Generally, busy facilities such as airports, factories affect the surrounding neighborhoods. To minimize such disturbances, residential homes and other critical facilities like schools and hospitals have henceforth been moved away. The disturbance problems involving the location of one or more facilities from a set of demand points have been the center of research in recent studies. This has taken into consideration both the nuisance generated by the facilities and the demand points. Whereas most of the available models take into consideration the location of only one facility, there is a need to increase the number of facilities for a given set of demand points to close the existing research gap.
The total disturbance has been minimized by maximizing the sum of the weighted distance between the closest factory and the neighborhoods as well as maximizing the minimum distance between the facilities and demand points. The former is designed to minimize the disturbance caused by the facility on all the demand points and vice versa while the latter is designed to protect the most affected demand point. These models address the objective of both obnoxious and non-obnoxious facility location models that represents facilities located far from the demand points and close to demand points respectively.
Recently, California State University-Fullerton researchers: Professor Pawel Kalczynski and Professor Zvi Drezner looked carefully at the objectives of maximizing the sum of the minimum distance between the facilities and the demands points. They used the multi-start sequential linear programming algorithm (accepted for publication in International Transactions in Operational Research), a solution of two problems: Max-Sum 1 considering obnoxious facilities by maximizing the total distance between the closet facility and demand points and Max-Sum 2 considering obnoxious demand points by maximizing the total distance between the closest demand point and the facilities. Specifically, the Max-Sum 2 problem was solved using a heuristic procedure based on Voronoi diagrams. To validate the provided solution approach, the two Professors formulated and solved four sets of instances and compared the results with that of the interior point and SNOPT solved in Matlab. The work is currently published in the journal, Computers and Industrial Engineering.
Interiors point in Matlab produced poor- and low-quality results as compared to the other methods. For Max-Sum 1, multi-start sequential linear programming produced reliable and high-quality results as compared to the SNOPT technique. However, the proposed heuristic approach was highly suitable for solving the Max-Sum 2 problem. Even though the quality differences in the results produced by the different techniques were not much significant, multi-start sequential linear programming method generally performed better than SNOPT and was much efficient in terms of computation time.
In summary, Kalczynski- Drezner study proposed a new solution for two multiple obnoxious facilities problems: Max-Sum 1 and Max-Sum 2. Multi-start sequential linear programming worked best for Max-Sum 1 while Voronoi heuristic technique was much suitable for solving Max-Sum 2. Altogether, their work provides important insights that will help minimize disturbances caused by various facilities on the surroundings.
Kalczynski, P., & Drezner, Z. (2019). Locating multiple facilities using the max-sum objective. Computers & Industrial Engineering, 129, 136-143.