the first step in solving operations research problem is mcq

270+ Operations Research Solved MCQs

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Operations Research

1. Operations Research approach is ______________.

• multi-disciplinary
• collect essential data

2. A feasible solution to a linear programming problem ______________.

• must satisfy all the constraints of the problem simultaneously
• need not satisfy all of the constraints, only some of them
• must be a corner point of the feasible region.
• must optimize the value of the objective function

3. If any value in XB column of final simplex table is negative, then the solution is ______________.

• no solution

4. For any primal problem and its dual______________.

• optimal value of objective function is same
• dual will have an optimal solution iff primal does too
• primal will have an optimal solution iff dual does too
• both primal and dual cannot be infeasible

5. The difference between total float and head event slack is ______________

• independent float
• interference float
• linear float

6. An optimal assignment requires that the maximum number of lines which can be drawn through squares with zero opportunity cost should be equal to the number of ______________.

• rows or columns
• rows and columns.
• rows+columns- 1
• rows-columns.

7. To proceed with the Modified Distribution method algorithm for solving an transportation problem, the number of dummy allocations need to be added are______________.

8. Select the correct statement

• EOQ is that quantity at which price paid by the buyer is minimum
• If annual demand doubles with all other parameters remaining constant, the Economic Order Quantity is doubled
• Total ordering cost equals holding cost
• Stock out cost is never permitted

9. Service mechanism in a queuing system is characterized by ______________.

• customers behavior
• servers behavior
• customers in the system
• server in the system

10. The objective of network analysis is to______________.

• minimize total project duration
• minimize toal project cost
• minimize production delays, interruption and conflicts
• maximize total project duration

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Operations Research Methodology

• Describing the problem;
• Formulating the OR model;
• Solving the OR model;
• Performing some analysis of the solution;
• Presenting the solution and analysis.
• Describing the Problem The aim of this step is to come up with a formal, rigorous model description. Usually you start an optimisation project with an abstract description of a problem and some data. Often you need to spend some time talking with the person providing the problem (usually known as the client ). By talking with the client and considering the data available you can come up with a more rigorous model description required for formulation. Sometimes not all the data will be relevant or you will need to ask the client if they can provide some other data. Sometimes the limitations of the available data may significantly change your model description and subsequent formulation.
• Formulating the OR Model The aim of this step is to translate the problem description into a valid OR model. The implementation of this step may be quite different depending on the OR model you are using. For example, if you are using linear programming to solve your problem, then formulating an OR model involves translating your problem into a linear programme. If you are using simulation to solve your problem, then formulating an OR model entails breaking down the behaviour of the system being simulated into a sequence of events and determining the random variables that "drive" the simulation.
• Solving the OR Model The aim of this step is to solve your OR model. Just as the formulation step depended on the OR model being used, this solution step depends on your OR model. Additionally, there may be more than one solution method for a particular OR model. For example, solving a linear programme may be done using the Revised Simplex Method or an interior point method. Often, in practice, OR models may not be solved completely due to time constraints. Other algorithms may partially solve OR models (for optimisation models, these algorithms are known as heuristics and terminate with a "good" solution that is not necessarily optimal).
• Performing analysis of the solution Often there is uncertainty in the problem description (either with the accuracy of the data provided or with the value(s) of data in the future). In this situation the robustness of our solution to the OR model can be examined using analysis. Analysis involves identifying how the solution would change under various changes to the problem data (for example, what would be the effect of a given cost increasing, or a particular machine failing?). This sort of analysis can also be useful for making tactical or strategic decisions (for example, if we invested in opening another factory, what effect would this have on our revenue?). Another important consideration in this step (and the next) is the validation of the OR model's solution. You should carefully consider what the solution means in terms of the original problem description. Make sure it makes sense to you and, more importantly, to your client. Hence, the next step, presenting the solution and analysis is very important.
• Periodic monitoring of the validity of your OR Model;
• Further analysis of your solution, looking for other benefits for your client;
• Identification of future OR opportunities.

How to Solve the Assignment Problem: A Complete Guide

Table of Contents

Assignment problem is a special type of linear programming problem that deals with assigning a number of resources to an equal number of tasks in the most efficient way. The goal is to minimize the total cost of assignments while ensuring that each task is assigned to only one resource and each resource is assigned to only one task. In this blog, we will discuss the solution of the assignment problem using the Hungarian method, which is a popular algorithm for solving the problem.

Understanding the Assignment Problem

Before we dive into the solution, it is important to understand the problem itself. In the assignment problem, we have a matrix of costs, where each row represents a resource and each column represents a task. The objective is to assign each resource to a task in such a way that the total cost of assignments is minimized. However, there are certain constraints that need to be satisfied – each resource can be assigned to only one task and each task can be assigned to only one resource.

Solving the Assignment Problem

There are various methods for solving the assignment problem, including the Hungarian method, the brute force method, and the auction algorithm. Here, we will focus on the steps involved in solving the assignment problem using the Hungarian method, which is the most commonly used and efficient method.

Step 1: Set up the cost matrix

The first step in solving the assignment problem is to set up the cost matrix, which represents the cost of assigning a task to an agent. The matrix should be square and have the same number of rows and columns as the number of tasks and agents, respectively.

Step 2: Subtract the smallest element from each row and column

To simplify the calculations, we need to reduce the size of the cost matrix by subtracting the smallest element from each row and column. This step is called matrix reduction.

Step 3: Cover all zeros with the minimum number of lines

The next step is to cover all zeros in the matrix with the minimum number of horizontal and vertical lines. This step is called matrix covering.

Step 4: Test for optimality and adjust the matrix

To test for optimality, we need to calculate the minimum number of lines required to cover all zeros in the matrix. If the number of lines equals the number of rows or columns, the solution is optimal. If not, we need to adjust the matrix and repeat steps 3 and 4 until we get an optimal solution.

Step 5: Assign the tasks to the agents

The final step is to assign the tasks to the agents based on the optimal solution obtained in step 4. This will give us the most cost-effective or profit-maximizing assignment.

Solution of the Assignment Problem using the Hungarian Method

The Hungarian method is an algorithm that uses a step-by-step approach to find the optimal assignment. The algorithm consists of the following steps:

• Subtract the smallest entry in each row from all the entries of the row.
• Subtract the smallest entry in each column from all the entries of the column.
• Draw the minimum number of lines to cover all zeros in the matrix. If the number of lines drawn is equal to the number of rows, we have an optimal solution. If not, go to step 4.
• Determine the smallest entry not covered by any line. Subtract it from all uncovered entries and add it to all entries covered by two lines. Go to step 3.

The above steps are repeated until an optimal solution is obtained. The optimal solution will have all zeros covered by the minimum number of lines. The assignments can be made by selecting the rows and columns with a single zero in the final matrix.

Applications of the Assignment Problem

The assignment problem has various applications in different fields, including computer science, economics, logistics, and management. In this section, we will provide some examples of how the assignment problem is used in real-life situations.

Applications in Computer Science

The assignment problem can be used in computer science to allocate resources to different tasks, such as allocating memory to processes or assigning threads to processors.

Applications in Economics

The assignment problem can be used in economics to allocate resources to different agents, such as allocating workers to jobs or assigning projects to contractors.

Applications in Logistics

The assignment problem can be used in logistics to allocate resources to different activities, such as allocating vehicles to routes or assigning warehouses to customers.

Applications in Management

The assignment problem can be used in management to allocate resources to different projects, such as allocating employees to tasks or assigning budgets to departments.

Let’s consider the following scenario: a manager needs to assign three employees to three different tasks. Each employee has different skills, and each task requires specific skills. The manager wants to minimize the total time it takes to complete all the tasks. The skills and the time required for each task are given in the table below:

The assignment problem is to determine which employee should be assigned to which task to minimize the total time required. To solve this problem, we can use the Hungarian method, which we discussed in the previous blog.

Using the Hungarian method, we first subtract the smallest entry in each row from all the entries of the row:

Next, we subtract the smallest entry in each column from all the entries of the column:

We draw the minimum number of lines to cover all the zeros in the matrix, which in this case is three:

Since the number of lines is equal to the number of rows, we have an optimal solution. The assignments can be made by selecting the rows and columns with a single zero in the final matrix. In this case, the optimal assignments are:

• Emp 1 to Task 3
• Emp 2 to Task 2
• Emp 3 to Task 1

This assignment results in a total time of 9 units.

I hope this example helps you better understand the assignment problem and how to solve it using the Hungarian method.

Solving the assignment problem may seem daunting, but with the right approach, it can be a straightforward process. By following the steps outlined in this guide, you can confidently tackle any assignment problem that comes your way.

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Operations Research

1 Operations Research-An Overview

• History of O.R.
• Approach, Techniques and Tools
• Phases and Processes of O.R. Study
• Typical Applications of O.R
• Limitations of Operations Research
• Models in Operations Research
• O.R. in real world

2 Linear Programming: Formulation and Graphical Method

• General formulation of Linear Programming Problem
• Optimisation Models
• Basics of Graphic Method
• Important steps to draw graph
• Multiple, Unbounded Solution and Infeasible Problems
• Solving Linear Programming Graphically Using Computer
• Application of Linear Programming in Business and Industry

3 Linear Programming-Simplex Method

• Principle of Simplex Method
• Computational aspect of Simplex Method
• Simplex Method with several Decision Variables
• Two Phase and M-method
• Multiple Solution, Unbounded Solution and Infeasible Problem
• Sensitivity Analysis
• Dual Linear Programming Problem

4 Transportation Problem

• Basic Feasible Solution of a Transportation Problem
• Modified Distribution Method
• Stepping Stone Method
• Unbalanced Transportation Problem
• Degenerate Transportation Problem
• Transhipment Problem
• Maximisation in a Transportation Problem

5 Assignment Problem

• Solution of the Assignment Problem
• Unbalanced Assignment Problem
• Problem with some Infeasible Assignments
• Maximisation in an Assignment Problem
• Crew Assignment Problem

6 Application of Excel Solver to Solve LPP

• Building Excel model for solving LP: An Illustrative Example

7 Goal Programming

• Concepts of goal programming
• Goal programming model formulation
• Graphical method of goal programming
• The simplex method of goal programming
• Using Excel Solver to Solve Goal Programming Models
• Application areas of goal programming

8 Integer Programming

• Some Integer Programming Formulation Techniques
• Binary Representation of General Integer Variables
• Unimodularity
• Cutting Plane Method
• Branch and Bound Method
• Solver Solution

9 Dynamic Programming

• Dynamic Programming Methodology: An Example
• Definitions and Notations
• Dynamic Programming Applications

10 Non-Linear Programming

• Solution of a Non-linear Programming Problem
• Convex and Concave Functions
• Kuhn-Tucker Conditions for Constrained Optimisation
• Quadratic Programming
• Separable Programming
• NLP Models with Solver

11 Introduction to game theory and its Applications

• Important terms in Game Theory
• Saddle points
• Mixed strategies: Games without saddle points
• 2 x n games
• Exploiting an opponent’s mistakes

12 Monte Carlo Simulation

• Reasons for using simulation
• Monte Carlo simulation
• Limitations of simulation
• Steps in the simulation process
• Some practical applications of simulation
• Two typical examples of hand-computed simulation
• Computer simulation

13 Queueing Models

• Characteristics of a queueing model
• Notations and Symbols
• Statistical methods in queueing
• The M/M/I System
• The M/M/C System
• The M/Ek/I System
• Decision problems in queueing

Research Methodology

• Introduction to Research Methodology
• Research Approaches
• Concepts of Theory and Empiricism
• Characteristics of scientific method
• Understanding the Language of Research
• 11 Steps in Research Process
• Research Design
• Different Research Designs
• Compare and Contrast the Main Types of Research Designs
• Cross-sectional research design
• Qualitative and Quantitative Research
• Descriptive Research VS Qualitative Research
• Experimental Research VS Quantitative Research
• Sampling Design
• Probability VS Non-Probability Sampling
• 40 MCQ on Research Methodology

MCQ on research Process

• MCQ on Research Design
• 18 MCQ on Quantitative Research
• 30 MCQ on Qualitative Research
• 45 MCQ on Sampling Methods
• 20 MCQ on Principles And Planning For Research

Q1. What is the first step in the research process?

A) Data analysis

B) Literature review

C) Hypothesis testing

D) Research design

Answer: B) Literature review

Q2. What is the purpose of a research hypothesis?

A) To summarize the research findings

B) To explain the research methodology

C) To predict the outcome of the research

D) To describe the research participant

Answer: C) To predict the outcome of the research

Q3. What is the purpose of formulating a research problem in operational terms?

a) To narrow down the scope of the problem

b) To make the problem more complex

c) To make the problem less specific

d) To discriminate relevant data from irrelevant ones

Answer: d) To discriminate relevant data from irrelevant ones

Q4. What is the purpose of replicating a research study?

a) To confirm that the hypothesis is incorrect

b) To prove that the study was flawed

c) To support the contention that the hypothesis cannot be rejected

d) To provide an opportunity to alter the hypothesis

Answer: c) To support the contention that the hypothesis cannot be rejected

Q5. The research process is:

a) a system of interrelated activities

b) a linear process with no interdependencies

c) a static process with fixed stages

d) a process that can be skipped or altered without consequences

Answer: a) a system of interrelated activities

Q6. Which stage of the research process involves formulating a hypothesis?

b) Stage II

c) Stage III

d) Stage IV

Answer: b) Stage III

Q7. What is a dependent variable in a research study?

A) A variable that is manipulated by the researcher

B) A variable that is not affected by other variables

C) A variable that is measured or observed in response to the independent variable

D) A variable that is controlled by the research participants

Answer: C) A variable that is measured or observed in response to the independent variable

Q8. What is the purpose of data analysis in the research process?

A)To collect data from research participants

B) To test the research hypothesis

C) To review the existing literature

D) To design the research study

Answer: B) To test the research hypothesis

Q9. What is a random sample?

A) A sample selected based on a specific criterion

B) A sample selected using a random process

C) A sample selected based on convenience

D) A sample selected based on the researcher’s judgment

Answer: B) A sample selected using a random process