Model For Location Problem Research Articles

A leader-follower model for discrete competitive facility location problem under the partially proportional rule with a threshold.

When consumers are faced with the choice of competitive chain facilities that offer exclusive services, current rules do not properly describe the behavior pattern of these consumers. To eliminate the gap between the current rules and this kind of customers behavior pattern, the partially proportional rule with a threshold is proposed in this paper. A leader-follower model for discrete competitive facility location problem is established under the partially proportional rule with a threshold. Combining with the greedy strategy and the 2-opt strategy, a heuristical algorithm (GFA) is designed to solve the follower's problem. By embedding the algorithm (GFA), an improved ranking-based algorithm (IRGA) is proposed to solve the leader-follower model. Numerical tests show that the algorithm proposed in this paper can solve the leader-follower model for discrete competitive facility location problem effectively. The effects of different parameters on the market share captured by the leader firm and the follower firm are analyzed in detail using a quasi-real example. An interesting finding is that in some cases the leader firm does not have a first-mover advantage.

Using optimization to provide decision support for strategic emergency medical service planning – Three case studies

To achieve high performing emergency medical services (EMS), planning is of vital importance. EMS planners face several challenges when managing ambulance stations and the fleet of ambulances. In this paper, three strategic cases for EMS planners are presented together with potential solutions. In the first case, the effects of closing down a local emergency room (ER) are analyzed together with how adding an ambulance station and an ambulance to the area affected by the closing of the ER can be used to mitigate the negative consequences from the closing. The second case investigates a change in the organization of EMS. Currently, many non-urgent transport assignments are performed by ambulances which make them unavailable for more urgent calls. The potential for a more effective utilization of the ambulances is explored through transferring these assignments to designated transport vehicles. The third case is more technical and challenges the common practice regarding how time dependent demand is handled. Looking at the busiest hour or the average daily demand, is compared with taking time varying demand into account. The cases and solutions are studied using a recently developed strategic ambulance station location and ambulance allocation model for the Maximum Expected Performance Location Problem with Heterogeneous Regions (MEPLP-HR). The model has been extended to also include multiple time periods. This article demonstrates an innovative use of the model and how it can be applied to find and evaluate solutions to real cases within the field of strategic planning of EMS. The model is found to be a useful decision support tool when analyzing the cases and the expected performance of potential solutions.

A mathematical model for P-hub median location problem to multiple assignments between non-hub to hub nodes under fuzzy environment

One group of the optimization problems is Hub location problem. Hub facilities are used in transportation network which are provided transfer of products, information, passengers and postal package through of intermediate node instead of direct transfer. One main group of these problems is discrete hub median location that seeks to minimize total transportation cost. In this paper, we present hub median location problem with multiple allocation of non-hub nodes to hub nodes, moreover it is possible to connect non-hub nodes directly with considering a penalty coefficient. The numerical example for CAB25data set -which is related to flow and distance between 25 cities in America- with establishment cost under fuzzy circumstance solved and presented.

Effects of Free-Floating Shared Bicycles on Urban Public Transportation

As a product of the development of the Internet and the sharing economy, shared bicycles are beneficial in solving the last mile problem of public transportation for urban residents and expanding the service area of urban public transportation to a certain extent. This paper analyses the spatial-temporal characteristics of shared bicycles in the city of Beijing by using kernel density estimation and statistical analysis methods. The maximum coverage location problem model is used to quantify the effects of shared bicycles on the subway and bus urban public transportation systems. The analysis results are of great importance to identify the effects of shared bicycle usage on an urban bus public transportation system from the view of space-time. The results show that (1) shared bicycles are largely located within 1.5 km from the subway station and 500 m from the bus stations; (2) the number of the shared bicycle usage changes along with the distance from the subway and bus stations; (3) subway and bus stations are divided into six types based on the sink-source characteristics of shared bicycles; (4) the service areas of subway and bus stations are expanded by approximately 2.34 and 1.33 times, respectively, after the implementation of shared bicycles.

A mathematical model for P-hub median location problem to multiple assignments between non-hub to hub nodes under fuzzy environment

One group of the optimization problems is Hub location problem. Hub facilities are used in transportation network which are provided transfer of products, information, passengers and postal package through of intermediate node instead of direct transfer. Methodology: One main group of these problems is discrete hub median location that seeks to minimize total transportation cost. Results: In this paper, we present hub median location problem with multiple allocation of non-hub nodes to hub nodes, moreover it is possible to connect non-hub nodes directly with considering a penalty coefficient. Conclusion: The numerical example for CAB25data set -which is related to flow and distance between 25 cities in America- with establishment cost under fuzzy circumstance solved and presented.

A two-stage robust model for a reliable p-center facility location problem

We propose a two-stage robust model for reliable facility location when some facilities can be disrupted, for instance by a natural disaster. A reliable network is designed in a “proactive” planning phase, and when a facility is disrupted, its original clients can be reallocated to another available facility in a “reactive” phase. When demand and cost are uncertain, the initial design is also robust against the realizations (scenarios) of these parameters, which will only be revealed post-disruption. Based on the p-center location model, which attempts to optimize the worst-case performance of the network, our model is concerned with the reliability for every client. Three solution methods have been implemented and tested to solve the model, namely, a linear reformulation, a Benders dual cutting plane method, and a column-and-constraint generation method. We present an extensive numerical study to compare the performance of these methods. We find that, depending on the size of the instance (as given by the number of client sites and scenarios), either the Benders dual cutting plane method or column-and-constraint generation performs best. The effectiveness of our model is also examined in comparison with alternative facility location models.

Allocation of emergency response centres in response to pluvial flooding-prone demand points using integrated multiple layer perceptron and maximum coverage location problem models

The increases in the frequency and intensity of rainfall events due to global climate change and the development of additional pavement, roads and water storage sites due to population growth have enhanced the probability of pluvial flooding (PF) in urban areas. The estimation of urban pluvial flood vulnerability and prompt emergency responses are crucial steps towards urban planning and risk mitigation. However, uncertainties exist in the optimal allocation of emergency response centres (ERCs). This study assessed the current situation of ERCs in terms of PF-prone demand points. In this study, fire and police stations, hospitals and military camps were defined as ERCs, and residential buildings, where people spend most of their time, were considered demand points. Our study area was Damansara City in Peninsular Malaysia, which is frequently affected by PF. We combined an optimised PF probability model with ideal location allocation methods on a geographic information system platform to construct the proposed model for achieving accurate ERC spatial planning. Firstly, PF-prone urban areas were identified using a recent machine learning multiple layer perceptron (MLP) model. Then, a Taguchi method was used to calibrate the MLP variables, namely, seed, momentum, learning rate, hidden layer attribute and class. Fourteen important PF contributing parameters were weighted on the basis of historical flood events. The predicted PF-prone areas were validated by comparing the predictions with the data from meteorological stations and observed inventory events. In addition, the current locations of ERCs were utilised in the location allocation model to assess the ideal time for providing essential services to elements at risk. Minimum impedance and maximum coverage location problem models were implemented to assess the current allocated location of ERCs and multiple scenarios. The coverage of existing ERCs was calculated, and their suitable and optimal locations were projected for vulnerable inhabitants with either redundant or late emergency response. Results showed that areas near downtown have high PF probability but are not covered by ERCs within the standard 5 km radius. The proposed model can conserve time, reduce cost and save human lives by ensuring that vulnerable people in the Damansara River basin are covered by the nearest ERC.

A MILP model and memetic algorithm for the Hub Location and Routing problem with distinct collection and delivery tours

In this paper, we study the capacitated single allocation Hub Location-Routing Problem (CSAHLRP) with independent collection and delivery processes. We focus on the design of less-than-truck load (LTL) transport networks for the transport of goods between many shippers and their clients using flow concentration hubs. We seek to integrate the hub location and vehicle routing strategies such that the location of the hubs, the allocation of supplier/client nodes to hubs, the design of routes between nodes allocated to the same hub, as well as the inter-hub freight transportations, can be determined efficiently. We propose a mixed integer linear programming model for the problem with the aim of minimizing the total fixed and variable costs. Computational experiments based on the Australian Post (AP) data set geographical network are conducted with the CPLEX solver. Furthermore, we propose a memetic algorithm (MA) to solve large problems. Computational results show that the exact method can find optimal solutions for small instances and good feasible solutions for some medium-sized tests. In addition to also solving small problems to optimality, the MA succeeds in finding high quality solutions for medium and large CSAHLRPs efficiently.

Developing the mathematical model for hub location problem in line with resistive economy approach

Developing the mathematical model for hub location problem in line with resistive economy approach

Developing the mathematical model for hub location problem in line with resistive economy approach

From the strategic managers' point of view, locating a hub facility with a structure based on maximising flow and minimising lost costs are important part of the strategic decisions of the organisation. Hence, the purpose of locating service providers is to reduce costs and create appropriate conditions in the service network because of the wide variety of costs involved and great effects have on managerial decisions. The present study introduces a new problem in the field of hub location with a preventive reliability approach for transmitting the flow before hubs failure in which high reliability flow is released. Due to importance of resistive economy, in this paper a multi-objective mixed-integer programming has been provided for the country's transport network in order to prevent the flow waste and the weighted-sum approach has been utilised to solve it.

A Bi-Level Bi-Objective Mathematical Model for Stop Location in a School Bus Routing Problem

Nowadays, due to expansion of urban areas and population growth, the number of travels in the cities has increased dramatically and private vehicles are raised as a competitor to public transportation. Hence, designing a proper transportation system to encourage individuals to use public transportation is important. In this paper, a bi-level model for a bus stop location and bus routing problem based on leader-follower games is developed. The proposed strategy in this model is based on a location-allocation-routing (LAR) strategy. The first level (i.e., leader) concerns the location and routing problem and the second level (i.e., follower) concerns the allocation problem, in which the first level is a bi-objective optimization problem. In order to solve the model, two approaches are used that are based on the explicit enumeration and hybrid methods, respectively. Finally, the proposed approaches are used to solve a number of random instance problems, whose results indicate the effectiveness of the proposed algorithms.

A Mathematical Model for Competitive Location Problem with Product Selection

In this paper, a new competitive location problem for a chain is considered. The chain’s owner can offer a variety of products. The model’s objective is to determine both the location of the new facilities and the optimal product type for each opened facility. The patronizing behavior of the customers is based on Huff rule and the location of new facilities is selected from a set of potential sites. As a result, the model is a nonlinear integer programming problem and for solving the proposed model, the problem is reformulated as a mixed integer linear programming and therefore a standard optimization solver can be used for obtaining the optimal solutions for small and medium-size problems. To cope with large-size problems, we develop two methods: 1) a heuristic method for a special case and 2) a hybrid heuristic-firefly algorithm for general cases. By using the proposed model, it is shown numerically that in multi-product industries in which owner of the facilities is able to offer different types of products, in addition to the optimal location, it is necessary to determine the best products. In the end, a real-world case study for locating a new bakery is presented.

Bi-objective Optimization of a Multi-product multi-period Fuzzy Possibilistic Capacitated Hub Covering Problem: NSGA-II and NRGA Solutions

The hub location problem is employed for many real applications, including delivery, airline and telecommunication systems and so on. This work investigates on hierarchical hub network in which a three-level network is developed. The central hubs are considered at the first level, at the second level, hubs are assumed which are allocated to central hubs and the remaining nodes are at the third level. In this research, a novel multi-product multi-objective model for capacitated hierarchical hub location problem with maximal covering under fuzzy condition first is suggested. Cost, time, hub and central hub capacities are considered as fuzzy parameters, whereas manyparameters are uncertainty and indeterministic in the real world. To solve the proposed fuzzy possibilistic multi-objective model, first, the model is converted to the equivalent auxiliary crisp model by hybrid method and then is solved by two meta-heuristic algorithms such as Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Non-Dominated Ranked Genetic Algorithm (NRGA) using MATLAB software The statistical results report that there is no significant difference between means of two algorithms exception CPU time criteria. In general, in order to show efficiency of two algorithms, we used Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), the resultsclearly show that the efficiency of NRGA is better than NSGA-II and finally, figures are achieved by MATLAB software that analyze the conflicting between two objectives.

Alternative-fuel station network design under impact of station failures

In this paper, we have formulated a mixed-integer non-linear programming model for alternative-fuel station location problem in which each station can fail with a site-specific probability. The model aims to maximise the total expected traffic volume that can be refuelled by the unreliable alternative-fuel stations. Based on the linearisation techniques, i.e., probability chains and piecewise-linear functions, we linearise the non-linearity of compound probability terms in the non-linear model to solve this problem efficiently. An efficient Tabu search algorithm is also developed to solve the large-size instances. In addition, we extend the model to deal with reliable multi-period alternative-fuel station network design. Computational experiments, carried out on the well-known benchmark instances where the probability of station failures is uniformly generated, show that the proposed models and algorithm can obtain the optimal solutions within a reasonable computation time. Compared to a standard station location model that disregards the potential for station failures, our model designs more reliable alternative-fuel station network under risk of station failures. A sensitivity analysis of failure probabilities in the station network design is investigated to demonstrate the robustness of our model and study how variability in the probability of station failure affects solution robustness.

Pengembangan Model Capacitated Maximal Covering Location Problem (CMCLP) Dalam Penentuan Lokasi Pendirian Gudang

A strategic location is a place for facility location that built and is able to give maximum advantages for the company. The problem of deciding location is important in optimization area. In general, the solution of that problem focuses on facility placement that is able to minimize or maximizing distribution time, distance, transportation cost or another parameter. Therefore, an appropriate model is needed to determine the strategic location of warehouse establishment. The purpose of this research is to develop a Capacitated Maximal Covering Location Problem (MCLP) model that can be used in determining the location of warehouse establishment that can maximize the number of demands that can be served. From the model, the company not only finds the optimum location to establish the facility but also they can know the number of goods allocated from the distribution center to each demand point as well as the maximum number of demand that can be served.

Pengembangan Model Capacitated Maximal Covering Location Problem (CMCLP) Dalam Penentuan Lokasi Pendirian Gudang

A strategic location is a place for facility location that built and is able to give maximum advantages for the company. The problem of deciding location is important in optimization area. In general, the solution of that problem focuses on facility placement that is able to minimize or maximizing distribution time, distance, transportation cost or another parameter. Therefore, an appropriate model is needed to determine the strategic location of warehouse establishment. The purpose of this research is to develop a Capacitated Maximal Covering Location Problem (MCLP) model that can be used in determining the location of warehouse establishment that can maximize the number of demands that can be served. From the model, the company not only finds the optimum location to establish the facility but also they can know the number of goods allocated from the distribution center to each demand point as well as the maximum number of demand that can be served.

The Reliable Facility Location Problem Under Random Disruptions

The classical location models implicitly assume that the facilities, once built, will always operate as planned. However, some of the facilities may become unavailable from time to time due to disruptions caused by natural disasters, key-supplier bankruptcy, terrorist attacks, or labor strikes. Therefore, supply chain disruptions have gained considerable attention by researchers and practitioners in the past few decades. The catastrophic accidents highlighted the urgent need for effective solutions to manage supply chain disruptions in spite of their low probability of occurrence. Therefore, it is critical to take account of disruptions when designing supply chain networks so that they perform well as a whole even after a disruption. Taking into account the random disruption risk, this paper proposes a mixed integer programming model for the reliable facility location problem. This model try to minimize the sum of initial facility construction costs and expected transportation costs in both the regular and the failure scenarios, and present a Lagrange relaxation algorithm to solve it. This paper also analyzes the algorithm’s solving performance by a numerical experiment.

A mathematical model for supermarket location problem with stochastic station demands

This paper aims to investigate the effect of station demands variations on supermarket location problem (SLP). This problem arises in the real-world assembly line part feeding (PF) context where supermarkets are used as the intermediate storage areas for stations. To this purpose a stochastic SLP model is developed to optimize the total cost of PF in terms of shipment, inventory and installation costs. The computational results over a real case as well as different test instances verify that the station demands variation has an effect on the SLP solutions.

Two strategies of two-level facility network design for autonomous ground vehicle operations

ABSTRACTWe compare two models of two-level facility location problems for network design in autonomous ground vehicle (AGV) operations. The two-level model consists of locations for charging stations (main facilities), as well as for storage locations (substations). Demand points will represent processing locations. In both formulations, demands are assigned to substations and substations are assigned to main facilities. The formulations differ in whether each connection between a facility and a substation is counted once in absolute terms, or once per demand. These represent two different views, in which transfer between a main facility and substation is carried out either in bulk, e.g. using a shuttle, or by each AGV independently. Selected experimental results are presented for geometric networks and networks consisting of uniformly distributed points on a regular mesh. These results indicate that the two formulations lead to vastly different network designs in terms of the number of facilities and connectivity.

A New Model for Location and Transportation Problem of Cross-Docks in Distribution Networks

A New Model for Location and Transportation Problem of Cross-Docks in Distribution Networks