Statistical modeling and optimization techniques find vast applications in management decision making process. Whether designing new products, streamlining a production process or evaluating current vs. prospective customers, today’s business managers face greater complexities than ever before. Running a shop on instinct no longer suffices. Statistics provide managers with more confidence in dealing with uncertainty in spite of the flood of available data, enabling managers to more quickly make smarter decisions and provide more stable leadership to staff relying on them. Statistical analysis of a representative group of consumers can provide a reasonably accurate, cost-effective snapshot of the market with faster and cheaper statistics than attempting a census of very single customer a company may ever deal with. The statistics can also afford leadership an unbiased outlook of the market, to avoid building strategy on uncorroborated presuppositions. Statistics back up assertions. Leaders can find themselves backed into a corner when persuading people to move in a direction or take a risk based on unsubstantiated opinions. Statistics can provide objective goals with stand-alone figures as well as hard evidence to substantiate positions or provide a level of certainty to directions to take the company. Statistics can point out relationships. A careful review of data can reveal links between two variables, such as specific sales offers and changes in revenue or dissatisfied customers and products purchased. Delving into the data further can provide more specific theories about the connections to test, which can lead to more control over customer satisfaction, repeat purchases and subsequent sales volume. Anyone who has looked into continuous improvement or quality assurance programs, such as Six Sigma or Lean Manufacturing, understands the necessity for statistics. Statistics provide the means to measure and control production processes to minimize variations, which lead to error or waste, and ensure consistency throughout the process. This saves money by reducing the materials used to make or remake products, as well as materials lost to overage and scrap, plus the cost of honoring warranties due to shipping defective products.

Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Because of its emphasis on human-technology interaction and because of its focus on practical applications, operations research has overlap with other disciplines, notably industrial engineering and operations management, and draws on psychology and organization science. Operations research is often concerned with determining the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost) of some real-world objective. Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries. Operational research (OR) encompasses a wide range of problem-solving techniques and methods applied in the pursuit of improved decision-making and efficiency, such as simulation, mathematical optimization, queuing theory and other stochastic-process models, Markov decision processes, econometric methods, data envelopment analysis, neural networks, expert systems, decision analysis, and the analytic hierarchy process. Nearly all of these techniques involve the construction of mathematical models that attempt to describe the system. Because of the computational and statistical nature of most of these fields, OR also has strong ties to computer science and analytics. Operational researchers faced with a new problem must determine which of these techniques are most appropriate given the nature of the system, the goals for improvement, and constraints on time and computing power.