The Capacitated Location-Allocation Problem Using the VAOMP (Vector Assignment Ordered Median Problem) Unified Approach in GIS (Geospatial Information Systam)

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.

A Branch-Price-and-Cut Procedure for the Discrete Ordered Median Problem

The discrete ordered median problem (DOMP) is formulated as a set-partitioning problem using an exponential number of variables. Each variable corresponds to a set of demand points allocated to the same facility with the information of the sorting position of their corresponding costs. We develop a column generation approach to solve the continuous relaxation of this model. Then we apply a branch-price-and-cut algorithm to solve small- to large-sized instances of DOMP in competitive computational time.