Linear programming is one of the most common tools of operations research. The idea of linear programming is setting up a problem that summarizes a problematic situation in which constraints are placed upon the problem solver. One such problem may be how to produce the most profitable combination of products when resources are limited. Linear programming solves these problems by finding the combinations that yield the optimum value given the limitations of the challenge.
Decision analysis is an extension of game theory, a method commonly used in economics. Operations researchers adapted game theory to fit situations in which aspects of the future are unknown and must be inferred through statistical methods. Decision analysis, in essence, combines game theory with Bayesian statistical analysis to help researchers produce the best decisions despite a lack of accurate data. Businesses commonly use decision analysis for marketing decisions in unstable market conditions.
Graph theory is a method of operations research that allows researchers to reduce complex problems to simple graphs. The researchers then analyze these graphs according to the question of interest. An example of such a problem is logistical planning: a company must decide how to assign routes to shipping trucks so that profit is maximized and speed is emphasized. The researchers write destinations and roads as nodes and edges of a graph and then use the graph to plan routing schedules. This method can be applied to many other areas such as city planning, online networking and marketing decision-making.
Random processes, also called stochastic processes, are mathematical models of random phenomena. Researchers in operations research can use these models to investigate large-scale patterns of phenomena that cannot be analyzed directly or in short time periods. Investors commonly use random processes such as Markov Chains and Wiener Processes to make predictions about the stock market and other investment options. Random processes are also important in business and logistics, as they can model semi-random phenomena such as traffic and queues.