuming a quasiconcave and non-decreasing value function of the DM we restrict the set of admissible objective vectors by excluding subsets, which cannot improve over the solutions already found. The procedures terminate if all Pareto optimal solutions have been either generated or excluded. In this case, the best Pareto point found is an optimal solution. Such convergence is expected in the special case of pure integer optimization; indeed, numerical simulation tests with multi-criteria facility location models and knapsack problems indicate reasonably fast convergence, in particular, under a linear value function. We also propose a procedure to test whether or not a solution is a supported Pareto point (optimal under some linear value function).

A Lagrangian relaxation-based method and models evaluation for multi-level lot sizing problems with backorders

The capacitated multi-level lot sizing problem with backorders has received a great deal of attention in extant literature on operations and optimization. The facility location model and the classical inventory and lot sizing model with (ℓ, S) cuts have been proposed to formulate this problem. However, their comparative effectiveness has not yet been explored and is not known. In this paper, we demonstrate that on linear programming relaxation, the facility location formulation yields tighter lower bounds than classical inventory and lot sizing model. It further shows that the facility location formulation is computationally advantageous for deriving both lower and upper bounds. The results are expected to provide guidelines for choosing an effective formulation during the development of solution procedures. We also propose a Lagrangian relaxation-based heuristic along with computational results that indicate its competitiveness with other heuristics and a prominent commercial solver, Cplex 11.2.

Design of Fuzzy Multiobjective Linear Program Integrated with Fuzzy Vikor for Facility Location

Production level of a company increases mainly based on the demand and needs of that location. Facility location models are used to determine the optimal locations based on operating cost, accessibility of the existing, and future facilities. Selection of Location in supply chain for constructing a firm, is based on quantitative and qualitative factors. It is assessed by linguistic variables under fuzzy environment where uncertainty, vagueness, and subjectivity are handled. This paper deals with the design of Fuzzy multi objective Linear Programming model, integrated with Fuzzy VIKOR method. Fuzzy VIKOR method is used for assessing the qualitative factors and mathematical model such as Fuzzy Mixed Integer Linear programming is used for assessing the quantitative factors. Fuzzy VIKOR focuses on ranking&selecting from a set of alternatives in the presence of conflicting criteria by comparing the measure of "Closeness" to the "ideal" alternative, and thus to discover a best solution. It provides a rational, systematic process, to discover a best solution. It is used to resolve a fuzzy multi-person, multi-criteria decision-making problem. It also allows decision makers to specify the preferred solution for a given decision problem in real organizational settings. Fuzzy Multi Objective Linear Programming is used to find the optimum solution. A case example is illustrated for location selection of a firm, and the results are validated by integrating Fuzzy Mixed Integer Linear Programming with Fuzzy VIKOR method.