Operations Research

Operations research is a vast branch of mathematics which encompasses many diverse areas of minimization and optimization. Thousands of books have been written worldwide on the subject of operations research.

The central objective of operations research is optimization, i.e., "to do things best under the given circumstances." This general concept has great many applications, for instance, in agricultural planning, biotechnology, data analysis, distribution of goods and resources, emergency and rescue operations, engineering systems design, environmental management, financial planning, health care management, inventory control, manpower and resource allocation, manufacturing of goods, military operations, production process control, risk management, sequencing and scheduling of tasks, telecommunications, and traffic control.

Closely related disciplines (with significant overlaps among these) include decision analysis, systems analysis, management science, control theory, game theory, optimization theory, constraint logic programming, artificial intelligence, fuzzy decision-making, multi-criteria analysis, and so on. All these disciplines share the objective of improving a quantitative decision making procedure. The same comment applies to operations research-related business applications such as supply-chain management, enterprise resource planning, total quality management, just-in-time production and inventory management, and materials requirements planning.

Following the general optimization paradigm, when applying operations research, a decision-maker selects the key decision variables that will influence the overall quality of decisions. This quality is expressed by the objective function that is maximized (profit, product quality, speed of service or job completion, and so on), or minimized (cost, loss, risk of some undesirable event, etc.). In addition to the objective function, a set of (physical, technical, economic, environmental, legal, societal, etc.) constraints is also considered. Then, by systematically adjusting the values of all decision variables, a "good" (feasible) or "very best" (optimal) solution is selected. Of course, feasibility and optimality can only be defined in the context of the given problem (model) formulation.

REFERENCES:

Bazaraa, M. S.; Sherali, H. D.; and Shetty, C. M. Nonlinear Programming: Theory and Algorithms. New York: Wiley, 1993.

Bertsekas, D. P. Nonlinear Programming, 2nd ed. Cambridge, MA: Athena Scientific, 1999.

Bronson, R. Schaum's Outline of Theory and Problems of Operations Research. New York: McGraw-Hill, 1982.

Chong, E. K. P. and Zak, S. H. An Introduction to Optimization, 2nd ed. New York: Wiley, 2001.

Edgar, T. F.; Himmelblau, D. M.; and Lasdon, L. S. Optimization of Chemical Processes, 2nd ed. New York: McGraw-Hill, 2001.

Horst, R. and Pardalos, P. M. (Eds.). Handbook of Global Optimization, Vol. 1. Dordrecht, Netherlands: Kluwer, 1995.

Hillier, F. S. and Lieberman, G. J. Introduction to Operations Research, 8th ed. New York: McGraw-Hill, 1990.

INFORMS. Operations Research: 50th Anniversary Issue. Linthicum, MD, 2002.

Marlow, W. H. Mathematics for Operations Research. New York: Dover, 1993.

Pardalos, P. M. and Resende, M. G. C. (Eds.). Handbook of Applied Optimization. Oxford, England: Oxford University Press, 2002.

Pardalos, P. M. and Romeijn, H. E. (Eds.). Handbook of Global Optimization, Vol. 2. Dordrecht, Netherlands: Kluwer, 2002.

Pintér, J. D. Global Optimization in Action. Dordrecht, Netherlands: Kluwer, 1996.

Pintér, J. D. Computational Global Optimization in Nonlinear Systems: An Interactive Tutorial. Atlanta, GA: Lionheart Publishing, 2001.

Pintér, J. D. Applied Nonlinear Optimization in Modeling Environments: Using Integrated Modeling and Solver Environments. Boca Raton, FL: CRC Press, 2005.

Sethi, S. P. and Thompson, G. L. Optimal Control Theory: Applications to Management Science and Economics. Dordrecht, Netherlands: Kluwer, 2000.

Singh, J. Great Ideas of Operations Research. New York: Dover, 1972.

Trick, M. "Michael Trick's Operations Research Page." http://mat.gsia.cmu.edu.

Weisstein, E. W. "Books about Operations Research." http://www.ericweisstein.com/encyclopedias/books/OperationsResearch.html.

Williams, H. P. Model Building in Mathematical Programming, 4th ed. New York: Wiley, 1999.

Winston, W. L. and Albright, S. C. Practical Management Science, 2nd ed. Pacific Grove, CA: Duxbury Press, 2001.