# Mathematics for Operations Research/Management Science/Industrial Engineering

### - Overview

Operations research (OR) is a branch of applied mathematics that uses analytical methods to help make better management decisions. It's also known as management science and industrial engineering.

OR is a mathematical science that focuses on optimal decision making and modeling deterministic and probabilistic systems. It uses techniques from other mathematical sciences, such as modeling, statistics, and optimization.

Some of the major mathematical tools of OR include: Vector calculus, Linear algebra, Differential and difference equations, Probability, Statistics, Computer programming.

Industrial engineers use mathematics to design, develop, test, and evaluate integrated systems for managing industrial production processes. These processes include:

- Human work factors
- Quality control
- Inventory control
- Logistics and material flow
- Cost analysis
- Production coordination

OR is an area of industrial engineering concerned with the allocation of scarce resources.

Operations research as we know it today is largely a product of military research during World War II that sought the best ways to allocate scarce resources. This includes questions such as, "How should patrol aircraft be deployed to maximize the expected number of enemy submarines found within the limited search hours?" and "How should the limited spare parts inventory be allocated between the field, advance warehouses, and distribution warehouses to minimize equipment downtime due to spare parts shortages?"

At the end of the war, most operations research researchers went to industry, similar questions about budgeting, planning, marketing, decision-making, and other aspects of management need answers.

**[More to come ...]**