The mathematical models of the field of operations research can be dichotomized as deterministic and probabilistic. Often the deterministic models reflect complex systems involving large numbers of decision variables and constraints and are broadly labeled mathematical programming models. Some of the most complex constrained optimization models involve tens of thousands of constraints and hundreds of thousands of decision variables. Operation researchers not only model these complex systems but also have developed algorithms that can efficiently search for optimal or near optimal solutions. Another class of deterministic models involves networks: routing through the network or optimal location on a network. Decisions involving multiple objectives can be addressed with a general class of models called Multi-Criteria Decision Analysis (MCDA).

Decision trees are a basic tool for structuring decisions in the presence of uncertainty. A tree is used to lay out the sequence of decisions and random events. The optimal solution maximizes an expected value function. Generally, models of complex probabilistic systems tend to be descriptive. Optimal or near optimal solutions are found by manipulating important parameters or a limited number of decision variables. The most flexible of all probabilistic system modeling techniques is computer simulation. Queueing theory is amongst the oldest and most widely known probabilistic modeling tools of operations research. Its beginning actually pre-dates the start of WWII operations research.

OR models can be used to model and optimize routine decisions and operations. Typically, this class of models will have nicely designed user interfaces and computerized data collection procedures. Often these models become automated and require limited or no managerial insight to tweak the results. Examples of these types of models are routinely used in gasoline blending, airline crew scheduling, or routing calls through telecommunications networks. Strategic models are designed to address a unique situation that may or may not ever occur again. Data is often subjective and based on expert opinion. Senior executives and their staff use strategic models to gain insight. They rarely simply implement the model's solution without an in-depth analysis and understanding of the ramifications of the recommended solution.

As the array of OR techniques and application areas developed, numerous sub-specialties evolved. Some of the specializations focused on specific modeling techniques as mentioned above. Others spawned broad application areas under the titles of: transportation science, marketing science, inventory and production management, and operations management. Recent additions to this array of application areas include: supply chain management, knowledge management, and customer relationship management.

Operations research has overlapping interests with a variety of other disciplines. Research into algorithms often parallels the work of computer scientists. Those operations researchers working in the area of quality and reliability interact with a number of engineering disciplines. Forecasting models, an area of interest to statisticians and economists, are often an important element of operations research-based decision support systems. Lastly, OR specialists in applied mathematical programming or game theory may work with colleagues in economics. Not surprisingly, several Nobel Prize winners in economics had strong links with the operations research community. (e.g. W. Leontief, 1973, L. V. Kantorovich and T. C. Koopmans, 1975, H. A. Simon, 1978 and J. F. Nash, 1994)

For more information about the field of operations research explore the websites maintained by INFORMS (Institute for Operations Research and the Management Sciences) www.informs.org and by the British Operational Research Society www.theorsociety.org.uk
G. D. Eppen, F. J. Gould, C. P. Schmidt, J. H. Moore, and L. R. Weatherford, Introductory Management Science, 5th edition (Upper Saddle River, NJ: Prentice Hall, 1998), 2-24.