scholarly journals Globally Optimal Facility Locations for Continuous-Space Facility Location Problems

2021 ◽  
Vol 11 (16) ◽  
pp. 7321
Author(s):  
Xuehong Gao ◽  
Chanseok Park ◽  
Xiaopeng Chen ◽  
En Xie ◽  
Guozhong Huang ◽  
...  

The continuous-space single- and multi-facility location problem has attracted much attention in previous studies. This study focuses on determining the globally optimal facility locations for two- and higher-dimensional continuous-space facility location problems when the Manhattan distance is considered. Before we propose the exact method, we start with the continuous-space single-facility location problem and obtain the global minimizer for the problem using a statistical approach. Then, an exact method is developed to determine the globally optimal solution for the two- and higher-dimensional continuous-space facility location problem, which is different from the previous clustering algorithms. Based on the newly investigated properties of the minimizer, we extend it to multi-facility problems and transfer the continuous-space facility location problem to the discrete-space location problem. To illustrate the effectiveness and efficiency of the proposed method, several instances from a benchmark are provided to compare the performances of different methods, which illustrates the superiority of the proposed exact method in the decision-making of the continuous-space facility location problems.

2015 ◽  
Vol 25 (3) ◽  
pp. 313-341 ◽  
Author(s):  
Chandra Irawan ◽  
Said Salhi

A facility location problem is concerned with determining the location of some useful facilities in such a way so to fulfil one or a few objective functions and constraints. We survey those problems where, in the presence of a large number of customers, some form of aggregation may be required. In addition, a review on conditional location problems where some (say q) facilities already exist in the study area is presented.


Author(s):  
Michael J. Brusco

There are a variety of discrete facility location models that have practical relevance for operations management and management science courses. Integer linear programming (ILP) is the standard technique for solving such problems. An alternative approach that is often conceptually appealing to students is to pose the problem as one of finding the best possible subset of p facilities out of n possible candidates. I developed an Excel workbook that allows students to interactively evaluate the quality of different subsets, to run a VBA macro that finds the optimal subset, or to solve an ILP formulation that finds the optimal subset. Spreadsheets are available for five classic discrete location models: (1) the location set-covering problem, (2) the maximal covering location problem, (3) the p-median problem, (4) the p-centers problem, and (5) the simple plant location problem. The results from an assignment in a master’s-level business analytics course indicate that the workbook facilitates a better conceptual understanding of the precise nature of the discrete facility location problems by showing that they can be solved via enumeration of all possible combinations of p subsets that can be drawn from n candidate locations. More important, students directly observe the superiority of ILP as a solution approach as n increases and as p approaches n/2.


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