Introduction to Operations Research
1.1. History of Operations Research
The first Operations Research activity took place during World War II in Britain, where the military administration called upon a group of scientists from different fields of knowledge to study strategic and tactical issues related to homeland defense.
The name Operations Research apparently arose because the team was conducting operations research activity (military).
Motivated by the encouraging results obtained by the British teams, U.S. military administrators began conducting similar research. They brought together a select group of specialists who began to achieve good results in their studies involving complex logistical problems, the planning of sea mines, and the effective use of electronic equipment.
At the end of the war, and attracted by the positive results achieved by military strategists, industrial managers began to apply Operations Research tools to solve problems arising due to the growing size and complexity of industries.
Although Britain is credited with initiating Operations Research as a new discipline, the United States soon took the lead in this rapidly growing field. The first widely accepted mathematical technique in Operations Research was the Simplex Method for Linear Programming, developed in 1947 by the American mathematician George B. Dantzig. Since then, new techniques have been developed through the efforts and cooperation of individuals interested in both academia and industry.
A second factor in the impressive progress of Operations Research was the development of the digital computer, with its tremendous capabilities of computational speed, storage, and information retrieval, which enabled faster and more accurate decision-making.
If it were not for the digital computer, Operations Research with its large computational problems would not have grown to the level it has today.
Operations Research is currently being implemented in many activities. These activities have gone beyond military and industrial applications to include hospitals, financial institutions, libraries, urban planning, transportation systems, and marketing systems.
1.3. Definition
Operations Research or Operational Research can be defined as follows: “Operations Research is the application by interdisciplinary groups of the scientific method to problems related to the control of organizations or systems to produce solutions that best serve the objectives of the entire organization.”
1.4. Methods of Operations Research
The Operations Research process includes the following phases:
- Formulation and definition of the problem
- Construction of the model
- Solution of the model
- Validation of the model
- Implementation of results
An explanation of each of the phases:
1. Formulation and definition of the problem
At this stage, you need: a description of the system’s objectives (i.e., what you want to optimize), to identify the variables involved (whether verifiable or not), and to identify the system’s constraints. We must also take into account the decision alternatives and constraints to produce a solution.
2. Construction of the model
In this phase, the operations researcher must decide which model to use for representing the system. It should be a model that relates the decision variables and constraints to the system’s parameters. The parameters (or known quantities) can be obtained either from past data or be estimated by some statistical method. It is recommended to determine if the model is probabilistic or deterministic. The model can be mathematical, simulation-based, or heuristic, depending on the complexity of the mathematical calculations required.
3. Solution of the model
Once you have the model, we proceed to derive a mathematical solution using various techniques and methods to solve mathematical problems and equations. We should note that the solutions obtained in this process are mathematical, and we must interpret them in the real world. In addition, for the solution of the model, we should perform sensitivity analysis, i.e., to see how the model changes with variations in the specifications and parameters of the system. This is because the parameters are not necessarily accurate, and restrictions may be incorrect.
4. Validation of the model
The validation of a model requires determining whether a model can accurately predict the behavior of the system. A common method to test the validity of the model is to submit available past data to the current system and see if it replicates past situations of the system. But as there is no assurance that the future behavior of the system will continue to replicate past behavior, then we must always be mindful of possible system changes over time in order to properly adjust the model.
5. Implementation of results
Once we have obtained the solution or solutions of the model, the next and final step is to interpret those results, draw conclusions, and take actions to optimize the system. If the model used can serve another problem, it is necessary to review, document, and update the model for new applications.
Operations Research: An Overview
Operations Research or Operational Research is a branch of mathematics that consists of using mathematical models, statistics, and algorithms to aid in the decision-making process. Often, it deals with the study of complex real systems to improve (or optimize) their operation. Operations Research allows the analysis of decision-making, taking into account the scarcity of resources, to determine how to optimize a defined objective, such as profit maximization or cost minimization.
Characteristics of Operations Research
Operations Research uses the scientific method to investigate the problem at hand. In particular, the process begins with careful observation and the formulation of the problem, including the collection of relevant data.
Operations Research adopts an organizational standpoint. In this way, it attempts to resolve conflicts of interest among members of the organization so that the result is the best for the entire organization.
Operations Research tries to find a better solution (the so-called optimal solution) to the problem under consideration. Instead of being content with improving the state of things, the goal is to identify the best course of action.
In Operations Research, it is necessary to use a team approach. This team should include staff with strong backgrounds in mathematics, statistics and probability theory, economics, business administration, computer science, engineering, etc. The team also needs to have the experience and skills to enable proper consideration of all the ramifications of the problem.
Operations Research has developed a series of very useful techniques and models for systems engineering. Among them: Nonlinear Programming, Queuing Theory, Integer Programming, Dynamic Programming, among others.
Operations Research tends to represent the problem quantitatively to analyze and evaluate a common approach.
Other Features
- Represent the system or problem to be solved through mathematical solutions
- Apply the scientific method for decision-making
- Find the best solution (optimal solution)