# Locating multiple facilities using the max-sum objective

### Significance

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.

Dr. Pawel Kalczynski is a Professor of Information Systems and Decision Sciences in the Mihaylo College of Business and Economics at California State University – Fullerton. He has 30 refereed journal articles in such publications as European Journal of Operational Research, Journal of the Operational Research Society, Omega, Computers and Operations Research, Journal of Scheduling, International Journal of Electronic Commerce, Information Processing and Management, Journal of Business Research and others. He has 28 other refereed publications including refereed proceedings articles and book chapters. He has received several research awards and grants and completed numerous consulting projects in the field of analytics.

Dr. Zvi Drezner, Professor emeritus at California State University, Fullerton  got his Ph.D. in Computer Science  in 1975 from the Technion, Israel institute of technology. He published two books and about 300 refereed journal articles including seven in Operations Research, four in Management Science, and 18 in IIE Transactions, in addition to many refereed book chapters and conference proceedings. One article was cited over 2,300 times, 29 were cited at least 100 times each, and 214 were cited at least 10 times each for a total of over 16,000 citations. His vita is available at  at the website http://mihaylofaculty.fullerton.edu/sites/zdrezner/.

He received the lifetime achievement in location analysis award by the INFORMS Section on Location Analysis in 2005.

He was honored as a “Luminary of Operations Research” in 2018. The full hour video interview is published in the official INFORMS website

The book “Contributions to Location Analysis In Honor of Zvi Drezner’s 75th Birthday” Eiselt, H. A., Marianov, Vladimir (Eds.)  is devoted to his accomplishments in the field of Location analysis.

### Reference

Kalczynski, P., & Drezner, Z. (2019). Locating multiple facilities using the max-sum objective. Computers & Industrial Engineering, 129, 136-143.