Operations research
Introduction
Operations research (OR), also known as operational research, is a multidisciplinary field that uses scientific methods, techniques, and tools to make better decisions and solve complex problems. It involves the use of mathematical modeling, statistical analysis, and mathematical optimization to perform a quantitative analysis of decision-making problems. The field is often concerned with optimizing the maxima (profit, performance, or yield) or minima (loss, risk, or cost) of some objective function.
History
The term "operations research" originated during World War II when military management in England called upon scientists to apply scientific methodology to the problems of warfare. The objective was to study the strategic and tactical problems of air and land defense with the objective of effective use of limited military resources against foreign enemies. It was soon recognized that these same techniques could be used in business, industry, and society.
Methodology
The methodology of operations research involves several interrelated steps:
1. Formulation of the Problem: The first step in the OR process is to define the problem. This involves understanding the system, observing its functioning, and identifying the problem.
2. Construction of a Mathematical Model: The next step is to represent the system through a set of mathematical equations or inequalities. This model represents the systems and the problems in mathematical form.
3. Solution of the Model: The mathematical model is then solved using various mathematical tools and techniques. The solution provides a decision that optimizes the objective function.
4. Validation of the Model: The model is then validated by comparing the solution obtained from the model with the real system. If the solution is not satisfactory, the model is reformulated and solved again.
5. Implementation of the Solution: The final step is to implement the solution obtained from the model in the real system.
Applications
Operations research has wide-ranging applications in various fields. Some of these include:
1. Supply chain management: OR techniques are used to manage and optimize the production, distribution, and inventory of goods.
2. Transportation: OR is used to optimize routes and schedules for transportation networks.
3. Healthcare: OR can help in scheduling and patient flow management in healthcare facilities.
4. Finance: OR techniques are used for portfolio optimization, risk management, and financial engineering.
5. Manufacturing: OR can help in production planning, scheduling, and quality control.
6. Telecommunications: OR is used in network design and management, routing, and capacity planning.
Techniques
There are several techniques used in operations research, including:
1. Linear programming: This is a mathematical method used to determine the best outcome in a mathematical model whose requirements are represented by linear relationships.
2. Integer programming: This is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.
3. Network analysis: This involves the use of graph theory to understand and map the concept of 'flow' in a system.
4. Simulation: This is a technique used to imitate the operation of a real-world process or system over time.
5. Game theory: This is the study of mathematical models of strategic interaction among rational decision-makers.
6. Decision analysis: This is a systematic, quantitative, and visual approach to addressing and informing complex decisions.
Future of Operations Research
With the advent of big data, artificial intelligence, and machine learning, the future of operations research looks promising. These technologies can help in analyzing large amounts of data and making complex decisions more efficiently. Moreover, the increasing complexity of operations in various sectors such as healthcare, manufacturing, and transportation will continue to drive the need for operations research.
