Mathematics plays a key role in solving problems and making more informed decisions for businesses in a variety of industries. Operations research offers a scientific approach to problem-solving and decision-making for organizations through the use of these mathematical and analytical principles. Learning more about operations research can help businesses make more informed decisions. In this article, we will present the definition of operations research, discuss the benefits it provides, list its key components, and provide an example to help you understand the topic. Happy reading!
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What is Operations Research?
Operations research is a methodological approach that is widely used today. This method, which focuses especially on solving problems, has an important place. Operations research is a subfield of applied mathematics that uses mathematical principles or analytical methods. In the research process, various studies are carried out in line with a determined target. In line with the studies carried out, it is aimed to achieve the goal successfully.
Operations research is one of the most frequently used research methods today. Generally, opportunities to identify problems and find solutions to them are identified. A series of emergency studies are carried out to achieve the goal. This research is especially preferred in engineering and design fields. In addition to providing an environment for best practices by ensuring the coordination of activities, it also contributes to the optimization of the working process.
One of the most curious questions about this subject is “Where is Operations Research Used?”. We wanted to answer this question immediately in the first part of our article. Operations research is often used in engineering fields. It is especially preferred in industrial engineering disciplines. It is also widely applied in other engineering fields. Operations research is among the techniques frequently used by engineering students in the transition from education processes to business life.
As a list, here are some areas of interest that have significant overlap with Operations Research and Management Science;
- Business analytics
- Computer science
- Data mining/Data science/Big data
- Decision analysis
- Decision intelligence
- Engineering
- Financial engineering
- Forecasting
- Game theory
- Geography/Geographic information science
- Graph theory
- Industrial engineering
- Inventory control
- Logistics
- Mathematical modeling
- Mathematical optimization
- Probability and statistics
- Project management
- Policy analysis
- Queueing theory
- Simulation
- Social network/Transportation forecasting models
- Stochastic processes
- Supply chain management
- Systems engineering
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Benefits of Operations Research
Operations research develops actionable solutions to complex business challenges. These solutions provide insights to help organization leaders improve results and make more informed decisions about the future of the company. This process generates knowledge by using data effectively. The benefits of operations research in general are as follows;
Provides a more detailed analysis
Operations research is based on the use of mathematical and scientific methods in analytics and various problems. This methodology provides decision-makers with more insight by offering a more in-depth and comprehensive analysis. This allows them to develop more detailed and well-established solutions to problems. It can also increase their understanding of how to address similar problems in the future.
Allows to eliminate uncertainties
Operations research can help companies eliminate potential uncertainties by using proven methods and modeling techniques. The input of realistic data into an existing effective model can reduce or eliminate companies’ uncertainties. Solving challenges based on reliable data can provide confidence to company leaders and make it easier to manage complex business processes.
Improves efficiency
Operations research helps to increase productivity in the workplace. It also reduces business uncertainty and improves coordination between different departments and teams. The advanced models used provide managers with the information they need to make more careful decisions, such as upgrading new technology or expanding into a new market. It is also useful for routine business tasks such as workforce planning.
Components of Operations Research
Operations research generally includes three basic features or components. These are;
Optimization
Optimization is the process of finding the optimal solution by taking into account certain constraints. These constraints are the limitations we may encounter in daily operations and determine how to act to optimize a situation in the best way. For example, staffing constraints within a business may be a constraint in the form of the maximum number of shifts that each employee can work due to legal regulations. When solving business problems with operations research, we can take such constraints into account and analyze in more depth the costs and benefits of each option.
Statistics and Algorithms
Operations research is based on a broad field of mathematics that includes statistics and algorithms. Optimization algorithms play an important role in operations research to find a minimum or maximum value based on a given probability distribution. For example, to determine the optimal number of staff and their working hours for a production facility, a company may use a specific algorithm to minimize operating costs. This algorithm takes into account factors such as the hourly wage and working time of each employee.
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Simulation
Simulation is a method that uses algorithms to evaluate potential outcomes in a process that has been or will be carried out and builds models before testing solutions. When working with optimization algorithms, a firm may try to achieve different results by changing some constraints or factors of the equation. By simulating a situation or event, operations research allows to identify potential outcomes more clearly and easily.
Operations Research Example
In operations research problems, variables are always shown with lowercase letters. These lowercase letters have a coefficient. These coefficients represent production quantities or some other parameter according to the definition.
Let us now clarify the situation with an operations research example.
Suppose we have two types of products with product names X and Y. We will use these symbols as variables representing production quantities. Let’s call the machines used to produce these products A, B, and C respectively.
Each product will spend a certain amount of time in each machine to produce X and Y products. The time spent in the machines for one product X is as follows;
- A Machine: 1 hour
- B Machine: 3 hours
- C Machine: 10 hours
The time spent in the machines for one product Y is as follows;
- A Machine: 1 hour
- B Machine: 8 hours
- C Machine 7 hours
The hour limits that the machines that constitute the constraints of the problem can use are as follows;
- A Machine: 40 hours
- B Machine: 240 hours
- C Machine: 350 hours
Determining the total profit from the sales of the products is the solution objective of the problem. That is, the goal of the problem is to maximize this total profit.
We can calculate the total sales profit by knowing the unit profits from the sale of unit quantities of products. Let the unit profits be as follows;
- Product X: 5 dollars
- Product Y: 7 dollars
The mathematical formula of the total amount of profit, which is the main objective of the problem, with variables x and y representing the production quantities of the products,
Z = 5x + 7y
is expressed in the form.
The solution to the problem requires maximizing the outcome of this mathematical expression by determining the values of the variables x and y.
Since the basic formula of the problem is a simple linear expression, maximizing the profit means finding the largest values of x and y. So while it might seem that the maximum value should be infinite, in reality, this is not the case. The production capacities of machines and time constraints do not make infinite production possible.
For the current solution, the values of x and y must be determined in such a way that they satisfy the constraints on the total production hours of the machine. These constraints are expressed by the following mathematical inequalities:
1x + 1y ≤ 40
3x + 8y ≤ 240
10x + 7y ≤ 350
There is also the condition that x and y are real numbers greater than zero.
Videos Related to Operations Research
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