What is operational research? And why is it important?
What are operations, and how can operational research help?
"Operation" is a word you hear on many occasions throughout life. But many people don’t have any idea what is meant by an operation. On occasion you might have heard of everyday tasks in a firm, like quality inspection, inventory management, and maintenance, being referred to as operations.
Operations can be simply defined as the ongoing activities carried out by an organization to produce outputs, generate revenue, and keep smooth functioning. Operational research is a field of mathematics that is applied to problems concerning how to conduct and coordinate operations and tries to find the best/optimal solution.
As you know, after the industrial revolution, business organizations have shown remarkable growth, and they have implemented labor division and segmented management responsibilities to make management of the organization as a whole a lot easier. However, sometimes these separate segments tend to grow into autonomous empires that pursue goals that aren’t aligned with the objectives of the overall organization and can be detrimental to the organization. Operational researchers try to adopt an organizational point of view in these conflicts of interest and try to find the best possible solutions for the organization as a whole rather than trying to promote one segment of the organization. The problems that may rise in between segments of the organizations can include arguments about resource allocation, management decisions, etc.
How is operational research conducted in the industry?
Full-fledged operational research studies for solving problems in the industry are approached as teams (they can be referred to as OR teams for convenience). These teams act in an advisory role by performing a detailed technical analysis of a given problem and then presenting recommendations to the management.
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Major phases of a typical Operational Research study
- Define the problem of interest.
- Gather relevant data.
- Create a mathematical model that represents the problem.
- Developing a computer-based procedure to solve the model.
- Testing and refining the model.
- Prepare for the model application as prescribed by the management.
- Implementation.
Define the problem of interest.
Let’s explain this using an example. Assume the management wants to find the best possible way to distribute resources among several departments. Now an operational research team had been chosen to do an analysis and determine the best possible way for the distribution to occur.
First they need to define what is best. Maybe increasing the longer-term profits. Maybe it can be that the organization has other objectives, such as increasing market share, product diversification, improving worker morale, raising company reputation, etc. Therefore, when defining the problem it is required to consider that the way your problem is defined or the way the optimization is done does not clash with the objectives of the organization.
Gather relevant data.
OR teams spend a surprisingly large time gathering information relevant to the problem. On many occasions, much of the required data will not be available at the beginning due to reasons like the information never having been kept or because what was kept is outdated or in the wrong form. The team will have to gather information from scratch on such situations. This normally necessitates the installation of a new computer-based ‘management information system’ routinely and in the required form.
Create a mathematical model that represents the problem.
Model means an idealized representation. We encounter models on many occasions throughout our lives. They can be 3D models of physical products, model airplanes or ships, etc. In this case we are talking about using a mathematical model to represent the problem at hand. This kind of mathematical model comprises a set of equations and related mathematical expressions that describe the problem.
Components of such a mathematical model are as follows.
Quantifiable choices that had to be made are represented as decision variables. (say x₁, x₂, …, x ₙ)
The objective function is the function of decision variables that represents the performance measure that we aim to optimize. (consider P = 6x₁ + 9x ₂)
Restrictions about how these decision variables can be handled are represented by constraints. (ex:- x₁+ x₂≤15)
The right-hand coefficients and constants of these mathematical expressions (both in the right & left-hand sides of the expressions) are considered as parameters.
The goal here is to optimize the objective function while conforming to the constraints.
The values assigned to parameters are estimated by the gathered data about the problem. These values are often rough estimates. The process of examining how the final outcome changes with the change of parameters is called sensitivity analysis.
Developing a computer-based procedure to solve the model.
First, a suitable algorithm (which is another word for a systematic solution procedure) for the optimization problem needs to be chosen. The objective of the algorithm is to give an optimum solution. But often in reality a satisfactory answer these algorithms output.
After choosing the approach, the next steps are usually as follows.
Select the solution platform—the solution can be obtained either by using spreadsheet software (e.g., Excel, Google Sheets), Python programming platforms (Google Colab, Jupyter Notebooks), dedicated OR solving software, or modern AI-powered software.
Implement the model in a computable form- Translate the decision variables, objective function, and constraints into the solution platforms’ input format. Follow necessary conventions relevant to the platform to ensure an accurate result.
Feed the model with data- Build a clean pipeline for decision variable values. Check for missing values, inconsistent units, outdated prices, and impossible bounds.
Run the solver and extract decisions: the raw output is usually variable, objective values and constraint statuses. They need to be converted into decisions that the management can act on such as quantities, assignments, routes, reorder points.
Testing and refining the model.
The initial version of such a large mathematical model undoubtedly contains some errors. Some relevant factors or interrelationships may not have been included in the model. Some parameters might have been incorrectly estimated. Therefore, the OR team need to successively improve the model until all the major flaws have been eliminated. Then the model can be declared to give reasonably valid results despite the possibility of some minor flaws remaining hidden. This overall process of testing and improving is called “model validation."
The exact nature of the model validation process heavily depends on the nature of the problem and the model being used. However, a generalized approach can be given as follows. After the details of the initial version of the model had been completed, a fresh look at the overall model needed to be taken to check for obvious errors or oversights. This should involve at least one team member who wasn’t involved in the formulation of the initial model to prevent oversights that can happen due to bias. Then the model should be compared with the problem definition, which may reveal additional errors. Then the consistency of the units used in mathematical expressions needs to be ensured. Finally, parameter and/or decision variable values need to be varied to see whether the model output behaves in a plausible manner.
A retrospective test can be proposed as a more systematic approach for testing and refining the model. In this method, the historical data is used to reconstruct the past and determine the effectiveness of the model if it had been implemented at that time by comparing results and what actually happened. This may indicate areas where the model has shortcomings and requires modification. A disadvantage here is that the data used for the testing are the same data that were used to formulate the model in the first place. The status quo can be temporarily continued to circumvent this, which provides new data that were unavailable at the model construction.
Documentation of the steps followed for model validation is important for future improvement and build confidence about the model.
Prepare for the model application as prescribed by the management.
A well-documented system needs to be installed for the repeated use of the developed model. This system should include the mathematical model, solution procedure, postoptimality tools, and clear operating procedures for using it. The documentation will help to keep the system running smoothly through situations like staff changes, arrival of new managers, and change of analysts.
Modern organizations tend to make this system computer-based with clear data pipelines and integration of databases. The system can arrive at the necessary solution automatically for new data and acts as a decision support system for managers. The system may be designed to give management friendly reports as well.
Developing and testing such a system may take months and it will need to kept well maintained for effective operations.
Implementation.
The last phase of an OR study is to implement the system as prescribed by the manager. It is in this phase that the benefits of the OR study can be reaped. For a successful implementation the support of top and operating management is critical. Which can be ensured by keeping them well informed as well as maintaining good communication between the OR team and the management. This implementation phase includes several steps.
Implementation Steps →
Explain the System: The OR team briefs operating management on the new system, linking it directly to real-world operations.
Develop Procedures: The OR team and management share responsibilities to create practical procedures for deployment of the system.
Train Personnel: Management then delivers detailed training to the staff in order to use the system.
Monitor and Adjust: The OR team keeps track of early results and identifies needed tweaks. Then they are refined to make the system suitable for long-term use.
It is important to continously gain feedback from the system and revisit if significant deviations are to rise.
References-
Hillier, F. S., & Lieberman, G. J. (2001). Introduction to operations research (7th ed.). McGraw-Hill.
