Vector Assignment Ordered Median Problem

Lei, Ting; Church, Richard L.

doi:10.1177/0160017612450710

Cited by 23 publications

(24 citation statements)

References 36 publications

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“…where r is the number of facilities, m is the number of demands, d ij is the network-based distance between the facility point j and demand point i based upon Dijkstra's algorithm, w i is the weight of demand point i, C j is the maximum capacity of facility j (C j = 50,000), A j is the allocated demand at facility j, and λ k is the weight of the kth rank of service [25].…”

Section: Minimizing the Distance Between The Demand And The Fire Stationmentioning

confidence: 99%

The Ordered Capacitated Multi-Objective Location-Allocation Problem for Fire Stations Using Spatial Optimization

Bolouri

Vafaeinejad

Alesheikh

et al. 2018

IJGI

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Determining the positions of facilities, and allocating demands to them, is a vitally important problem. Location-allocation problems are optimization NP-hard procedures. This article evaluates the ordered capacitated multi-objective location-allocation problem for fire stations, using simulated annealing and a genetic algorithm, with goals such as minimizing the distance and time as well as maximizing the coverage. After tuning the parameters of the algorithms using sensitivity analysis, they were used separately to process data for Region 11, Tehran. The results showed that the genetic algorithm was more efficient than simulated annealing, and therefore, the genetic algorithm was used in later steps. Next, we increased the number of stations. Results showed that the model can successfully provide seven optimal locations and allocate high demands (280,000) to stations in a discrete space in a GIS, assuming that the stations' capacities are known. Following this, we used a weighting program so that in each repetition, we could allot weights to each target randomly. Finally, by repeating the model over 10 independent executions, a set of solutions with the least sum and the highest number of non-dominated solutions was selected from among many non-dominated solutions as the best set of optimal solutions.

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Section: Minimizing the Distance Between The Demand And The Fire Stationmentioning

confidence: 99%

The Ordered Capacitated Multi-Objective Location-Allocation Problem for Fire Stations Using Spatial Optimization

Bolouri

Vafaeinejad

Alesheikh

et al. 2018

IJGI

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“…Weaver and Church [20] proposed the vector assignment p-median problem, where a certain percentage of customers could be serviced by the kth nearest facility. The problem was extended by Lei and Tong [10] to the expected median location problem and Lei and Church [9] to the vector assignment ordered median problem. Pirkul [17] studied a similar problem in which customers are served by two facilities designated as primary and secondary facilities.…”

Section: Introductionmentioning

confidence: 99%

Distribution of the Ratio of Distances to the First and Second Nearest Facilities

Miyagawa

2017

JORSJ

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This paper deals with the ratio of the distances to the first and second nearest facilities. The ratio represents the reliability of facility location when the nearest facility is closed and customers are serviced by the second nearest facility. The distribution of the ratio is derived for grid and random patterns of facilities. Distance is measured as the Euclidean and rectilinear distances. The distribution shows how the ratio is distributed in a study region, and will supply building blocks for facility location models with closing of facilities. The distribution of the ratio of the road network distances is also calculated for actual facility location.

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“…The ( p, q )‐center problem represents a conservative location strategy and may be overpessimistic because the worst case scenario represents only one of a very large number of possible scenarios of facility failure and may rarely happen. Lei and Church () and Lei et al () developed a general model structure called the Vector Assignment Ordered Median Problem that account for reliable facility location involving nonclosest assignment as well as different location objectives including the p ‐center objective. At least in principle, both the ( p , q )‐center problem and the proposed vector assignment p ‐center problem can be solved as a special case of the VAOMP problem.…”

Section: Introductionmentioning

confidence: 99%

Designing Reliable Center Systems: A Vector Assignment Center Location Problem

Lei

2016

Geographical Analysis

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The p-center problem is one of the most important models in location theory. Its objective is to place a fixed number of facilities so that the maximum service distance for all customers is as small as possible. This article develops a reliable p-center problem that can account for system vulnerability and facility failure. A basic assumption is that located centers can fail with a given probability and a customer will fall back to the closest nonfailing center for service. The proposed model seeks to minimize the expected value of the maximum service distance for a service system. In addition, the proposed model is general and can be used to solve other fault-tolerant center location problems such as the (p, q)-center problem using appropriate assignment vectors. I present an integer programming formulation of the model and computational experiments, and then conclude with a summary of findings and point out possible future work.

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Vector Assignment Ordered Median Problem

Cited by 23 publications

References 36 publications

The Ordered Capacitated Multi-Objective Location-Allocation Problem for Fire Stations Using Spatial Optimization

The Ordered Capacitated Multi-Objective Location-Allocation Problem for Fire Stations Using Spatial Optimization

Distribution of the Ratio of Distances to the First and Second Nearest Facilities

Designing Reliable Center Systems: A Vector Assignment Center Location Problem

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