# Operations Research: Evolution, Process, Characteristics, and Pros & Cons, [PDF Inside]

**Operations research (OR) is a field of applied mathematics, engineering, and management science that deals with the application of advanced analytical methods to help make better decisions. OR uses quantitative models and data analysis to address complex issues in a variety of fields, including business, government, and healthcare.**

OR problems typically involve the optimization of some objective, such as minimizing cost or maximizing profit. OR models are often used to help make decisions about resource allocation, scheduling, and transportation.

What you are going to learn?

**Evolution of Operations Research**

The evolution of OR can be traced through four distinct phases:

**The early years (1930s-1950s)**:- This was the period when OR was first developed and applied to military problems. During this time, OR practitioners developed many of the basic tools and techniques that are still used today, such as linear programming, queuing theory, and game theory.

**The growth years (1950s-1970s)**:- OR began to be applied to a wider range of problems in the 1950s and 1960s. This was due in part to the development of new computing technologies, which made it possible to solve more complex problems. During this time, OR also began to be taught in universities, which helped to increase the number of OR practitioners.

**The maturity years (1970s-1990s)**:- OR reached a level of maturity in the 1970s and 1980s. During this time, OR practitioners focused on developing more specialized tools and techniques for solving specific problems. OR also began to be used in a wider range of industries, including healthcare, transportation, and manufacturing.

**The modern era (1990s-present)**:- OR has continued to evolve in the modern era. During this time, OR practitioners have made use of new technologies, such as artificial intelligence and big data, to solve even more complex problems. OR has also become more internationalized, with practitioners working in countries all over the world.

Today, OR is a well-established discipline with a wide range of applications. It is used by businesses, governments, and other organizations to improve efficiency, reduce costs, and make better decisions. OR is a valuable tool that can help organizations achieve their goals.

Here are some of the key developments that have shaped the evolution of OR:

- The development of new mathematical and statistical techniques
- The development of new computing technologies
- The increasing availability of data
- The growing recognition of the importance of decision-making
- The increasing globalization of business

These developments have enabled OR practitioners to solve more complex problems, work with more data, and have a greater impact on organizations. As a result, OR is now a widely used discipline that is helping organizations to improve their performance.

**Characteristics of Operations Research**

There are three essential characteristics of operations research:

**Systems orientation:**- OR problems are typically viewed as systems, in which the parts are interrelated and interact with each other. This requires OR practitioners to take a holistic view of the problem and to consider the impact of their decisions on all parts of the system.

**Interdisciplinary teams:**- OR problems are often too complex to be solved by a single individual. As a result, OR practitioners typically work in teams that include people with a variety of skills and backgrounds, such as mathematics, engineering, statistics, and computer science.

**Scientific method:**- OR practitioners use the scientific method to solve problems. This involves defining the problem, developing a model of the problem, solving the model, and testing the solution in the real world.

OR has been used to solve a wide variety of problems in a variety of industries, including:

**Business:**- OR has been used to improve decision-making in areas such as production, inventory, scheduling, and marketing.

**Government:**- OR has been used to improve decision-making in areas such as defense, transportation, and healthcare.

**Nonprofit:**- OR has been used to improve decision-making in areas such as education, social welfare, and environmental protection.

OR is a valuable tool that can help organizations make better decisions. By using OR, organizations can improve their efficiency, effectiveness, and profitability.

Here are some additional characteristics of operations research:

**Quantitative:**- OR uses quantitative methods, such as mathematics, statistics, and computer science, to solve problems.

**Mathematical modeling:**- OR practitioners often use mathematical models to represent real-world systems.

**Data-driven:**- OR practitioners use data to inform their decision-making.

**Innovative:**- OR practitioners are often creative and innovative in their approach to solving problems.

**Collaborative:**- OR practitioners often work with other professionals, such as managers, engineers, and scientists, to solve problems.

Operations research is a growing field with a wide range of applications. As organizations continue to face complex and challenging problems OR will become an increasingly important tool for decision-making.

**Process of Operations Research**

The process of operations research (OR) can be broadly broken down into the following steps:

**1. Problem Formulation**

The first step is to identify and define the problem that needs to be solved. This involves understanding the goals of the organization, the constraints that are imposed on the solution, and the factors that influence the outcome.

The problem formulation step is critical to the success of the OR project. If the problem is not properly defined, it will be difficult to develop a model that accurately represents the problem.

**2. Modeling**

The next step is to develop a mathematical model of the problem. This involves representing the problem in a way that can be analyzed using mathematical techniques.

In this step, the OR practitioner’s skills and knowledge come into play. The model should be accurate, but it should also be simple enough to be solved.

**3. Solution**

The third step is to solve the model and obtain a solution to the problem. This can be done using a variety of mathematical techniques, such as linear programming, integer programming, and dynamic programming.

**4. Sensitivity Analysis**

The fourth step is to perform a sensitivity analysis on the solution. This involves examining how the solution changes in response to changes in the model’s parameters.

It is important because it helps to identify the factors that have the greatest impact on the solution. This information can be used to make decisions about how to implement the solution.

**5. Implementation**

The final step is to implement the solution. This involves putting the solution into practice and monitoring its effectiveness.

In this step, the solution is put into practice. This can be a challenging step, as there may be resistance to change from within the organization.

**Operations Research Models**

There are many different models used in operations research (OR). Some of the most common models include:

**Linear programming:**

Linear programming is a mathematical optimization technique that can be used to find the best solution to a problem when the objective function and all the constraints are linear. The linear programming model can be represented by the following equation:

**maximize or minimize z = c1x1 + c2x2 + … + cnxnsubject toa1x1 + a2x2 + … + anxn <= bx1 >= 0, x2 >= 0, …, xn >= 0**

where:

- z is the objective function
- c1, c2, …, cn are the coefficients of the objective function
- x1, x2, …, xn are the decision variables
- a1, a2, …, an are the coefficients of the constraints
- b is the right-hand side of the constraints

**Integer Programming:**

Integer programming is a type of linear programming where the decision variables must be integers. Integer programming is used to solve problems where the decision variables must be whole numbers, such as the number of machines to use or the number of workers to hire. The integer programming model can be represented by the following equation:

Maximize or minimize:

z = a1x1 + a2x2 + … + anxn

Subject to:

c1x1 + c2x2 + … + cnxn <= b

x1, x2, …, xn are integers

**Dynamic Programming**

Dynamic programming is a technique for solving problems that involve a sequence of decisions. Dynamic programming works by breaking the problem down into smaller subproblems and then solving the subproblems recursively. The dynamic programming model can be represented by the following set of equations:

V(n) = optimal value of the problem with n stages

V(n) = max(V(n-1) + f(n), V(n-2) + g(n), …, V(0) + h(n))

The models used in OR are constantly evolving as new techniques are developed and as the problems that need to be solved become more complex. By understanding the different types of models that are available, OR practitioners can select the best model for the specific problem that they are trying to solve.

**Importance of Operations Research**

**Improved decision-making:**

OR can help organizations make better decisions by providing them with a systematic approach to problem-solving. OR techniques can be used to identify the best course of action, given the available information and constraints.

**Increased efficiency:**

OR can help organizations improve their efficiency by identifying ways to reduce costs, improve productivity, and optimize resource allocation. OR techniques can be used to identify bottlenecks and inefficiencies in production processes, transportation networks, and other systems.

**Reduced risk:**

OR can help organizations reduce risk by identifying and mitigating potential problems. OR techniques can be used to assess the likelihood of different events occurring and to develop contingency plans in case of unexpected events.

**Increased innovation:**

OR can help organizations develop new products and services, improve existing products and services, and enter new markets. OR techniques can be used to identify new opportunities, assess the feasibility of new ideas, and develop prototypes of new products and services.

**Uses of Operation Research**

Operations research (OR) is a discipline that deals with the application of mathematical, statistical, and analytical techniques to help make better decisions. OR problems typically involve the allocation and control of limited resources, and they can arise in a wide variety of settings, including business, government, and the military.

**OR practitioners use a variety of tools and techniques to solve problems, including:**

**Mathematical modeling:**

This involves developing mathematical models of the problem that can be used to simulate different scenarios and evaluate the impact of different decisions.

**Statistical analysis:**

This involves collecting and analyzing data to identify trends and patterns that can be used to make better decisions.

**Data mining:**

This involves using statistical techniques to extract hidden patterns and trends from large datasets.

**Computer simulation:**

This involves using computers to create virtual models of real-world systems that can be used to test different hypotheses and solutions.

**OR has been used to solve a wide variety of problems, including:**

**Optimizing production schedules:**

OR can be used to help companies determine the best way to schedule production in order to minimize costs and maximize output.

**Routing delivery vehicles:**

OR can be used to help companies determine the best way to route delivery vehicles in order to minimize travel time and fuel costs.

**Allocating resources:**

OR can be used to help companies allocate resources, such as personnel and equipment, in order to maximize efficiency and minimize costs.

**Managing risk:**

OR can be used to help companies manage risk, such as the risk of stock market fluctuations or natural disasters.

OR is a powerful tool that can be used to improve decision-making in a wide variety of settings. By applying OR techniques, companies can save money, improve efficiency, and increase profits.

**Nature and Scopes of Operations Research **

The nature of OR is to be a problem-solving tool that can be used to improve the efficiency and effectiveness of organizations. OR can be used to solve a wide variety of problems, including:

**Production planning and scheduling****Inventory management****Transportation and logistics****Financial planning****Risk management****Customer service****Military operations**

The scope of OR is broad and encompasses a wide range of industries and organizations. OR is used by businesses, government agencies, and non-profit organizations to improve their operations. OR has been used to solve problems in a variety of industries, including:

**Manufacturing****Retail****Healthcare****Transportation****Utilities****Government****Military**

OR is a valuable tool for organizations that are looking to improve their performance. By using OR, organizations can make better decisions, improve efficiency, and reduce costs.

Here are some of the key benefits of using operations research:

**Improved decision-making:**OR can help organizations make better decisions by providing them with a more systematic and analytical approach to problem-solving.**Increased efficiency:**OR can help organizations improve their efficiency by identifying and eliminating waste and inefficiency.**Reduced costs:**OR can help organizations reduce their costs by finding ways to save money on resources, such as materials, labor, and energy.**Increased customer satisfaction:**OR can help organizations improve customer satisfaction by providing them with better products and services, and by providing them with a more efficient and convenient way to do business.

If you are looking for a way to improve your organization’s performance, operations research is a valuable tool that you should consider using.

**Concept of Optimizing**

Optimization is a key concept in operations research. It is the process of finding the best possible solution to a problem, given a set of constraints. Optimization problems can be classified into two types:

**Deterministic optimization**problems have known values for all of the variables in the problem.**Stochastic optimization**problems have some variables that have uncertain values.

**There are a variety of methods that can be used to solve optimization problems. Some of the most common methods include:**

**Linear programming**is a method for solving deterministic optimization problems where the objective function and the constraints are linear.**Nonlinear programming**is a method for solving deterministic optimization problems where the objective function or the constraints are nonlinear.**Stochastic programming**is a method for solving stochastic optimization problems.

The choice of method for solving an optimization problem depends on the specific problem and the available resources.

In operations research, optimization is used to solve a wide variety of problems. Some of the most common applications of optimization in operations research include:

**Production planning****Inventory management****Transportation and logistics****Financial planning****Risk management****Customer service****Military operations**

Optimization is a powerful tool that can be used to improve the efficiency and effectiveness of organizations. By using optimization, organizations can make better decisions, improve their operations, and reduce their costs.

**Here are some examples of how optimization has been used in operations research:**

**Production planning:**A company can use optimization to determine the optimal production schedule for a product. This can help the company to reduce costs and improve efficiency.**Inventory management:**A company can use optimization to determine the optimal inventory levels for a product. This can help the company to reduce costs and improve customer service.**Transportation and logistics:**A company can use optimization to determine the optimal transportation and logistics network for its products. This can help the company to reduce costs and improve delivery times.**Financial planning:**A company can use optimization to determine the optimal investment portfolio for its shareholders. This can help the company to maximize shareholder returns.**Risk management:**A company can use optimization to determine the optimal risk management strategy for its operations. This can help the company to reduce the risk of financial losses.**Customer service:**A company can use optimization to determine the optimal customer service strategy for its customers. This can help the company to improve customer satisfaction and retention.**Military operations:**The military can use optimization to determine the optimal deployment of troops and resources for a military campaign. This can help the military to achieve its objectives with minimal casualties.

These are just a few examples of how optimization has been used in operations research. Optimization is a powerful tool that can be used to improve the efficiency and effectiveness of organizations in a wide variety of industries.

**Vogel’s approximation method (VAM)** **of Transportation Problem**

Vogel’s approximation method (VAM) is a heuristic algorithm for solving transportation problems. It is a greedy algorithm, which means that it makes local decisions that do not guarantee an optimal solution, but that often lead to good solutions.

VAM works by finding the cell with the highest penalty in each row and column. The penalty for a cell is the difference between the smallest cost in the row or column and the second smallest cost. The cell with the highest penalty in each row and column is then assigned a flow equal to the minimum of the supply or demand in that row or column.

VAM is a simple and efficient algorithm that can be used to solve transportation problems quickly. It is not guaranteed to find an optimal solution, but it often finds good solutions.

Here are the steps involved in Vogel’s approximation method:

1. Identify the two lowest costs in each row and column of the given cost matrix and then write the absolute row and column difference. These differences are called penalties.

2. Identify the row or column with the maximum penalty and assign the corresponding cell’s min(supply, demand). If two or more columns or rows have the same maximum penalty, then we can choose one among them as per our convenience.

3. Repeat steps 1 and 2 until all supply and demand is met.

Here is an example of how Vogel’s approximation method can be used to solve a transportation problem:

Given:

Source Destination Cost

——- ——– ——–

A B 3

A C 4

B D 2

C D 5

Supply: 10

Demand: 12

The first step is to identify the two lowest costs in each row and column. The two lowest costs in row A are 3 and 4, the two lowest costs in column B are 2 and 5, and the two lowest costs in column C are 4 and 5. The absolute row and column differences are then calculated. The absolute row difference for row A is 1, the absolute row difference for column B is 3, and the absolute row difference for column C is 1. The row with the maximum penalty is column B, so the corresponding cell is assigned a flow of 10. The supply in column B is now 0, so it is removed from the problem.

The next step is to repeat steps 1 and 2. The two lowest costs in row A are now 4 and 5, the two lowest costs in column D are 2 and 5, and there are no costs in column C. The absolute row difference for row A is 1, the absolute row difference for column D is 3, and there is no row difference for column C. The row with the maximum penalty is column D, so the corresponding cell is assigned a flow of 2. The demand in column D is now 0, so it is removed from the problem.

The final step is to repeat steps 1 and 2 until all supply and demand is met. There is no supply or demand left, so the problem is solved. The optimal solution is to send 10 units from A to B and 2 units from A to D.

VAM is a simple and efficient algorithm for solving transportation problems. It is not guaranteed to find an optimal solution, but it often finds good solutions.

**N.W. Corner’s method of Transportation Probloem**

The Northwest Corner Method is a simple and efficient algorithm for solving transportation problems. It is a greedy algorithm, which means that it makes local decisions that do not guarantee an optimal solution, but that often lead to good solutions.

The Northwest Corner Method works by starting in the top left corner of the transportation matrix and assigning as much as possible to that cell. Then, it moves to the next cell in the row or column, whichever has the smallest remaining supply or demand, and repeats the process. This continues until all supply or demand is met.

The Northwest Corner Method is not guaranteed to find an optimal solution, but it often finds good solutions quickly. It is a good choice for problems with a small number of sources and destinations.

Here are the steps involved in the Northwest Corner Method:

- Start in the top left corner of the transportation matrix.
- Assign as much as possible to that cell.
- If the supply or demand in that cell is met, move on to the next cell in the row or column.
- If the supply or demand in that cell is not met, assign as much as possible to that cell.
- Repeat steps 3 and 4 until all supply or demand is met.

Here is an example of how the Northwest Corner Method can be used to solve a transportation problem:

Given:

Source Destination Cost

——- ——– ——–

A B 3

A C 4

B D 2

C D 5

Supply: 10

Demand: 12

The first step is to start in the top left corner of the transportation matrix. The top left corner is cell (A,B), so we assign as much as possible to that cell. The minimum of the supply in row A and the demand in column B is 10, so we assign 10 to cell (A,B).

The next step is to move to the next cell in the row or column, whichever has the smallest remaining supply or demand. In this case, the smallest remaining supply is in row A, so we move to cell (A,C). The minimum of the supply in row A and the demand in column C is 2, so we assign 2 to cell (A,C).

The next step is to repeat steps 3 and 4 until all supply or demand is met. In this case, there is still 8 units of supply in row A and 4 units of demand in column D. The minimum of 8 and 4 is 4, so we assign 4 to cell (A,D).

There is no supply or demand left, so the problem is solved. The optimal solution is to send 10 units from A to B, 2 units from A to C, and 4 units from A to D.

The Northwest Corner Method is a simple and efficient algorithm for solving transportation problems. It is not guaranteed to find an optimal solution, but it often finds good solutions quickly. It is a good choice for problems with a small number of sources and destinations.

**Conclusion**

Operations research is a broad field that uses mathematical, statistical, and computer-based techniques to solve complex problems in a variety of fields, including business, government, and healthcare. It is a powerful tool that can help organizations make better decisions, improve efficiency, and increase profits.

One of the key benefits of operations research is that it can help organizations to make better decisions. By using mathematical models and simulations, operations researchers can help organizations to understand the impact of different decisions on their operations. This can help organizations to make more informed decisions that are more likely to achieve their desired outcomes.

Another key benefit of operations research is that it can help organizations to improve efficiency. By identifying and eliminating waste in their operations, organizations can save money and improve their bottom line. Operations research can also help organizations to improve their customer service by reducing wait times and improving the quality of their products and services.

Finally, operations research can help organizations to increase profits. By optimizing their operations, organizations can increase their output and reduce their costs. This can lead to increased profits and a stronger bottom line.

Overall, operations research is a powerful tool that can help organizations to make better decisions, improve efficiency, and increase profits. If you are looking for a way to improve your organization’s performance, then operations research is a great place to start.