This semester I am teaching Linear Programming (LP). This year, we have students from many different backgrounds and departments taking the class, which I think is great news for our field. The more we make OR accessible to other fields, the better. Anyway, this year I decided to do something different and wanted to show the students all the different uses of linear programming in real life. So, I searched INFORMS journals + more for applications of LP. Even though many real-world problems involve nonlinearities and integer decision variables, the list of applications of LP turned out to be pretty impressive. Take a look:
∙ This is an application in health-care:
Remeijn, H., Ahuja, R., Dempsey, J. and A. Kumar, “A New Linear Programming Approach to Radiation Therapy Treatment Planning Problems,” Operations Research, 54(2): 201-216, 2006.
∙ This is an application in alternative energy (specifically wind energy). I came across this while reading GreenOR. Here’s the original entry on it. This application has been developed by the US National Renewable Energy Laboratory (NREL) to determine the expansion of wind electric generation and transmission capacity. It passes information from a Geographic Information System (GIS) into a linear program.
∙ This application is in finance:
Chalermkraivuth, K. C., Bollapragada, S., Clark, M. C., Deaton, J., Kiaer, L., Murdzek, J.P., Neeves, W., Scholz, B.J. and D. Toledano, “GE Asset Management, Genworth Financial, and GE Insurance Use a Sequential-Linear-Programming Algorithm to Optimize Portfolios,” Interfaces, 35: 370 – 380, September-October 2005.
∙ This application is in data mining (classification, statistics):
Eva K. Lee, Richard J. Gallagher, David A. Patterson, “A Linear Programming Approach to Discriminant Analysis with a Reserved-Judgment Region,” INFORMS Journal on Computing, 15(1): pp. 23–41, 2003.
∙ And, this is an application in Sports:
I. Horowitz, “Aggregating Expert Ratings Using Preference-Neutral Weights: The Case of the College Football Polls,” Interfaces, 34(4): 314–320, July–August 2004.
There are many more of course, but the above sample alone makes a strong case for the versatility and power of LP.