Operations research
Question Bank
Q1) Define Operations Research.
A1) This is an analytical method that helps management make decisions. The name of this method is that research (O.R.) is comparatively new, but the tactic used for it's not new. Operations research involves the application of scientific principles and methods to strategic issues.
The subject of operations research was born in the United Kingdom during World War II and was used in military strategy. During World War II, a group of scientists with representatives from mathematics, statistics, physics, and social sciences was commissioned to study various military operations. The team was very successful and contributed significantly to the meticulous response to the overall operation and related operational issues.
As military strategies and their decisions were so important and costly that it became necessary to allocate such research to operations, the best scientists were grouped with the support of military institutions to develop scientific methods and methods. Adopted and provided quantitative information Decision.
After World War II, its application began in industry, trade, agriculture, planning and various other economic areas.
Operations research can be defined as:
Definition:
(I) Application of scientific methods, techniques, and tools to problems related to operating the system in order to provide system controllers with the best solution to the problem.
(II) Research may be a tool for creating decisions that seek optimal results that are like the general purpose and constraints of the organization.
(III) O.R. Is a scientific method that provides the executive department with a quantitative basis for making decisions about the operations under its control?
(IV) A scientific approach to problem solving for management.
(V) It helps executives make decisions by providing the necessary quantitative information based on scientific analysis.
(VI) It is the requisition of the latest methods of mathematical science to complicated problems involving the management of huge systems of labor, machinery, materials, and money in industry, business, government, and defence. A distinctive approach is to develop a scientific model of the system that comes with measurement of things like chance and risk to predict and compare the result of alternative decisions, strategies, or controls.
(VII) It is the application of scientists and subject experts to the study of specific manipulations of the scientific method. Its purpose is to provide management, which is the basis for quantitatively predicting the most effective outcomes of operations under a given set of variable conditions, thereby providing a sound basis for "decision-making". That is.
In fact, operations research uses research and scientific methods for analysis, as well as for investigating current and future problems. Therefore, operations research provides management with an alternative plan for the problem to make a decision.
It is very clear that Operations Research does not make management decisions, but instead, this method presents management with a careful scientific and quantitative analysis of the problem, allowing management to make healthier decisions. You will be during a better position to try to.
Q2) Explain the phases in OR decision making process.
A2) Since then, the main purpose of operations research has been to provide better quantitative information for decision making. Now our goal is to learn how to make better decisions.
The decision-making process in OR research typically involves the following phases:
B. Survey phase:
C. Action phase:
In the absence of an OR, these phases are often performed completely, otherwise important steps are skipped. Judgment and subjective decision making are not enough. Therefore, the industry is looking for more objective ways to make decisions from operations research. It turns out that the method used also needs to take into account emotional and subjective factors.
For example, skills and a creative workforce are key elements of our business, and if a manager wants to have a new place, he considers the employee's personal feelings about the place he chooses is needed.
Q3) What are the some of the issues that operations research can analyse?
A3) Here are some of the issues that operations research can analyse:
1. Finance, budgeting, investment:
- Billing procedure and
2. Marketing:
3. Purchase:
4. Production control:
5. Personnel management:
6. R & D:
Q4) What are the features of OR?
A4) Features of operations research (features):
The main features of operations research (O.R.) are as follows.
This requires an interdisciplinary team that includes individuals with skills in mathematics, statistics, economics, engineering, materials science, computers, and more.
2. A holistic approach to the system:
When assessing decisions, look at key interactions and their impact on the organization as a whole on the functions they were originally involved in.
3. Methodological approach:
Use scientific methods to solve O.R. problems
4. Objective approach:
We will try to find the best or best solution to the problem under consideration, taking into account the goals of the O.R. organization.
Q5) Explain Operations research model
A5) An operations research model is an ideal representation of a real-life situation, representing one or more aspects of reality. The purpose of the model is to provide a means to analyse system behaviour and improve performance.
Model classification:
Models can be classified on the following elements:
1. Depends on the degree of abstraction:
a) Mathematical model.
b) Language model.
2. by function:
a) Descriptive model.
b) Predictive model.
c) A normative model of repetitive problems.
3. by structure:
a) Physical model.
b) Analog (graphical) model.
c) Symbolic or mathematical model.
4. Depends on the nature of the environment:
a) Deterministic model.
b) Probabilistic model.
5. by time horizon:
a) Static model.
b) Dynamic model.
Q6) Write short note on Model building.
A6) A mathematical model is a set of equations that describes a system or problem. The equations represent the objective functions and constraints. The objective function is the formula for the purpose (cost or benefit of the operation), and the constraint is the formula for the limit on the achievement of the purpose.
These expressions consist of controllable and uncontrollable variables.
The general form of a mathematical model is:
O = f (xi, yi)
Where O = objective function
xi = controllable variables
yi = variables that cannot be controlled
Relationship between f = O and xi, yi.
Not all variables are included because the model is only an approximation of the actual situation.
Simplification of operations research model:
When building a model, you should try to simplify the model, but only to the extent that the accuracy is not significantly reduced.
Some of the common simplifications are:
Q7) What are the methods of OR?
A7) The important methods of operations research are explained below.
(I) Inventory management model:
Operations research balances inventory costs with one or more of the following costs:
This study will help you make decisions about:
The most well-known usage is the form of economic order quantity equations for finding economic lot sizes.
(II) Standby line model:
These models are used with their associated costs to minimize latency and idle time.
There are two types of standby line models:
(A) Queuing theory. This can be applied to determine the number of service facilities and / or the timing of arrival for the service.
(B) An ordering theory that can be applied to determine the order of services.
(III) Replacement model:
These models are used to determine when items should be replaced or maintained.
(I) Abolished or
(II) Usage efficiency deteriorates
(III) It becomes uneconomical to repair or maintain.
(IV) Assignment model:
(IV) Competitive strategy:
This type of strategy is adopted when the efficiency of one institution's decisions depends on the decisions of another institution. Examples of such strategies are card and chespel games, price fixing in competitive markets where these strategies are called "theory".
(V) Linear programming:
These techniques are used to solve the problem of operations with many variables that are subject to certain restrictions. For such issues, the objectives are profit, cost, production quantity, etc., but the limits are as follows: Government policy, plant capacity, product demand, raw material availability, water or electricity, storage capacity, etc.
(VI) Sequence model:
These involve choosing the right sequence to run a set of jobs running on a service facility or machine in order to optimize the efficiency measurement of system performance.
(VII) Simulation model:
Simulation is an exploratory way to study behaviour over time.
(VIII) Network model:
This is an approach for planning, scheduling, and controlling complex projects.
Q8) What techniques are to apply for wide selection of problems?
A8) These techniques apply to a really wide selection of problems.
(I) Distribution or transportation issues:
For such issues, we are given different centers in demand and we also know different warehouses with inventory locations. By using linear programming, you can find the most economical distribution of products from different warehouses to different centers.
(II) Product composition:
You can apply these techniques to determine the best product and available resource combination for your plant to get the maximum profit or the lowest production cost.
(III) Production plan:
These techniques can also be applied to assign different jobs to different machines to maximize profits, maximize production, and minimize total production time.
(IV) Personnel allocation:
Similarly, this technique can be applied to assign different people with different aptitudes to different jobs in order to complete a task in a minimum amount of time.
(V) Agricultural production:
You can also apply this technique to maximize the grower's interests. This involves growing a large number of items with different returns and harvest times on different types of land with different fertility.
(VI) Financial application:
Many financial decision-making problems are often solved by using applied mathematics.
Some of them are:
(I) select the optimal portfolio to maximize the return on investment from alternative investment opportunities such as bonds and stocks. Such problems are commonly faced by managers of investment trusts, banks and insurance companies.
(II) Determining a financial mix strategy, including the choice of means such as funding companies, projects and inventories.
Q9) Write note on Origins and development of Operations Research.
A9) The term operations research was first coined in 1940 by Macro ski and Treften in the small English town of Bawsey. This new science was born in a military context. During World War II, military management called on scientists from various disciplines and teamed them up to help solve strategic and tactical problems (i.e., improve the execution of various military projects). Discussed, evolved and proposed methods and means. Through their joint efforts, experience and deliberation, they proposed a specific approach that showed remarkable progress. To systematic and scientific research on the operation of the system. This new approach was called Operations Research or Operations Research (OR for short).
In 1950, O.R. was recognized as a subject worthy of academic research at the university. Since then, this subject has become increasingly important to students in economics, business administration, public administration, behavioural science, social welfare, mathematics, commerce, and engineering.
The American Operations Research Association was founded in 1950, and the International Federation of OR Associations was founded in 1957. In some countries, OR's International Scientific Journals are now available in a variety of languages. Major journals include operations research, traffic science, business science, operations research quarterly, and the journal of the Operations Research Society of Canada, operations research mathematics, and international journals of game theory.
Operations Research in India
In India, operations research was born in 1949 when the Operations Research Unit was established at the Regional Research Institute in Hyderabad. In 1953, the Operations Research Unit was established at the Indian Institute of Statistics in Calcutta, applying operations research methods to national planning and research. The Operations Research Association of India was founded in 1957. In 1959, he became a member of the Federation of International Operations Research Associations. In 1959, the first conference of the Indian Operations Research Association was held in Delhi. The Operations Research Association of India has launched a journal. Other journals dealing with operations research include: Journal of National Productivity Council, Journal of Materials Management in India, Journal of Defence Science.
In recent organized development, O.R we have successfully resolved many research cases in the military, government, and industry. The basic problem of most developing countries in Asia and Africa is to get rid of poverty and hunger as soon as possible. Therefore, economists, statisticians, managers, politicians, engineers work in teams, O.R. There is a large range to solve this problem approach.
On the other hand, due to the rapid population growth and the accompanying food shortages, countries face the problem of optimally allocating land to different crops, depending on climatic conditions and available facilities. Developing countries face the problem of optimal distribution of water from resources such as canals for irrigation purposes. Therefore, a considerable amount of scientific research can be done in this direction.
Q10) What is the nature of OR?
A10) These techniques apply to a really wide selection of problems.
This section describes only some of the common applications.
(I) Distribution or transportation issues:
For such issues, we are given different centers in demand and we also know different warehouses with inventory locations. By using linear programming, you can find the most economical distribution of products from different warehouses to different centers.
(II) Product composition:
You can apply these techniques to determine the best product and available resource combination for your plant to get the maximum profit or the lowest production cost.
(III) Production plan:
These techniques can also be applied to assign different jobs to different machines to maximize profits, maximize production, and minimize total production time.
(IV) Personnel allocation:
Similarly, this technique can be applied to assign different people with different aptitudes to different jobs in order to complete a task in a minimum amount of time.
(V) Agricultural production:
You can also apply this technique to maximize the grower's interests. This involves growing a large number of items with different returns and harvest times on different types of land with different fertility.
(VI) Financial application:
Many financial decision-making problems are often solved by using applied mathematics.
Some of them are:
(I) select the optimal portfolio to maximize the return on investment from alternative investment opportunities such as bonds and stocks. Such problems are commonly faced by managers of investment trusts, banks and insurance companies.
(II) Determining a financial mix strategy, including the choice of means such as funding companies, projects and inventories.
Q11) Explain the Models and Modelling in Operations Research.
A11) An operations research model is a simplified representation of an operation or process that considers only the basic aspects or most important features of a typical problem under investigation.
Model type
There are many ways to classify models, so decision makers need to identify which type of model is best suited for their decision problem.
Physical model
These models provide the physical appearance of the actual object under investigation. Physical models that are reduced in size or enlarged are easy to observe, build, and describe, and are only useful for design issues.
Iconic Models:
Iconic models retain some of the physical characteristics and characteristics of the systems they represent.
Analog model:
A model represents a system with a set of properties that differ from the original system and is not physically similar.
Symbolic model
These models use letters, numbers, and other symbols to represent system properties.
Oral models:
These models describe the situation in written or spoken language.
Example:-text, books, etc.
Mathematical Models:
These models use mathematical symbols, letters, numbers, and mathematical operators (+,-, ÷, ×) to represent relationships between various variables in the system and describe their properties or behaviour to do.
Descriptive model
These models only describe some aspects of the situation based on observations, surveys, survey results, or other available data, and are not predictions or recommendations.
Example: -Plant layout diagram
Predictive model
These models are used to predict the outcome of a particular alternative to the problem. These models do not have an objective function as part of the model for evaluating decision choices.
Optimization model
These models provide the "best" or "optimal" solution for problems that are subject to certain restrictions on resource usage.
Static mode
The static model presents the system at a specific time and does not take into account changes over time.
Dynamic model
In the dynamic model, time is considered one of the variables and recognizes the effects of time-generated changes in choosing the best course of action.
Deterministic model
A model is said to be deterministic if it is assumed that the relationships between all parameters, constants, and functions are known reliably when the decision is made.
Example:-Linear programming model.
Probabilistic (stochastic model)
A model in which at least one parameter or determinant is a random variable is called a stochastic (or stochastic) model. Since at least one decision variable is random, the independent variable, which is a function of the dependent variable, is also random. This means that you cannot reliably predict the consequences or rewards of a particular change in the independent variable. However, it is possible to predict the pattern of values for both variables by the probability distribution.
Example:-Insurance against risks such as fire, accidents and illness.
Analytical model
These models have a specific mathematical structure and can be solved by known analytical or mathematical methods. All optimization models (which require maximization or minimization of the objective function) are analytical models.
Simulation model
These models also have a mathematical structure, which cannot be solved by applying a mathematical structure, but cannot be solved by applying a mathematical method. Instead, a simulation model is essentially a computer-assisted experiment on the mathematical structure of a real problem to describe and evaluate its behaviour under certain assumptions over a period of time.
Q12) How do we classify OR model?
A12) An operations research model is an ideal representation of a real-life situation, representing one or more aspects of reality. The purpose of the model is to provide a means to analyse system behaviour and improve performance.
Models can be classified on the following elements:
1. Depends on the degree of abstraction:
a) Mathematical model.
b) Language model.
2. by Function:
a) Descriptive model.
b) Predictive model.
c) A normative model of repetitive problems.
3. By structure:
a) Physical model.
b) Analog (graphical) model.
c) Symbolic or mathematical model.
4. Depends on the nature of the environment:
a) Deterministic model.
b) Probabilistic model.
5. By time horizon:
a) Static model.
b) Dynamic model.
Good model features:
- It should be easy to create.
Q13) What are Operations Research Methodology?
A13) Operations research is a scientific approach to decision making, so you need to follow these steps:
1. Problem formulation:
First you need to clearly define the problem. It is common to start O.R. as study with a tentative formulation of the problem. This is reformulated many times during the study. Economic aspects should also be considered in this study.
Developing O.R. in a study, analysts need to analyse the following key components:
(I) Environment:
The environment includes physical, social, and economic factors that can affect the issue under consideration. The O.R. team or analyst should investigate the content of the organization, including men, materials, machinery, suppliers, consumers, competitors, governments, and the general public.
(II) Decision maker:
Operations analysts need to investigate the relationship between decision makers and the problem at hand.
(III) Purpose:
You need to define the purpose with the whole problem in mind.
(IV) Alternative:
O.R. studies determine which alternative behavioural policies are most effective in achieving the desired objectives. You should also consider the expected reaction of your competitors to the alternatives.
2. Solution derivation:
The model is used to determine the solution, either by simulation or mathematical analysis. Mathematical analysis to derive the optimal solution involves analytical or numerical procedures and uses different disciplines of mathematics.
3. Model and solution testing:
A well-formulated and properly manipulated model can help predict the impact of control variable changes on system-wide effectiveness. The validity of the solution is checked by comparing the results with the results obtained without the use of a model.
4. Establishing control over the solution:
The solution derived from the model remains valid as long as the uncontrolled variables hold their values and relationships. When the value of one or more variables changes or the relationships between variables change, the solution goes out of control. In this situation, you need to change the model to take the changes into account.
5. Solution implementation:
The solution thus obtained should be translated into operating procedures so that stakeholders can easily understand and apply it. After applying the solution to the system, O.R the group should investigate the system's response to the changes made.
Q14) Explain the Methods for solving O.R. models.
A14) In OR, there is no single general approach to solving all the mathematical models that actually occur. Instead, the type and complexity of the mathematical model determines the nature of the solution.
The most prominent OR method is linear programming. . Other techniques include integer programming (variables take integer values), dynamic programming (the original model can be decomposed into smaller sub-problems), network programming (the problem can be modeled as a network), and Includes nonlinear programming. Programming (model functions are non-linear).
A feature of most OR methods is that solutions are generally not available in closed form (like equations). Instead, they are determined by the algorithm. The algorithm provides fixed computational rules that are iteratively applied to the problem at each iteration (called an iteration) to get the solution closer to the optimum.
Some mathematical models are so complex that it is not possible to solve them with any of the available optimization algorithms. In such cases, you may need to stop searching for the best solution and use heuristics or heuristics to find the right solution.
In general, there are three methods used to resolve the OR model:
1. Analysis method:
If the OR model is solved using all the tools of classical mathematics, such as derivative calculations and finite differences available for this task, then such a type of solution is called an analytical solution. Solutions for various inventory models are obtained by adopting so-called analytical procedures.
2. Iterative method:
If the classic method fails due to constraints or a complex number of variables, you usually have to adopt the iterative method. Such a procedure begins with a trial solution and a set of rules to improve it. The process is then repeated until the trial solution is replaced with an improved solution and no further improvement is possible or the cost of further computation cannot be justified.
The iterative method can be divided into three groups:
After a finite number of iterations, no further improvement is possible.
Consecutive iterations improve the solution, but the solution is guaranteed only as the limit of an infinite process.
Finally, including trial and error, even using a computer can be time consuming, laborious, and costly.
3. Monte Carlo method:
The basis of the so-called Monte Carlo method is to randomly sample the value of a variable from the distribution of the variable. Monte Carlo refers to the use of sampling methods to estimate the values of non-random variables. Following is the way to solve method:
Step 1: To get an overview of the system, first draw a flow diagram of the system.
Step 2: Next, make the correct sample observations and select the right model for your system. In this step, you will calculate the probability distribution of the variable of interest.
Step 3: Next, convert the probability distribution to a cumulative distribution function.
Step 4: Use the random number table to select a series of random numbers.
Step 5: Next, use the sequence of random numbers obtained in Step 4 to determine the sequence of values for the variable of interest.
Step 6: Finally, create some standard math functions for the values obtained in step 5.
Q15) What methodology is used in OR models?
A15) Methodology of Operation Research:
Step 1-Defining and Identifying the Problem-
When formulating the problem, you need to fully establish the purpose, alternative course of action, constraints, and effects of the system under investigation.
Step-2-Building a Mathematical Model-
The next step is to build a mathematical model of the problem using the following basic elements:-
Variables and parameters that can be decided or controlled or variables that cannot be controlled: Variables that can be controlled are variables that the decision maker can directly control. The values of these variables are determined. Uncontrollable variables are variables that are not under the direct control of the decision maker Former government policy price increase.
Constraints or Limits – You need to include constraints in your model to see the physical limits of your system.
Objective function: That is, a formula for the benefit or cost of a particular operation.
Example: 2 products P1 and P2 2 machines M1M2
One unit of P1 requires 3 hours for M1 and 1 hour for M2.
One unit of P2 requires 2 hours for M1 and 2 hours for M2.
The number of hours available per week on M1 and M2 is 60 and 40. The profit contribution of P1 and P2 is Rs. 60 and rupees. 50 per unit. I wanted to maximize my profits. Create a mathematical model.
11 → x1 and x2 = you cannot control all the controllable variables whose values are determined, the profit per unit, and the cost / unit amount of resources.
Equation (i) = Objective functions (ii) and (iii) are constraints
Step 3 – Derivation of solution –
The next step is to get the solution. That is, it determines the value of the coefficient of determination that optimizes a particular purpose (maximizing profits and minimizing costs).
Step 4-Testing the model and solution –
Contain testing of your model. Models are useful when they can provide reliable predictions of system performance. Good operations research analysts are continually trying to update their models.
Step 5-Implementation and control
The next step is to implement a derived solution. The solution description is given in terms of the procedures used in the actual system. After applying the solution, observe the system response. Control of the solution is established by appropriate feedback.
Q16) What is the scope of OR in commercial applications?
A16) In recent organized development, O.R we have successfully resolved many research cases in the military, government, and industry. The basic problem of most developing countries in Asia and Africa is to get rid of poverty and hunger as soon as possible. Therefore, economists, statisticians, managers, politicians, engineers work in teams, O.R. There is a large range to solve this problem approach.
On the other hand, due to the rapid population growth and the accompanying food shortages, countries face the problem of optimally allocating land to different crops, depending on climatic conditions and available facilities. Developing countries face the problem of optimal distribution of water from resources such as canals for irrigation purposes. Therefore, a considerable amount of scientific research can be done in this direction.
In the field of industrial engineering, there are problems from procuring materials to shipping finished products. Management is always interested in optimizing profits.
Therefore, to make a scientifically based decision, O.R the research team will consider various alternatives and their impact on existing systems. This approach is equally useful for economists, managers, planners, irrigation or agriculture professionals and statisticians.
The operations research approach is useful for operations management. Operations management can be defined as the management of a system for providing goods or services and involves the design and operation of the system for manufacturing, transportation, supply, or service. The operating system translates the input to meet the needs of the customer.
Therefore, operational management is concerned with optimal resource utilization, that is, effective use of resources with minimal loss in utilization or waste. In other words, it concerns satisfactory customer service and optimal resource use. Inputs to the operating system can be materials, machines, and human resources.
The O.R. study will only be completed if the human factors of the available alternatives are also taken into account. Operations research is conducted by a team of scientists or experts from a variety of relevant disciplines.
For example, O.R. to solve problems related to inventory management. The team should include engineers, cost agents, mathematicians, and statisticians who know about store and material management. For large and complex problems, the team should include mathematicians, statisticians, one or two engineers, economists, computer programmers, psychologists, and more.
Q17) Explain the issues that operations research can analyse?
A17) Here are some of the issues that operations research can analyse:
1. Finance, budgeting, investment:
2. Marketing:
3. Purchase:
5. Production control:
5. Personnel management:
6. R & D:
Q18) What components do an analysts need to analyse?
A18) Developing O.R. in a study, analysts need to analyse the following key components:
(I) Environment:
The environment includes physical, social, and economic factors that can affect the issue under consideration. The O.R. team or analyst should investigate the content of the organization, including men, materials, machinery, suppliers, consumers, competitors, governments, and the general public.
(II) Decision maker:
Operations analysts need to investigate the relationship between decision makers and the problem at hand.
(III) Purpose:
You need to define the purpose with the whole problem in mind.
(IV) Alternative:
O.R. studies determine which alternative behavioural policies are most effective in achieving the desired objectives. You should also consider the expected reaction of your competitors to the alternatives.
2. Solution derivation:
The model is used to determine the solution, either by simulation or mathematical analysis. Mathematical analysis to derive the optimal solution involves analytical or numerical procedures and uses different disciplines of mathematics.
3. Model and solution testing:
A well-formulated and properly manipulated model can help predict the impact of control variable changes on system-wide effectiveness. The validity of the solution is checked by comparing the results with the results obtained without the use of a model.
4. Establishing control over the solution:
The solution derived from the model remains valid as long as the uncontrolled variables hold their values and relationships. When the value of one or more variable changes or the relationships between variables change, the solution goes out of control. In this situation, you need to change the model to take the changes into account.
5. Solution implementation:
The solution thus obtained should be translated into operating procedures so that stakeholders can easily understand and apply it. After applying the solution to the system, O.R the group should investigate the system's response to the changes made.
Q19) What problems do OR solve?
A19) Operations Research does not make management decisions, but instead, this method presents management with a careful scientific and quantitative analysis of the problem, allowing management to make healthier decisions. You will be during a better position to try to.
It can be used to solve various types of problems, including:
However, you may remember that operations research never replaces managers as decision makers. The ultimate and complete responsibility for analysing all factors and making decisions rests with the manager.
In a broader sense, operations research does not deal with everyday issues such as output or machine capacity by a single worker. Instead, it concerns the overall aspects of business operations, such as inventory, sales, production, and scheduling relationships. It may also trades in with the overall circulation of goods and services from the factory to the consumer.
The operations research team may include statisticians, psychologists, labor professionals, mathematicians, etc., depending on the requirements of the problem.
Q20) Write short note on Action Phase.
A20) Action phase:
In the absence of an OR, these phases are often performed completely, otherwise important steps are skipped. Judgment and subjective decision making are not enough. Therefore, the industry is looking for more objective ways to make decisions from operations research. It turns out that the method used also needs to take into account emotional and subjective factors.
For example, skills and a creative workforce are key elements of our business, and if a manager wants to have a new place, he considers the employee's personal feelings about the place he chooses is needed.
