Learn & Review: Operations Research: History, OR Today, Models, Structure

Introduction to Operations Research: Part 1 Summary

This lecture provides an introduction to Operations Research (OR), covering its history, modern applications, modeling techniques, mathematical approaches, study phases, and the structure of mathematical models.

What is Operations Research?

• Definition: Operations Research is the application of scientific methods, techniques, and tools to complex problems in the direction and management of large systems involving men, machines, materials, and money. Its goal is to provide optimal solutions to those in control of the system.

History of Operations Research

• Origins: OR traces its roots back to World War II.

  • England: A group of scientists was hired to optimize military operations, specifically radar and bomber operations.
  • America: Following England's success, the US also employed scientists to address complex logistical problems, develop new flight patterns, plan sea mining, and improve the utilization of electronic equipment.

• Post-War Expansion: The success in military applications led to the adoption of OR by industries to solve complex executive problems, serve organizational objectives, and utilize effective tools.

• Key Development: The simplex method for linear programming, developed by George B. Dantzig, was the first major mathematical technique in OR.

  George B. Dantzig, as a PhD student, famously solved previously unsolved mathematical problems by mistaking them for homework assignments, leading to the development of the simplex method.

Operations Research Today

• OR is no longer limited to military use and is now applied in:
  • Business
  • Hospitals
  • Financial institutions
  • Libraries
  • City planning
  • Transportation systems
  • Crime investigations

Models in Operations Research

There are several types of models used in OR:

• Iconic Models: Physical replicas or prototypes of real-life systems (e.g., a toy plane representing a real plane).
• Analog Models: Abstract representations of real systems (e.g., graphs).
• Symbolic or Mathematical Models: Represent real systems using mathematical equations and functions (e.g., a linear program).
• Heuristics: Rule-of-thumb or practical techniques that may be useful, though not guaranteed to be optimal (e.g., scheduling tasks with the shortest processing time first).
• Simulation Models: Digital representations that imitate the behavior of a system using computers, accumulating performance statistics.

Mathematical Techniques for Operations Research

Key mathematical techniques include:

• Linear Programming (LP)
• Dynamic Programming
• Nonlinear Programming
• Stochastic Programming
• Integer Programming

(Note: Each of these will be discussed in-depth in future lectures.)

Phases of an Operations Research Study

An OR study typically involves the following phases:

1. Define the Problem: Crucial step to understand the core issue and identify potential challenges.
2. Construction of the Model: Creating mathematical models (e.g., linear or integer programs) to replicate the real system.
3. Solution of the Model: Solving the mathematical model developed in the previous stage.
4. Validation of the Model: Verifying the correctness of the model's solution, often by testing it on a prototype system.
5. Implementation of the Final Results: Applying the validated solutions to the real-world system.

Structure of Mathematical Models

A typical mathematical model, such as a linear program, consists of:

• Objective Function: The goal to be optimized (maximized or minimized).
• Decision Variables: The variables that can be controlled or decided upon.
• Parameters: Known constants or values within the model.
• Constraints: Limitations or restrictions on the decision variables.

(Note: These elements will be explained in detail in Part 2 of the lecture.)