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Summary of Operations Research (OR)

Operations Research (OR) is a scientific methodology for analyzing problems and making informed decisions. OR professionals focus on understanding and structuring complex situations to predict system behavior and enhance performance, primarily through analytical and numerical techniques that involve mathematical and computer models of organizational systems.

Historical Background

• Origins: The field emerged before World War II, particularly during British preparations for air warfare, including radar development and its application in directing fighter planes.

• Early Experiments: A multi-disciplinary team studied real-world operating conditions, leading to the term "operations research." Their efforts significantly contributed to the success in the Battle of Britain.

• Expansion: Similar teams were formed in the U.S. military to improve various operations, including convoy protection and anti-submarine warfare.

Evolution of the Field

• Professionalization: In the 1950s, OR became a recognized profession with the establishment of societies, journals, and academic programs.

• Broader Application: OR expanded beyond military use to private companies and government organizations, notably in the petrochemical industry.

Current Applications

Operations Research is utilized across various industries, including:

• Airlines: Scheduling, pricing, and fleet planning.

• Pharmaceuticals: Research and development management.

• Logistics: Routing and planning.

• Financial Services: Credit scoring and marketing.

• Lumber and Wood Products: Forest management.

• Local Government: Emergency service deployment.

• Policy Studies: Addressing issues like environmental pollution and criminal justice.

Methodological Focus

The field has shifted from interdisciplinary teams to a focus on mathematical modeling, which includes:

• Deterministic Models: Such as mathematical programming and network flows.

• Probabilistic Models: Including queuing, simulation, and decision trees.

These modeling techniques are central to master's and doctoral programs in OR, offered in engineering and business schools, with introductory courses available in mathematics departments.

Summary of Linear Programming

Linear programming, pioneered by George Dantzig between 1947 and 1949, emerged from his work during WWII on military logistics and training schedules. Dantzig recognized that planning problems could be framed as systems of linear inequalities. He introduced the concept of an objective function, a mathematical representation of a goal, which was a significant shift from the vague goals previously used by managers.

To find optimal solutions for these linear inequalities, Dantzig developed the simplex algorithm, which efficiently maximizes or minimizes an objective function. This innovation garnered interest from economists, leading to significant advancements in economic modeling, with several contributors later winning Nobel prizes.

Dantzig's first problem involved creating a minimum cost diet solution, which required solving nine equations with seventy-seven decision variables. This task took 120 man-days using manual calculators, a stark contrast to modern capabilities where personal computers can solve similar problems in seconds, aided by tools like Excel's "solver."

As computing technology advanced in the 1950s, industries such as petroleum and chemicals began applying the simplex algorithm to practical problems, like optimizing gasoline blending costs. The field of linear programming expanded, leading to developments in non-linear programming and integer programming, collectively known as mathematical programming.

Universal Teacher

Summary of Brief History of Operations Research

Operations Research (O.R.) is an interdisciplinary field that employs mathematical models, statistics, and algorithms to solve complex decision-making problems, aiming to optimize performance in various systems. It focuses on maximizing or minimizing objective functions, such as profit or cost, to help management achieve its goals through scientific methods.

Origin and Historical Development

• Early Foundations: Charles Babbage is often regarded as the father of O.R. for his work on transportation costs and mail sorting, which contributed to the establishment of England's Penny Post in 1840.

• 1940s Evolution: The term "operations research" emerged during World War II when a group of scientists in the UK, known as Blackett’s Circus, applied scientific techniques to military operations, leading to the formalization of the discipline.

• Post-War Expansion: After WWII, O.R. methods transitioned into business and industry. In the UK, many military O.R. professionals were released to assist in rebuilding production facilities, while in the U.S., defense research funding increased, allowing O.R. to flourish within military and industrial contexts.

• Technological Advances: The war spurred advancements in communication, computation, and control, laying the groundwork for automation and the broader application of O.R. techniques in industries like petrochemicals, logistics, and finance.

• Global Spread: India began utilizing O.R. in 1949 with the establishment of its first unit in Hyderabad. The Indian Statistical Institute set up an O.R. unit in 1953, focusing on national planning. The Operations Research Society of India was founded in 1955, marking its integration into international O.R. communities.

Today, O.R. techniques are widely applied across various sectors, extending beyond military applications to encompass numerous fields at all organizational levels.

INFORMS

Summary of Operations Research and Analytics

Operations Research (O.R.) and Analytics are essential tools that help organizations convert complex challenges into opportunities by transforming data into actionable insights for improved decision-making.

Definitions:

• Operations Research (O.R.): A scientific process that transforms data into insights to facilitate better decision-making.

• Analytics: The application of scientific and mathematical methods to analyze complex systems. It is categorized into three types:

  • Descriptive Analytics: Insights into past events using historical data.

  • Predictive Analytics: Insights on future events.

  • Prescriptive Analytics: Provides actionable advice for decision-making.

Key Differences:

• While both fields aim to enhance decision-making, they differ in focus:

  • Analytics: Primarily analyzes data to create predictive models and optimize business processes.

  • O.R.: Utilizes advanced methods and tools (like simulation, optimization, probability, and statistics) to deliver analytical capabilities beyond standard software.

Collaborative Impact:

Together, O.R. and Analytics, along with related fields such as management science, data science, computer science, and decision science, drive performance and change across various organizations. They empower leaders to tackle complex problems, make informed decisions, and enhance strategies and operations in both public and private sectors.

Britannica

Summary of Operations Research

Basic Aspects

Operations research (OR) provides a quantitative basis for decision-making in organized systems, focusing on overall system performance rather than individual components. It involves interdisciplinary teams applying scientific methods to managerial problems, often emphasizing human behavior. Historically, OR aimed to improve existing systems, while systems engineering focused on new developments.

History

OR emerged in 1937 in Britain, initially to enhance military radar operations. By World War II, formal OR groups were established across British military services, leading to similar developments in the U.S. and other countries. Post-war, OR expanded into industrial applications, with academic programs and professional societies forming in the 1950s.

Essential Characteristics

1. Systems Orientation: Recognizes that changes in one part of a system affect the whole.

2. Interdisciplinary Teams: Combines diverse scientific disciplines to tackle complex problems.

3. Scientific Methodology: Employs models and simulations to analyze and improve systems.

Methodology

The OR process includes:

• Problem Formulation: Identifying objectives, decision-makers, and relevant variables.

• Model Construction: Creating simplified representations of real-world systems.

• Deriving Solutions: Using mathematical and statistical methods to find optimal solutions.

• Testing and Implementation: Validating models and solutions through real-world application and adjustments.

Applications

OR is applied in various fields, including:

• Resource Allocation: Distributing resources to minimize costs or maximize returns.

• Linear Programming: Optimizing resource allocation through mathematical techniques.

• Inventory Control: Managing stock levels to balance costs.

• Queuing Theory: Analyzing waiting lines to optimize service facilities.

• Network Routing: Finding optimal paths in transportation and communication systems.

Frontiers of Operations Research

OR is evolving to address strategic planning, system design, and the complexities of different organizational types. It increasingly integrates behavioral sciences to better understand human factors in decision-making.

Conclusion

Operations research is a dynamic field that continues to grow, applying scientific methods to solve complex organizational problems and improve decision-making processes across various sectors.

PHP Simplex

Summary of the History of Operations Research

Operations Research (OR) has roots tracing back to ancient military strategies, with notable contributions from figures like Archimedes during the II Punic War, who devised defensive mechanisms for Syracuse. Leonardo Da Vinci also applied engineering principles in warfare in the early 1500s.

In the 20th century, F.W. Lanchester developed mathematical models for military engagements, leading to Lanchester's Square Law. Thomas Edison contributed to antisubmarine warfare, while mathematicians like Newton and Fourier laid foundational work for optimization and linear programming.

The formal establishment of OR as a discipline occurred during World War II, particularly in Britain, where scientists were mobilized to enhance radar effectiveness against Luftwaffe attacks. This led to the creation of groups focused on optimizing military strategies, including the U.S. project SCOOP, which produced the Simplex algorithm by George Dantzig.

Post-war, OR techniques were applied to various sectors, including logistics and resource management, exemplified by the Berlin Airlift, which optimized supply routes under challenging conditions. The development of computers in the 1950s further accelerated OR applications, allowing for complex problem-solving in military and commercial contexts.

By the 1960s, OR expanded into industries, addressing logistical challenges and optimizing operations across various fields, including agriculture and transportation. The discipline evolved from earlier analytical methods, significantly enhancing efficiency and decision-making processes.