Abstract
The Vector Assignment Ordered Median Problem (VAOMP) is a new unified approach for location-allocation problems, which are one of the most important forms of applied analysis in GIS (Geospatial Information System). Solving location-allocation problems with exact methods is difficult and time-consuming, especially when the number of objectives and criteria increases. One of the most important criteria in location-allocation problems is the capacity of facilities. Firstly, this study develops a new VAOMP approach by including capacity as a criterion, resulting in a new model known as VAOCMP (Vector Assignment Ordered Capacitated Median Problem). Then secondly, the results of applying VAOMP, in scenario 1, and VAOCMP, in scenario 2, for the location-allocation of fire stations in Tehran, with the objective of minimizing the arrival time of fire engines to an incident site to no more than 5 min, are examined using both the Tabu Search and Simulated Annealing algorithms in GIS. The results of scenario 1 show that 52,840 demands were unable to be served with 10 existing stations. In scenario 2, given that each facility could not accept demand above its capacity, the number of demands without service increased to 59,080, revealing that the number of stations in the study area is insufficient. Adding 35 candidate stations and performing relocation-reallocation revealed that at least three other stations are needed for optimal service. Thirdly, and finally, the VAOMP and VAOCMP were implemented in a modest size problem. The implementation results for both algorithms showed that the Tabu Search algorithm performed more effectively.
Highlights
Location-allocation is one of the most important analyses in GIS science, identifying optimal facility locations for optimal services to specific demands [1]
This study investigates the application of the Vector Assignment Ordered Median Problem (VAOMP) and VAOCMP models to the specific study area of fire stations in Tehran, with a demand capacity of 50,000 people and the goal of minimizing the arrival time of fire engines to the incident site to 5 min
The VAOMP model was developed to include the capacity criterion, and the results of the VAOMP model were investigated with the VAOCMP model to examine the status of the existing fire stations in the study area, with the aim of minimizing arrival time using the Tabu Search and Simulated Annealing algorithms
Summary
Location-allocation is one of the most important analyses in GIS science, identifying optimal facility locations for optimal services to specific demands [1]. Demands can be allocated to facilities based on factors, such as minimum distance, minimum cost, the capacity of facilities, etc. Sci. 2020, 10, 8505 location for each facility depends on such criteria as optimal distance, capacity, population density, and optimal cost. An unsuitable location for a facility would adversely affect that facility in providing an effective service. The capacity of facilities is a factor in the effectiveness of their service. The location of the facilities must be well-defined and distributed in such a way that they can respond to the demand, in terms of their capacity.
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