The science and art of math modeling is a fundamental technique that all OR practitioners build upon. A "model" here refers to a set of mathematical equations that describes the relevant aspects of the problems to be solved. In operations research, the mathematical representation of the problem is called a "formulation." Since there are many types of problem sets for which solution techniques are well known, the skill lies in formulating the math model of the real-life problem at hand into one such set and then obtaining the solution.
The techniques around optimization form the core of operations research. "Optimization is the process of finding the best way of using your resources, at the same time not violating any of the constraints that are imposed" as defined by Dash Optimization, the developers of one computer-based solver. In OR most real-life problems that require optimization are cast either as linear programs or as integer programs.
The techniques of decision analysis were first developed at Stanford University. Decision analysis is very useful when complex sequences of events are dependent on probabilities that far exceed the ability of human intuitions. The techniques in this branch of operations research involve using graphs (called "decision trees") and assigning probabilities to various outcomes. These techniques help in making decisions by estimating the most likely outcomes under various risk scenarios that are assumed.
Game theory is the science of social interaction, applied to situations in which groups of people cooperate or compete against each other. All the participants are assumed to be intelligent and operating to maximize their own personal gains. The "prisoners' dilemma" is a very common example of a game theoretical problem, with different techniques leading to various outcomes.
The techniques mentioned above are theoretical in nature. However, for very complex situations (such as in a manufacturing factory, or at an airport) these models often prove to be inadequate. In those cases, operations researchers will rely on mathematical simulation. These are computer programs that can be made to simulate discrete parts of a complex operation. Multiple replications (called "simulation runs") are then made, and the results provide insights into the complex operations.
A skilled operations research practitioner will know when to rely on which technique and will combine them depending on the real-world problem at hand. Whether the problem at hand is maximizing profits (or minimizing costs) for a business, or whether the decision at hand is to maximize social and economic good, given resource constraints, the OR practitioner will typically start with a math formulation, then attempt optimization and build in complexity in order to obtain solutions and insights.