introduction to assignment problem

Assignment Problem: Meaning, Methods and Variations | Operations Research

After reading this article you will learn about:- 1. Meaning of Assignment Problem 2. Definition of Assignment Problem 3. Mathematical Formulation 4. Hungarian Method 5. Variations.

Meaning of Assignment Problem:

An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total cost or maximize total profit of allocation.

The problem of assignment arises because available resources such as men, machines etc. have varying degrees of efficiency for performing different activities, therefore, cost, profit or loss of performing the different activities is different.

Thus, the problem is “How should the assignments be made so as to optimize the given objective”. Some of the problem where the assignment technique may be useful are assignment of workers to machines, salesman to different sales areas.

Definition of Assignment Problem:

ADVERTISEMENTS:

Suppose there are n jobs to be performed and n persons are available for doing these jobs. Assume that each person can do each job at a term, though with varying degree of efficiency, let c ij be the cost if the i-th person is assigned to the j-th job. The problem is to find an assignment (which job should be assigned to which person one on-one basis) So that the total cost of performing all jobs is minimum, problem of this kind are known as assignment problem.

The assignment problem can be stated in the form of n x n cost matrix C real members as given in the following table:

• In the above asignment problem, we have to provide assignments such that there is one to one assignments and the overall cost is minimized.

How Assignment Problem is related to LPP? OR Write mathematical formulation of Assignment Model.

→ Assignment Model is a special application of Linear Programming (LP).

→ The mathematical formulation for Assignment Model is given below:

→ Let, C i j \text {C}_{ij} C ij ​ denotes the cost of resources 'i' to the task 'j' ; such that

→ Now assignment problems are of the Minimization type. So, our objective function is to minimize the overall cost.

→ Subjected to constraint;

(i) For all j t h j^{th} j t h task, only one i t h i^{th} i t h resource is possible:

(ii) For all i t h i^{th} i t h resource, there is only one j t h j^{th} j t h task possible;

(iii) x i j x_{ij} x ij ​ is '0' or '1'.

Types of Assignment Problem:

(i) balanced assignment problem.

• It consist of a suqare matrix (n x n).
• Number of rows = Number of columns

(ii) Unbalanced Assignment Problem

• It consist of a Non-square matrix.
• Number of rows ≠ \not=  = Number of columns

Methods to solve Assignment Model:

(i) integer programming method:.

In assignment problem, either allocation is done to the cell or not.

So this can be formulated using 0 or 1 integer.

While using this method, we will have n x n decision varables, and n+n equalities.

So even for 4 x 4 matrix problem, it will have 16 decision variables and 8 equalities.

So this method becomes very lengthy and difficult to solve.

(ii) Transportation Methods:

As assignment problem is a special case of transportation problem, it can also be solved using transportation methods.

In transportation methods ( NWCM , LCM & VAM), the total number of allocations will be (m+n-1) and the solution is known as non-degenerated. (For eg: for 3 x 3 matrix, there will be 3+3-1 = 5 allocations)

But, here in assignment problems, the matrix is a square matrix (m=n).

So total allocations should be (n+n-1), i.e. for 3 x 3 matrix, it should be (3+3-1) = 5

But, we know that in 3 x 3 assignment problem, maximum possible possible assignments are 3 only.

So, if are we will use transportation methods, then the solution will be degenerated as it does not satisfy the condition of (m+n-1) allocations.

So, the method becomes lengthy and time consuming.

(iii) Enumeration Method:

It is a simple trail and error type method.

Consider a 3 x 3 assignment problem. Here the assignments are done randomly and the total cost is found out.

For 3 x 3 matrix, the total possible trails are 3! So total 3! = 3 x 2 x 1 = 6 trails are possible.

The assignments which gives minimum cost is selected as optimal solution.

But, such trail and error becomes very difficult and lengthy.

If there are more number of rows and columns, ( For eg: For 6 x 6 matrix, there will be 6! trails. So 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720 trails possible) then such methods can't be applied for solving assignments problems.

(iv) Hungarian Method:

It was developed by two mathematicians of Hungary. So, it is known as Hungarian Method.

It is also know as Reduced matrix method or Flood's technique.

There are two main conditions for applying Hungarian Method:

(1) Square Matrix (n x n). (2) Problem should be of minimization type.

Suggested Notes:

Modified Distribution Method (MODI) | Transportation Problem | Transportation Model

Stepping Stone | Transportation Problem | Transportation Model

Vogel’s Approximation Method (VAM) | Method to Solve Transportation Problem | Transportation Model

Transportation Model - Introduction

North West Corner Method | Method to Solve Transportation Problem | Transportation Model

Least Cost Method | Method to Solve Transportation Problem | Transportation Model

Tie in selecting row and column (Vogel's Approximation Method - VAM) | Numerical | Solving Transportation Problem | Transportation Model

Crashing Special Case - Multiple (Parallel) Critical Paths

Crashing Special Case - Indirect cost less than Crash Cost

Basics of Program Evaluation and Review Technique (PERT)

Numerical on PERT (Program Evaluation and Review Technique)

Network Analysis - Dealing with Network Construction Basics

Construct a project network with predecessor relationship | Operation Research | Numerical

Graphical Method | Methods to solve LPP | Linear Programming

Basics of Linear Programming

Linear Programming Problem (LPP) Formulation with Numericals

All comments that you add will await moderation. We'll publish all comments that are topic related, and adhere to our Code of Conduct .

Want to tell us something privately? Contact Us

Post comment

Education Lessons

Stay in touch, [notes] operation research, [notes] dynamics of machinery, [notes] maths, [notes] science, [notes] computer aided design.

OPERATIONS RESEARCH

Lesson 9. solution of assignment problem.

Current course

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.

How useful was this post?

Click on a star to rate it!

Average rating 0 / 5. Vote count: 0

No votes so far! Be the first to rate this post.

We are sorry that this post was not useful for you! 😔

Let us improve this post!

Tell us how we can improve this post?

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

• Maths Notes Class 12
• NCERT Solutions Class 12
• RD Sharma Solutions Class 12
• Maths Formulas Class 12
• Maths Previous Year Paper Class 12
• Class 12 Syllabus
• Class 12 Revision Notes
• Physics Notes Class 12
• Chemistry Notes Class 12
• Biology Notes Class 12
• CBSE Class 12 Maths Notes: Chapter Wise Notes 2024

Chapter 1: Relations and Functions

• Types of Functions
• Composite functions - Relations and functions
• Invertible Functions
• Composition of Functions
• Inverse Functions
• Verifying Inverse Functions by Composition

Chapter 2: Inverse Trigonometric Functions

• Inverse Trigonometric Functions
• Graphs of Inverse Trigonometric Functions - Trigonometry | Class 12 Maths
• Properties of Inverse Trigonometric Functions
• Inverse Trigonometric Identities

Chapter 3: Matrices

• Types of Matrices
• Matrix Operations
• Matrix Addition
• Matrix Multiplication
• Transpose of a Matrix
• Symmetric and Skew Symmetric Matrices
• Elementary Operations on Matrices
• Inverse of a Matrix by Elementary Operations - Matrices | Class 12 Maths
• Invertible Matrix

Chapter 4: Determinants

• Determinant of a Matrix with Solved Examples
• Properties of Determinants
• Area of a Triangle using Determinants
• Minors and Cofactors
• Adjoint of a Matrix
• Applications of Matrices and Determinants

Chapter 5: Continuity and Differentiability

• Continuity and Discontinuity in Calculus - Class 12 CBSE
• Differentiability of a Function | Class 12 Maths
• Derivatives of Inverse Functions
• Derivatives of Implicit Functions - Continuity and Differentiability | Class 12 Maths
• Derivatives of Composite Functions
• Derivatives of Inverse Trigonometric Functions | Class 12 Maths
• Derivative of Exponential Functions
• Logarithmic Differentiation - Continuity and Differentiability
• Proofs for the derivatives of eˣ and ln(x) - Advanced differentiation
• Rolle's Theorem and Lagrange's Mean Value Theorem
• Derivative of Functions in Parametric Forms
• Second Order Derivatives in Continuity and Differentiability | Class 12 Maths
• Mean Value Theorem
• Algebra of Continuous Functions - Continuity and Differentiability | Class 12 Maths

Chapter 6: Applications of Derivatives

• Critical Points
• Derivatives as Rate of Change
• Increasing and Decreasing Functions
• Increasing and Decreasing Intervals
• Tangents and Normals
• Equation of Tangents and Normals
• Relative Minima and Maxima
• Absolute Minima and Maxima
• Concave Function
• Inflection Point
• Curve Sketching
• Approximations & Maxima and Minima - Application of Derivatives | Class 12 Maths
• Higher Order Derivatives

Chapter 7: Integrals

• Integration by Substitution
• Integration by Partial Fractions
• Integration by Parts
• Integration of Trigonometric Functions
• Functions Defined by Integrals
• Definite Integral
• Computing Definite Integrals
• Fundamental Theorem of Calculus
• Finding Derivative with Fundamental Theorem of Calculus
• Evaluating Definite Integrals
• Properties of Definite Integrals
• Definite Integrals of Piecewise Functions
• Improper Integrals
• Riemann Sum
• Riemann Sums in Summation Notation
• Trapezoidal Rule
• Definite Integral as the Limit of a Riemann Sum
• Antiderivatives
• Indefinite Integrals
• Particular Solutions to Differential Equations
• Integration by U-substitution
• Reverse Chain Rule
• Partial Fraction Expansion
• Trigonometric Substitution

Chapter 8: Applications of Integrals

• Area under Simple Curves
• Area Between Two Curves - Calculus
• Area between Polar Curves
• Area as Definite Integral

Chapter 9: Differential Equations

• Differential Equations
• Homogeneous Differential Equations
• Separable Differential Equations
• Exact Equations and Integrating Factors
• Implicit Differentiation
• Implicit differentiation - Advanced Examples
• Advanced Differentiation
• Disguised Derivatives - Advanced differentiation | Class 12 Maths
• Derivative of Inverse Trig Functions
• Logarithmic Differentiation

Chapter 10: Vector Algebra

• Vector Algebra
• Dot and Cross Products on Vectors
• How to Find the Angle Between Two Vectors?
• Section Formula - Vector Algebra

Chapter 11: Three-dimensional Geometry

• Direction Cosines and Direction Ratios
• Equation of a Line in 3D
• Angles Between two Lines in 3D Space
• Shortest Distance Between Two Lines in 3D Space | Class 12 Maths
• Points, Lines and Planes

Chapter 12: Linear Programming

Linear programming.

• Graphical Solution of Linear Programming Problems

Chapter 13: Probability

• Conditional Probability and Independence - Probability | Class 12 Maths
• Multiplication Theorem
• Dependent and Independent Events
• Bayes' Theorem
• Probability Distribution
• Binomial Distribution in Probability
• Binomial Mean and Standard Deviation - Probability | Class 12 Maths
• Bernoulli Trials and Binomial Distribution
• Discrete Random Variable
• Expected Value
• NCERT Solutions for Class 12 Maths -Chapter Wise with PDF
• RD Sharma Class 12 Solutions for Maths

Linear programming is a mathematical concept that is used to find the optimal solution of the linear function. This method uses simple assumptions for optimizing the given function. Linear Programming has a huge real-world application and it is used to solve various types of problems.

Linear programming is used in various industries such as shipping industries, manufacturing industries, transportation industries, telecommunications, and others.

Term “linear programming” consists of two words linear and programming, the word linear tells the relation between various types of variables of degree one used in a problem and the word programming tells us the step-by-step procedure to solve these problems.

In this article, we will learn about linear programming, its examples, formulas, and other concepts in detail.

Table of Content

What is Linear Programming? 

Components of linear programming, linear programming examples, linear programming problems, types of linear programming problems, linear programming formula, how to solve linear programming problems, linear programming methods, linear programming simplex method, linear programming graphical method, linear programming applications, importance of linear programming, up-to-date applications of linear programming, linear programming in operations research, simplex method.

Linear programming or Linear optimization is a technique that helps us to find the optimum solution for a given problem, an optimum solution is a solution that is the best possible outcome of a given particular problem.

In simple terms, it is the method to find out how to do something in the best possible way. With limited resources, you need to do the optimum utilization of resources and achieve the best possible result in a particular objective such as least cost, highest margin, or least time. 

The situation that requires a search for the best values of the variables subject to certain constraints is where we use linear programming problems. These situations cannot be handled by the usual calculus and numerical techniques.

Linear Programming Definition

Linear programming is the technique used for optimizing a particular scenario. Using linear programming provides us with the best possible outcome in a given situation. It uses all the available resources in a manner such that they produce the optimum result.

The basic components of a linear programming(LP) problem are:

• Decision Variables: Variables you want to determine to achieve the optimal solution.
• Objective Function: M athematical equation that represents the goal you want to achieve
• Constraints: Limitations or restrictions that your decision variables must follow.
• Non-Negativity Restrictions: In some real-world scenarios, decision variables cannot be negative

Additional Characteristics of Linear Programming

• Finiteness: The number of decision variables and constraints in an LP problem are finite.
• Linearity: The objective function and all constraints must be linear functions of the decision variables . It means the degree of variables should be one.

We can understand the situations in which Linear programming is applied with the help of the example discussed below,

Suppose a delivery man has to deliver 8 packets in a day to the different locations of a city. He has to pick all the packets from A and has to deliver them to points P, Q, R, S, T, U, V, and W. The distance between them is indicated using the lines as shown in the image below. The shortest path followed by the delivery man is calculated using the concept of Linear Programming.

Linear Programming Problems (LPP) involve optimizing a linear function to find the optimal value solution for the function. The optimal value can be either the maximum value or the minimum value.

In LPP, the linear functions are called objective functions. An objective function can have multiple variables, which are subjected to conditions and have to satisfy the linear constraints .

There are many different linear programming problems(LPP) but we will deal with three major linear programming problems in this article.

Manufacturing Problems

Manufacturing problems are a problem that deals with the number of units that should be produced or sold to maximize profits when each product requires fixed manpower, machine hours, and raw materials.

Diet Problems

It is used to calculate the number of different kinds of constituents to be included in the diet to get the minimum cost, subject to the availability of food and their prices.

Transportation Problems

It is used to determine the transportation schedule to find the cheapest way of transporting a product from plants /factories situated at different locations to different markets.

A linear programming problem consists of,

• Decision variables
• Objective function
• Constraints
• Non-Negative restrictions

Decision variables are the variables x, and y, which decide the output of the linear programming problem and represent the final solution. 

The objective function , generally represented by Z, is the linear function that needs to be optimized according to the given condition to get the final solution. 

The restrictions imposed on decision variables that limit their values are called constraints.

Now, the general formula of a linear programming problem is,

Objective Function : Z = ax + by

Constraints: cx + dy ≥ e, px + qy ≤ r

Non-Negative restrictions: x ≥ 0, y ≥ 0

In the above condition x, and y are the decision variables.

Before solving the linear programming problems first we have to formulate the problems according to the standard parameters. The steps for solving linear programming problems are,

Step 1: Mark the decision variables in the problem. Step 2: Build the objective function of the problem and check if the function needs to be minimized or maximized. Step 3: Write down all the constraints of the linear problems. Step 4: Ensure non-negative restrictions of the decision variables. Step 5: Now solve the linear programming problem using any method generally we use either the simplex or graphical method.

We use various methods for solving linear programming problems. The two most common methods used are,

• Graphical Method

Let’s learn about these two methods in detail in this article,

One of the most common methods to solve the linear programming problem is the simplex method. In this method, we repeat a specific condition ‘n’ a number of times until an optimum solution is achieved.

The steps required to solve linear programming problems using the simplex method are,

Step 1: Formulate the linear programming problems based on the given constraints. Step 2: Convert all the given inequalities to equations or equalities of the linear programming problems by adding the slack variable to each inequality where ever required. Step 3: Construct the initial simplex table. By representing each constraint equation in a row and writing the objective function at the bottom row. The table so obtained is called the Simplex table. Step 4: Identify the greatest negative entry in the bottom row the column of the element with the highest negative entry is called the pivot column Step 5: Divide the entries of the right-most column with the entries of the respective pivot column, excluding the entries of the bottommost row. Now the row containing the least entry is called the pivot row. The pivot element is obtained by the intersection of the pivot row and the pivot column. Step 6: Using matrix operation and with the help of the pivot element make all the entries in the pivot column to be zero. Step 7: Check for the non-negative entries in the bottommost row if there are no negative entries in the bottom row, end the process else start the process again from step 4. Step 8: The final simplex table so obtained gives the solution to our problem.

Graphical Method is another method than the Simplex method which is used to solve linear programming problems. As the name suggests this method uses graphs to solve the given linear programming problems. This is the best method to solve linear programming problems and requires less effort than the simplex method. 

While using this method we plot all the inequalities that are subjected to constraints in the given linear programming problems. As soon as all the inequalities of the given LPP are plotted in the XY graph the common region of all the inequalities gives the optimum solution. All the corner points of the feasible region are calculated and the value of the objective function at all those points is calculated then comparing these values we get the optimum solution of the LPP.

Example: Find the maximal and minimal value of z = 6x + 9y when the constraint conditions are,

• 2x + 3y ≤ 12
• x and y ≥ 0

Step 1 : First convert the inequations into normal equations. Hence the equations will be 2x+3y = 0, x = 0, y = 0 and x + y = 5. Step 2 : Find the points at which 2x + 3y and x + y = 5 cut the x-axis and y-axis. To find the point of intersection of the x-axis put y = 0 in the respective equation and find the point. Similarly for y-axis intersection points put x = 0 in the respective equation. Step 3 : Draw the two lines cutting the x-axis and y-axis. We find that the two axes cut each other at (3,2). Step 4 : For x ≥ 0 and y ≥ 0, we find that both inequations are followed. Hence the region will include an area region enclosed by two axes and both lines including the origin. The plotted region is shown below in the figure. Step 5 : Find Z for each point and maxima and minima. Coordinates Z = 6x + 9y (0,5) Z = 45 (0,4) Z = 36 (5,0) Z = 30 (6,0) Z = 36 (3,2) Z = 36 Hence, we find that Z = 6x + 9y is maximum at (0,5) and minimum at (5,0).

Linear Programming has applications in various fields. It is used to find the minimum cost of a process when all the constraints of the problems are given. It is used to optimize the transportation cost of the vehicle, etc. Various applications of Linear Programming are

Engineering Industries

Engineering Industries use linear programming to solve design and manufacturing problems and to get the maximum output from a given condition.

Manufacturing Industries

Manufacturing Industries use linear programming to maximize the profit of the companies and to reduce the manufacturing cost.

Energy Industries

Energy companies use linear programming to optimize their production output.

Transportation Industries

Linear programming is also used in transportation industries to find the path to minimize the cost of transportation.

Linear Programming has huge importance in various industries it maximizes the output value while minimizing the input values according to various constraints.

LP is highly applicable when we have multiple conditions while solving a problem and we have to optimize the output of the problem i.e. either we have to find the minimum or the maximum value according to a given condition.

Linear Inequalities Algebraic Solution of Linear Inequalities

Problem 1: A company manufactures and sells two types of products and the cost of production of each unit a and b is rupees 200 and 150 respectively each unit of product yields a profit of 20 rupees and each unit of product b yields a profit of 15 rupees on selling. The company estimates the monthly demand of A and B to be at a maximum of the harvested unit in all the production budget for the month is set at rupees 50000. How many units should the company manufacture to earn maximum profit from its monthly sales from a and b?

Let x = number of units of type A y = Number of units of type B Maximize Z = 40x + 50y Subject to the constraints 3x + y ≤ 9 x + 2y ≤ 8 and x, y ≥ 0 Consider the equation, 3x + y = 9 x = 3 y = 0 and x + 2y = 8 x = 8 y = 0 Now, we can determine the maximum value of Z by evaluating the value of Z at the four points (vertices) is shown below Vertices Z = 40x + 50y (0, 0) Z = 40 × 0 + 50 × 0 = Rs. 0 (3, 0) Z = 40 × 3 + 50 × 0 = Rs. 120 (0, 4)  Z = 40 × 0 + 50 × 4 = Rs. 200 (2, 3) Z = 40 × 2 + 50 × 3 = Rs. 230 Maximum profit, Z = Rs. 230 ∴ Number of units of type A is 2 and the number of units of type B is 3.

Problem 2: Maximize Z = 3x + 4y.

Subject to constraints , x + y ≤ 450, 2x + y ≤ 600 and x, y ≤ 0.

We have from the given Constraints (1) X + Y = 450 Putting x = 0, ⇒ 0 + y = 450 ⇒ y = 450 Putting y = 0, ⇒ x + 0 = 450 ⇒ x = 450 From, Constraints (2) 2x + y = 600 Putting x = 0, ⇒ 0 + y = 600 ⇒ y = 600 Putting  y = 0, ⇒ 2x + 0 = 600 ⇒ x = 300 Now, we have the points co-ordinate Z = 3x + 4y

Therefore, the optimal solution maximum Z = 1800 at co-ordinate x = 0 and y = 450. The graph is given below.

Linear programming, a powerful mathematical technique, is used to solve optimization problems in various industries. Here are some modern applications:

• Supply Chain Optimization : Linear programming helps companies minimize costs and maximize efficiency in their supply chains. It’s used for determining the most cost-effective transportation routes, warehouse operations, and inventory management strategies.
• Energy Management : In the energy sector, linear programming is utilized to optimize the mix of energy production methods. This includes balancing traditional energy sources with renewable ones to reduce costs and environmental impact while meeting demand.
• Telecommunications Network Design : Linear programming aids in designing efficient telecommunications networks. It helps in allocating bandwidth, designing network layouts, and optimizing the flow of data to ensure high-speed communication at lower costs.
• Financial Planning : Businesses and financial analysts use linear programming for portfolio optimization, risk management, and capital budgeting. It helps in making investment decisions that maximize returns while minimizing risk.
• Healthcare Logistics : In healthcare, linear programming is applied to optimize the allocation of resources, such as hospital beds, medical staff, and equipment. It’s crucial for improving patient care, reducing wait times, and managing costs effectively.
• Manufacturing Process Optimization : Linear programming is used to determine the optimal production levels for multiple products within a manufacturing facility, considering constraints like labor, materials, and machine availability.
• Agricultural Planning : Farmers and agricultural planners use linear programming to decide on crop selection, land use, and resource allocation to maximize yields and profits while conserving resources.
• Airline Crew Scheduling : Airlines employ linear programming to schedule crews efficiently, ensuring that flights are staffed in compliance with regulations and minimizing operational costs.

These applications demonstrate the versatility and power of linear programming in solving complex optimization problems across various sectors, showcasing its relevance in today’s data-driven world.

• Core Tool : Linear programming is a foundational tool in operations research for optimizing resources.
• Decision Making : Helps in making the best decisions regarding resource allocation, maximizing profits, or minimizing costs.
• Wide Applications : Used in various fields such as logistics, manufacturing, finance, and healthcare for solving complex problems.
• Modeling Real-World Problems : Transforms real-world problems into mathematical models to find the most efficient solutions.
• Optimization Algorithm : The Simplex Method is a powerful algorithm used in linear programming to find the optimal solution to linear inequalities.
• Step-by-Step Approach : It iteratively moves towards the best solution by navigating the edges of the feasible region defined by constraints.
• Efficiency : Known for its efficiency in solving large-scale linear programming problems.
• Versatility : Applicable in various domains like diet planning, network flows, production scheduling, and more, showcasing its versatility.

Linear Programming – FAQs

What is linear programming.

Linear programming is a mathematical concept which is used to optimize a given linear problem which has a variety of constraints. Using linear programming we the optimum output of the given problem

What are Linear Programming Problems?

Linear Programming Problems (LPP) are the problems which give the optimum solution to the given conditions.

What is Linear Programming Formula?

General Linear Programming Formulas are, Objective Function: Z = ax + by Constraints: px + qy ≤ r, sx + ty ≤ u Non-Negative Restrictions: x ≥ 0, y ≥ 0

What are the different types of Linear Programming?

Different types of linear programming methods are, Linear Programming by Simplex Method Linear Programming by R Method Linear Programming by Graphical Method

What are requirements of Linear Programming?

Various requirements of linear programming problems are, Linearity Objective Function Constraints Non-negativity

What are the advantages of Linear Programming?

Various advantages of linear programming are, It provides the optimal solution to any given linear problem. It is easy to use and always gives consistent results It helps to maximize profits and to reduce the input cost.

Please Login to comment...

Similar reads.

• Math-Concepts
• Maths-Class-12
• Technical Scripter 2020
• Mathematics
• School Learning
• Technical Scripter
• CBSE Exam Format Changed for Class 11-12: Focus On Concept Application Questions
• 10 Best Waze Alternatives in 2024 (Free)
• 10 Best Squarespace Alternatives in 2024 (Free)
• Top 10 Owler Alternatives & Competitors in 2024
• 30 OOPs Interview Questions and Answers (2024)

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

Encyclopedia of Optimization pp 1153–1162 Cite as

Generalized Assignment Problem

• O. Erhun Kundakcioglu 3 &
• Saed Alizamir 3  
• Reference work entry

2817 Accesses

15 Citations

Article Outline

Introduction

  Multiple-Resource Generalized Assignment Problem

  Multilevel Generalized Assignment Problem

  Dynamic Generalized Assignment Problem

  Bottleneck Generalized Assignment Problem

  Generalized Assignment Problem with Special Ordered Set

  Stochastic Generalized Assignment Problem

  Bi-Objective Generalized Assignment Problem

  Generalized Multi-Assignment Problem

  Exact Algorithms

  Heuristics

Conclusions

This is a preview of subscription content, log in via an institution .

Buying options

• Available as PDF
• Read on any device
• Instant download
• Own it forever
• Durable hardcover edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Albareda-Sambola M, van der Vlerk MH, Fernandez E (2006) Exact solutions to a class of stochastic generalized assignment problems. Eur J Oper Res 173:465–487

Article   MATH   Google Scholar  

Amini MM, Racer M (1994) A rigorous computational comparison of alternative solution methods for the generalized assignment problem. Manag Sci 40(7):868–890

Amini MM, Racer M (1995) A hybrid heuristic for the generalized assignment problem. Eur J Oper Res 87(2):343–348

Asahiro Y, Ishibashi M, Yamashita M (2003) Independent and cooperative parallel search methods for the generalized assignment problem. Optim Method Softw 18:129–141

Article   MathSciNet   MATH   Google Scholar  

Balachandran V (1976) An integer generalized transportation model for optimal job assignment in computer networks. Oper Res 24(4):742–759

Barnhart C, Johnson EL, Nemhauser GL, Savelsbergh MWP, Vance PH (1998) Branch-and-price: column generation for solving huge integer programs. Oper Res 46(3):316–329

Beasley JE (1993) Lagrangean heuristics for location problems. Eur J Oper Res 65:383–399

Cario MC, Clifford JJ, Hill RR, Yang J, Yang K, Reilly CH (2002) An investigation of the relationship between problem characteristics and algorithm performance: a case study of the gap. IIE Trans 34:297–313

Google Scholar  

Cattrysse DG, Salomon M, Van LN Wassenhove (1994) A set partitioning heuristic for the generalized assignment problem. Eur J Oper Res 72:167–174

Cattrysse DG, Van LN Wassenhove (1992) A survey of algorithms for the generalized assignment problem. Eur J Oper Res 60:260–272

Ceselli A, Righini G (2006) A branch-and-price algorithm for the multilevel generalized assignment problem. Oper Res 54:1172–1184

Chalmet L, Gelders L (1976) Lagrangean relaxation for a generalized assignment type problem. In: Advances in OR. EURO, North Holland, Amsterdam, pp 103–109

Chu EC, Beasley JE (1997) A genetic algorithm for the generalized assignment problem. Comput Oper Res 24:17–23

Cohen R, Katzir L, Raz D (2006) An efficient approximation for the generalized assignment problem. Inf Process Lett 100:162–166

de Farias Jr, Johnson EL, Nemhauser GL (2000) A generalized assignment problem with special ordered sets: a polyhedral approach. Math Program, Ser A 89:187–203

de Farias Jr, Nemhauser GL (2001) A family of inequalities for the generalized assignment polytope. Oper Res Lett 29:49–55

DeMaio A, Roveda C (1971) An all zero-one algorithm for a class of transportation problems. Oper Res 19:1406–1418

Diaz JA, Fernandez E (2001) A tabu search heuristic for the generalized assignment problem. Eur J Oper Res 132:22–38

Drexl A (1991) Scheduling of project networks by job assignment. Manag Sci 37:1590–1602

Dyer M, Frieze A (1992) Probabilistic analysis of the generalised assignment problem. Math Program 55:169–181

Article   MathSciNet   Google Scholar  

Feltl H, Raidl GR (2004) An improved hybrid genetic algorithm for the generalized assignment problem. In: SAC '04; Proceedings of the 2004 ACM symposium on Applied computing. ACM Press, New York, pp 990–995

Chapter   Google Scholar  

Fisher ML, Jaikumar R (1981) A generalized assignment heuristic for vehicle routing. Netw 11:109–124

Fisher ML, Jaikumar R, van Wassenhove LN (1986) A multiplier adjustment method for the generalized assignment problem. Manag Sci 32:1095–1103

Fleischer L, Goemans MX, Mirrokni VS, Sviridenko M (2006) Tight approximation algorithms for maximum general assignment problems. In SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm. ACM Press, New York, pp 611–620

Book   Google Scholar  

Freling R, Romeijn HE, Morales DR, Wagelmans APM (2003) A branch-and-price algorithm for the multiperiod single-sourcing problem. Oper Res 51(6):922–939

French AP, Wilson JM (2002) Heuristic solution methods for the multilevel generalized assignment problem. J Heuristics 8:143–153

French AP, Wilson JM (2007) An lp-based heuristic procedure for the generalized assignment problem with special ordered sets. Comput Oper Res 34:2359–2369

Garey MR, Johnson DS (1990) Computers and Intractability; A Guide to the Theory of NP-Completeness. Freeman, New York

Gavish B, Pirkul H (1991) Algorithms for the multi-resource generalized assignment problem. Manag Sci 37:695–713

Geoffrion AM, Graves GW (1974) Multicommodity distribution system design by benders decomposition. Manag Sci 20(5):822–844

Glover F, Hultz J, Klingman D (1979) Improved computer based planning techniques, part ii. Interfaces 4:17–24

Gottlieb ES, Rao MR (1990) \( (1,k) \) -configuration facets for the generalized assignment problem. Math Program 46(1):53–60

Gottlieb ES, Rao MR (1990) The generalized assignment problem: Valid inequalities and facets. Math Stat 46:31–52

MathSciNet   MATH   Google Scholar  

Guignard M, Rosenwein MB (1989) An improved dual based algorithm for the generalized assignment problem. Oper Res 37(4):658–663

Haddadi S (1999) Lagrangian decomposition based heuristic for the generalized assignment problem. Inf Syst Oper Res 37:392–402

Haddadi S, Ouzia H (2004) Effective algorithm and heuristic for the generalized assignment problem. Eur J Oper Res 153:184–190

Hajri-Gabouj S (2003) A fuzzy genetic multiobjective optimization algorithm for a multilevel generalized assignment problem. IEEE Trans Syst 33:214–224

Janak SL, Taylor MS, Floudas CA, Burka M, Mountziaris TJ (2006) Novel and effective integer optimization approach for the nsf panel-assignment problem: a multiresource and preference-constrained generalized assignment problem. Ind Eng Chem Res 45:258–265

Article   Google Scholar  

Jörnsten K, Nasberg M (1986) A new lagrangian relaxation approach to the generalized assignment problem. Eur J Oper Res 27:313–323

Jörnsten KO, Varbrand P (1990) Relaxation techniques and valid inequalities applied to the generalized assignment problem. Asia-P J Oper Res 7(2):172–189

Klastorin TD (1979) An effective subgradient algorithm for the generalized assignment problem. Comp Oper Res 6:155–164

Klastorin TD (1979) On the maximal covering location problem and the generalized assignment problem. Manag Sci 25(1):107–112

Kogan K, Khmelnitsky E, Ibaraki T (2005) Dynamic generalized assignment problems with stochastic demands and multiple agent task relationships. J Glob Optim 31:17–43

Kogan K, Shtub A, Levit VE (1997) Dgap – the dynamic generalized assignment problem. Ann Oper Res 69:227–239

Kuhn H (1995) A heuristic algorithm for the loading problem in flexible manufacturing systems. Int J Flex Manuf Syst 7:229–254

Laguna M, Kelly JP, Gonzfilez-Velarde JL, Glover F (1995) Tabu search for the multilevel generalized assignment problem. Eur J Oper Res 82:176–189

Lawler E (1976) Combinatorial Optimization: Networks and Matroids. Holt, Rinehart, Winston, New York

MATH   Google Scholar  

Lin BMT, Huang YS, Yu HK (2001) On the variable-depth-search heuristic for the linear-cost generalized assignment problem. Int J Comput Math 77:535–544

Lorena LAN, Narciso MG (1996) Relaxation heuristics for a generalized assignment problem. Eur J Oper Res 91:600–610

Lorena LAN, Narciso MG, Beasley JE (2003) A constructive genetic algorithm for the generalized assignment problem. J Evol Optim

Lourenço HR, Serra D (1998) Adaptive approach heuristics for the generalized assignment problem. Technical Report 288, Department of Economics and Business, Universitat Pompeu Fabra, Barcelona

Lourenço HR, Serra D (2002) Adaptive search heuristics for the generalized assignment problem. Mathw Soft Comput 9(2–3):209–234

Martello S, Toth P (1981) An algorithm for the generalized assignment problem. In: Brans JP (ed) Operational Research '81, 9th IFORS Conference, North-Holland, Amsterdam, pp 589–603

Martello S, Toth P (1990) Knapsack Problems: Algorithms and Computer Implementations. Wiley, New York

Martello S, Toth P (1992) Generalized assignment problems. Lect Notes Comput Sci 650:351–369

MathSciNet   Google Scholar  

Martello S, Toth P (1995) The bottleneck generalized assignment problem. Eur J Oper Res 83:621–638

Mazzola JB, Neebe AW (1988) Bottleneck generalized assignment problems. Eng Costs Prod Econ 14(1):61–65

Mazzola JB, Wilcox SP (2001) Heuristics for the multi-resource generalized assignment problem. Nav Res Logist 48(6):468–483

Monfared MAS, Etemadi M (2006) The impact of energy function structure on solving generalized assignment problem using hopfield neural network. Eur J Oper Res 168:645–654

Morales DR, Romeijn HE (2005) Handbook of Combinatorial Optimization, supplement vol B. In: Du D-Z, Pardalos PM (eds) The Generalized Assignment Problem and extensions. Springer, New York, pp 259–311

Narciso MG, Lorena LAN (1999) Lagrangean/surrogate relaxation for generalized assignment problems. Eur J Oper Res 114:165–177

Nauss RM (2003) Solving the generalized assignment problem: an optimizing and heuristic approach. INFORMS J Comput 15(3):249–266

Nauss RM (2005) The elastic generalized assignment problem. J Oper Res Soc 55:1333–1341

Nowakovski J, Schwarzler W, Triesch E (1999) Using the generalized assignment problem in scheduling the rosat space telescope. Eur J Oper Res 112:531–541

Nutov Z, Beniaminy I, Yuster R (2006) A  \( (1-1/e) \) ‐approximation algorithm for the generalized assignment problem. Oper Res Lett 34:283–288

Park JS, Lim BH, Lee Y (1998) A lagrangian dual-based branch-and-bound algorithm for the generalized multi-assignment problem. Manag Sci 44(12S):271–275

Pigatti A, de Aragao MP, Uchoa E (2005) Stabilized branch-and-cut-and-price for the generalized assignment problem. In: Electronic Notes in Discrete Mathematics, vol 19 of 2nd Brazilian Symposium on Graphs, Algorithms and Combinatorics, pp 385–395,

Osman IH (1995) Heuristics for the generalized assignment problem: simulated annealing and tabu search approaches. OR-Spektrum 17:211–225

Racer M, Amini MM (1994) A robust heuristic for the generalized assignment problem. Ann Oper Res 50(1):487–503

Romeijn HE, Morales DR (2000) A class of greedy algorithms for the generalized assignment problem. Discret Appl Math 103:209–235

Romeijn HE, Morales DR (2001) Generating experimental data for the generalized assignment problem. Oper Res 49(6):866–878

Romeijn HE, Piersma N (2000) A probabilistic feasibility and value analysis of the generalized assignment problem. J Comb Optim 4:325–355

Ronen D (1992) Allocation of trips to trucks operating from a single terminal. Comput Oper Res 19(5):445–451

Ross GT, Soland RM (1975) A branch and bound algorithm for the generalized assignment problem. Math Program 8:91–103

Ross GT, Soland RM (1977) Modeling facility location problems as generalized assignment problems. Manag Sci 24:345–357

Ross GT, Zoltners AA (1979) Weighted assignment models and their application. Manag Sci 25(7):683–696

Savelsbergh M (1997) A branch-and-price algorithm for the generalized assignment problem. Oper Res 45:831–841

Shmoys DB, Tardos E (1993) An approximation algorithm for the generalized assignment problem. Math Program 62:461–474

Shtub A (1989) Modelling group technology cell formation as a generalized assignment problem. Int J Prod Res 27:775–782

Srinivasan V, Thompson GL (1973) An algorithm for assigning uses to sources in a special class of transportation problems. Oper Res 21(1):284–295

Stützle T, Hoos H (1999) The Max-Min Ant System and Local Search for Combinatorial Optimization Problems. In: Voss S, Martello S, Osman IH, Roucairol C (eds) Meta-heuristics; Advances and trends in local search paradigms for optimization. Kluwer, Boston, pp 313–329

Toktas B, Yen JW, Zabinsky ZB (2006) Addressing capacity uncertainty in resource-constrained assignment problems. Comput Oper Res 33:724–745

Trick M (1992) A linear relaxation heuristic for the generalized assignment problem. Nav Res Logist 39:137–151

Trick MA (1994) Scheduling multiple variable-speed machines. Oper Res 42(2):234–248

Wilson JM (1997) A genetic algorithm for the generalised assignment problem. J Oper Res Soc 48:804–809

Wilson JM (2005) An algorithm for the generalized assignment problem with special ordered sets. J Heuristics 11:337–350

Yagiura M, Ibaraki T, Glover F (2004) An ejection chain approach for the generalized assignment problem. INFORMS J Comput 16:133–151

Yagiura M, Ibaraki T, Glover F (2006) A path relinking approach with ejection chains for the generalized assignment problem. Eur J Oper Res 169:548–569

Yagiura M, Yamaguchi T, Ibaraki T (1998) A variable depth search algorithm with branching search for the generalized assignment problem. Optim Method Softw 10:419–441

Yagiura M, Yamaguchi T, Ibaraki T (1999) A variable depth search algorithm for the generalized assignment problem. In: Voss S, Martello S, Osman IH, Roucairol C (eds) Meta-heuristics; Advances and Trends in Local Search paradigms for Optimization, Kluwer, Boston, pp 459–471

Zhang CW, Ong HL (2007) An efficient solution to biobjective generalized assignment problem. Adv Eng Softw 38:50–58

Zimokha VA, Rubinshtein MI (1988) R & d planning and the generalized assignment problem. Autom Remote Control 49:484–492

Download references

Author information

Authors and affiliations.

Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA

O. Erhun Kundakcioglu & Saed Alizamir

You can also search for this author in PubMed   Google Scholar

Editor information

Editors and affiliations.

Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

Christodoulos A. Floudas

Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry.

Kundakcioglu, O.E., Alizamir, S. (2008). Generalized Assignment Problem . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_200

Download citation

DOI : https://doi.org/10.1007/978-0-387-74759-0_200

Publisher Name : Springer, Boston, MA

Print ISBN : 978-0-387-74758-3

Online ISBN : 978-0-387-74759-0

eBook Packages : Mathematics and Statistics Reference Module Computer Science and Engineering

Share this entry

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research

How to Write An Assignment Introduction Like A Pro

Assignments become a crucial part of students’ academic lives as they have to encounter writing assignments daily. Writing an assignment in itself is a big and tough task, but most students face problems in writing an introduction for such assignments. 

An introduction has to be precise and complete to give a brief about your assignment, and there is a fixed word limit for writing an introduction of an assignment. That is why the most searched question about the assignment is 

How To Write An Assignment Introduction!

Table of Contents

If you want to make sure that your assignment’s introduction is eye-catching and précis, then follow the following guidelines on how to write an introduction for an assignment.

What is the Assignment Introduction?

The introduction gives an outline of the whole paper. It is the presentation of key ideas and also the purpose of your work. The introduction tells the readers about what you are going to tell in the assignment. An introduction has its own grading rules as it is counted distinctly from the body.

Significance of Writing Assignment Introduction

First, we need to understand the significance of writing a good introduction to an assignment. So you must have heard that the first impression is the last impression, and an introduction of your assignment works as a first impression for your assignment. 

Thus, if you wish to attract your examiner’s attention or your readers, you should write a good introduction for your assignment. Moreover, the important role of the introduction is to give an overview of the assignment, which helps the reader determine whether they want to read it.

Hence, before writing an assignment, it is very important to understand how to write an introduction of an assignment .

Strategies: How to write an assignment introduction

• A good introduction to the assignment manifests the following strategies –
• It must show the main objective and purpose of the assignment.
• The importance of assignment.
• The purview of the assignment’s study that is what it includes.
• A brief description of the assignment’s content and its organization.

Characteristics of Good Introduction

Before knowing how to write an assignment introduction, the most crucial thing is to know the characteristics of a good introduction. Because then only you can write a good introduction. So following are the essential characteristics of a good introduction-

• A good introduction is written precisely and clearly so that everyone can understand it. In short, there must not be any language errors.
• It must be written while remembering that it should be attention-grabbing so that it can grab the attention of its readers.
• A good introduction always shows the purpose of the study and what the study is about.
• A Good Assignment should be grammatical error free and plagiarism free. It will be a wise decision to take help from AI Content Detector tool like Content at Scale’s AI detector.
• Best Guide on How to Write a Case Study Assignment?
• Useful Guide on How to Submit Assignment on Google Classroom
• Handy Tips on How to Write an Assignment From Scratch

Elements: How to Write Introduction For Assignment

1.   background.

The first thing you have to write in an introduction is a brief background of the study. You have to give an overview of your assignment, what your assignment is about, its impact, and its area of study.

2.   Context in brief

You have to include a gist of the context of your assignment. It helps the readers to get information about the scope of the study in the assignment.

3.   Your Contention

You have to write your stance on the question involved in the statement. It should be limited to one statement. It will help the readers understand your stance on such points and that the assignment is based on such points.

4.   Main points of study

You will write one line on the main points of your study as it will help the readers circumscribe the assignment’s limits.

5.   Definition of the Topic

The most important step in how to write an introduction for an assignment is to write a definition of the topic of the assignment very briefly. So that readers can understand the title of the study at once.

6.   Why are you writing on this topic only

It is always suggested that you write in the introduction of an assignment why you are writing on this topic only.

7.   Outline

Write briefly about the outline or structure of the assignment so that readers can read accordingly, and also it will help you to define the scope of the assignment in short.

However, students often look for how to write assignment pdf. So, below we provide the assignment introduction pdf.

How To Write An Introduction Of An Assignment Pdf

Download this PDF of how to write an introduction on an assignment:

How Long Should An Assignment Introduction Be?

It is true that students find this question while looking for an answer on the assignment’s introduction page. Let’s state that while writing an assignment, the introduction section should not be too long. Furthermore, the context should not be more than a few pages long.

Keep your assignment’s introduction simple and readable. Replace difficult words with simpler ones to fix readability issues (if any). To save time and effort, online paraphrasing tools such as Editpad or Paraphraser can be used to paraphrase text in a simple way.

If you are writing a 2000-word assignment, the introduction should be 200-250 words long.

But if you are writing a 3000-word assignment, the introduction should be 350-400 words long.

Guidelines/Tips On How To Write An Assignment Introduction

• Always start your assignment’s introduction with a broad idea about the topic of the assignment. After giving a broader picture of the study, you have to narrow down the discussion and write the main object of the study.
• Don’t forget to state the significance of your assignment in brief. It is the prominent part of the introduction.
• You have to smartly write about the tasks you are dealing with in the assignment in brief.
• Make sure you use easy and understandable language so that readers don’t find it difficult to understand the introduction; otherwise, they will not read the other parts of the assignment as well.
• Double-check and proofread your assignment introduction to ensure it is free from spelling mistakes and grammar mistakes.

These guidelines are very important in writing a good introduction to your assignment. If you want to be well-versed in writing an assignment introduction, it is mandatory first to be acquainted with these tips and guidelines.

Assignment Introduction Example

For more clarity, you can see the following assignment example;

Is There Any Other Way To Write Or Get An Effective Assignment Introduction?

Yes, there is! 

It has been seen that there are several writers who are confused when it comes to the assignment’s introduction writing. And it is true that they struggle to summarise the broad issue and write an introduction without conducting sufficient research. However, because the subject experts or online assignments help provide experts who are well-versed in the field, they easily write the introduction in minutes.

• The majority of students do not properly understand the English language. The experts who work in the writing industry have years of experience in writing assignments. That is why they always make sure to write an engaging introduction that also seems professional.
• Furthermore, the requirements of the writer are always given priority by the professionals. After that, they write a professional article that will, without a doubt, engage the reader.
• The expert not only helps the student in preparing the assignment’s introduction. They offer their support in completing the entire home task and guarantee that they will get an A+ grade.
• Besides that, the professionals’ support is available 24/7/365/366 days. So you won’t have to worry about coming up with a solution for your writing task.

What Makes A Good Introduction?

As you already know that, the rules are always subject to change, and our perspectives may be different. However, the academic standards for writing an introduction are quite clear. When creating a great introduction for an assignment, you have to make sure some of the points that are given below:

• Motivates the audience.
• Introduces your thesis statement.
• Defines the topic you’re talking about.
• Emphasizes the significance of your topic.
• Highlights the main points you want to discuss.
• Provides your reasoning for approaching your topic.
• Gives a high-level overview of your methodology.
• Provides statistical information and the purpose of your methodology.

Note: Remember that even creative writing tasks require an inspiring introduction that discusses your purpose for writing.

On the other hand, writing an introduction is relatively easy. Some important things must be clear, including:

• Your topic’s importance.
• The goal of your paper.
• An element of explanation.
• A powerful opening hook sentence.
• Include a link to your thesis statement.

Quick recap

To write an engaging assignment introduction, remember to:

• Make their introduction interesting, 
• outline the reasons, 
• make the audience curious about your assignment, 
• and keep the audience guessing.

Experts warn that rephrasing the assignment question or telling everything in the opening like a story synopsis is not a good idea. You must stick to your tutor’s specified word limit for the assignment introduction and write it with a clear, focused approach.

Since the time assignments have become a crucial part of our studies and grades, and the need to learn the concept and structure of assignments has arisen. 

An introduction is the important part of the assignment to grab readers’ attention and tell in brief about the background and information of the assignment. Thus it is very important to learn how to write assignment introductions. The introduction of an assignment should be eye-catching and alluring to capture the audience and make them read the whole assignment.

Frequently Asked Questions

Q1. what are the 3 parts of an introduction paragraph.

Following are the three parts of an introduction:  1. Parts of an introduction 2. The opening statement 3. The supporting sentences 4. The introductory topic sentence.

Q2. What are the key elements of an introduction?

The introduction must have the following responsibilities: 1. Get the audience’s attention 2. Introduce the topic 3. Explain its relevance to the audience 4. State a thesis or purpose 5. Outline the main points.

Q3. How to write introduction for assignment?

A good introduction shows the reader that the essay will provide a relevant answer to the assignment question. As a result, the introduction should link back to the question. That is done by writing a paragraph that deals with all the key content mentioned in the assignment question.

Related Posts

7+ Tips On How To Get Higher Grades In Exams In 2023

How to Write a Research Paper- A guide From Professionals

Browse Course Material

Course info, instructors.

• Prof. Charles Leiserson
• Prof. Erik Demaine

Departments

• Electrical Engineering and Computer Science
• Mathematics

As Taught In

• Algorithms and Data Structures

Learning Resource Types

Introduction to algorithms (sma 5503), assignments.

The problem sets for the course included both exercises and problems that students were asked to solve. Students were required to turn in only the problems but were encouraged to solve the exercises to help master the course material. Many of the exercise questions were taken from the course textbook.

You are leaving MIT OpenCourseWare

Let's start a new assignment project together, Get Exclusive Free Assistance Now!

Need Help? Call Us :

• Assignment Writing Service
• Assignment Editing Service
• Assignment Masters
• Assignment Provider
• Buy Assignment Online
• Do My Assignment
• Assignment Writers
• College Assignment Help
• Essay Writing Service
• Online Essay Help
• Do My Essay
• Write My Essay
• Essay Assignment Help
• Essay Writer
• Essay Typer
• College Essay Help
• Essay Editor
• Types Of Essays
• Expository Essays
• Types Of Expository Essays
• Narrative Essays
• Narrative Essay Examples
• Narrative Essay Hooks
• Narrative Essay Childhood Memory
• Descriptive Essay About An Event
• Types Of Essays In Ielts
• Application Essay
• Argumentative Essay
• Essay Writing
• Essay Types
• Paper Writing Service
• Research Paper Help
• Term Paper Help
• Write My paper
• Paper Editor
• Research Proposal Help
• Thesis Writing Help
• Thesis Statement Help
• Homework Help
• Do My Homework
• Statistics Homework Help
• Physics Homework Help
• Word Problem Solver
• Accounting Homework Help
• Math Homework Help
• Solve my Math Problem
• College Homework Help
• Online Tutoring Service
• Algebra Homework Help
• CPM Homework Help
• Homework Answers
• Lab Report Help
• Pestel Analysis Help
• Business Report Help
• Book Review Help
• Book Report Help
• University Assignment Help
• Capstone Project Help
• Resume Writing Services
• Annotated Bibliography
• Ghostwriter
• Personal Statement Help
• Speech Writer
• Proofreading
• computation assignment help
• dbms assignment help
• microprocessor assignment help
• oracle assignment help
• pascal assignment help
• perl assignment help
• ruby assignment help
• sql assignment help
• uml assignment help
• web designing assignment help
• epidemiology assignment help
• nursing assignment help
• pharmacology assignment help
• psychology assignment help
• brand management assignment help
• construction management assignment help
• customer relationship management
• healthcare management assignment help
• mba assignment help
• myob assignment help
• recruitment assignment help
• strategy analysis assignment help
• pricing strategy assignment help
• business analytics assignment help
• business communication assignment help
• e commerce assignment help
• international finance assignment help
• quantitative analysis assignment help
• engineering mathematics assignment help
• civil engineering assignment help
• transportation assignment
• electronics assignment help
• geotechnical engineering assignment help
• telecommunication assignment help
• biomedical engineering assignment help
• mechanical engineering assignment help
• system analysis and design assignment help
• rationalism assignment help
• religion assignment help
• physics assignment help
• biology assignment help
• botany assignment help
• bioinformatics assignment help
• eviews assignment help
• linear programming assignment help
• minitab assignment help
• probability assignment help
• spss assignment help
• stata assignment help
• android assignment help
• c programing assignment help
• c sharp assignment help
• c plus plus assignment help
• fortran assignment help
• haskell assignment help
• html assignment help
• java assignment help
• python programming assignment help
• sap assignment help
• web programming assignment help
• Taxation Law Aassignment Help
• Constitutional Law Assignment help
• contract law assignment help
• civil law assignment help
• company law assignment help
• property law assignment help
• international law assignment help
• human rights law assignment help
• agriculture assignment help
• anthropology assignment help
• childcare assignment help
• english assignment help
• fashion assignment help
• music assignment help
• How It Works
• Uncategorized

How Do You Write An Introduction to An Assignment? (With Examples of Assignment Introduction)

Whether you’re in school or college, you can’t avoid academic writing. It’s essential to write assignments to complete your course and graduate from it successfully. As a student, you must have discussed your assignments and academic writing projects with your friends, seniors, and mentors. Most assignments aim to gauge students’ knowledge about the subject and how well they express themselves while solving a problem or presenting their ideas and opinions. 

Writing an assignment introduction paves the way of how a reader or a teacher perceives an entire assignment and can be considered a face of an assignment. Our assignment help experts are here to offer you the best tips on how to write an assignment introduction.

How to introduce an assignment?

As they say – well begun is half done. Our assignment writers agree and believe in this adage. Countless times, you must have skipped a video because you didn’t find its first 5 seconds interesting or catchy enough to hold your attention. Or you must have chosen to watch a movie because you liked its trailer. Similarly, an introduction is a bait for your readers to read your assignment, report, essay, or dissertation with interest. It’s the first impression you will cast on your professors.

GoAssignmentHelp assignment assistance experts who handle hundreds of ‘ do my assignment ’ requests every month share that most students find it difficult to write an introductory paragraph that is clear and concise. Here, we will simplify the process of writing an introduction for the given assignment for you.

A good introduction to an assignment example is always one that gives a clear idea to the readers about what your assignment topic is or what are you going to talk about in the rest of the copy. An old trick is to talk about general ideas about the topic and narrow down your discussion to the specific problem or aspect of the topic you are going to discuss.

An introduction is a guide to your assignment. It should include:

• Some background about the assignment topic, and
• An outline of opinions and arguments you are going to present.

An assignment introduction example or two can perhaps give you a better idea of what needs to be done.

Contact our experts for a powerful introduction to your assignment!

Different Elements of the Introduction of an Assignment

Before we delve into introduction assignment examples, you must understand elements that constitute a good introduction to an assignment:

• Importance of an assignment topic or the purpose of essay writing or dissertation writing,
• Keywords from the essay topic or assignment question to show how well you have understood the writing task,
• What is the proper definition of the assignment topic or the key terms it contains – and what can readers expect from the written piece,
• Student’s reason for writing on the topic. You may get some hints on it from what your teacher mentions on the assignment list or what he/she shares in the class about it,
• A quick bird-eye’s view of your approach on the assignment topic,
• Key points of your discussion that you will elaborate in the body of the paper,
• Quick discussion on previous studies, articles, news, or other works on the topic, and
• What are some of the limitations of the topic?

You don’t have to include everything in an introduction – just enough to make your reader or teacher curious about the topic. The following example of introduction for assignment starts with a central issue, goes on to add some background, and then, presents the argument the assignment writer elaborated further in the essay. It ends with a smooth transition statement meant to transport the reader to the next part of the essay.

How to write an introduction for a report?

When you are stuck with how to start a writing assignment, writing an introduction can solve most of your problems. Different types of assignments have different types of introductory paragraphs. The student introduction assignment example mentioned above is suitable for an essay. Now, we will see an example of an assignment introduction for a report.

Note that this kind of assignment introduction contains:

• A Background: A quick mention of previous studies and articles on the topic gives your teachers a perspective on what is already known about the topic, key issues that need to be addressed, and what you are going to discuss in your report.
• An Objective or a Thesis Statement: A hypothesis or a thesis statement is based on earlier findings and previous works on the topic. It provides a structure to your report. Check how the assignment writing service expert has mentioned the purpose of the study and a quick outline of the entailing discussion in one statement – right after the background.
• Importance of the Study: If you’ve not already highlighted the importance of the study yet, you may include a few more lines to mention the gaps in the topic research and how your paper is going to bridge those gaps.

Consult our assignment writers for fresh ideas and introduction samples for any type of assignment!

How to write an introduction for a thesis or a dissertation?

Most students come across a dissertation or a thesis writing task in their Master’s or Ph.D. degree course. A few need to write a dissertation in their Bachelor’s degree programs. But since they are new to dissertation writing, they wonder how to write an introduction for an assignment that is much longer than a normal essay writing task they have encountered yet. The truth is that writing an introduction for a dissertation is not much different from writing an introduction for an essay or a report (depending on the nature of your dissertation topic).

You can use the points mentioned above to learn how to write a good assignment introduction longer than a paragraph. The ideal length for a dissertation introduction is 5-7% of the total length of your research paper. Most Master’s dissertations are around 15,000 to 50,000 words long – depending on the subject area. Hence, their introductions can have anywhere between 750 and 2,500 words.

We provide affordable writing services for students who find it difficult to paraphrase their ideas succinctly in an introduction. Besides the general introduction, we also help students write an introduction for each chapter, which will help you include more references throughout your research paper. It will also help research paper writers to remind their readers of the purpose of the dissertation again and to retain their interest.

You must also read :  Tips and Examples of The Conclusion Section of Assignments

Tips of Top-Rated Experts on How to Start an Assignment

Our essay writers advise students on how to write a good introduction for an assignment all the time. Besides what’s mentioned above, they also advise students to:

• make their introduction eye-catching,
• build up curiosity,
• outline the arguments, and
• maintain suspense.

Experts warn that merely stating the assignment question in other words or trying to state everything in the introduction like a summary of a story is not a good idea at all. You must follow the word limit suggested by your instructor for the assignment introduction and maintain a sharp, focused approach while penning the intro.

Need help with how to start an assignment introduction?

Introduction matters! Whether it’s a superstar or an assignment, the introduction is a key to his/its popularity. GoAssignmentHelp is a leading online assignment help service that brings you the best and most experienced assignment writers from the major cities of Canada, such as Calgary, Edmonton, Montreal, Ottawa, Quebec City, Winnipeg, and more. You can seek help from them for writing the best introduction for your homework , essays , dissertations , thesis , and research papers .

Looking for an assignment introduction sample? Ask our experts!

0 responses on "How Do You Write An Introduction to An Assignment? (With Examples of Assignment Introduction)"

Leave a message cancel reply.

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Recent Posts

• Figurative Language and Its Importance
• A’s and B’s: The True Story Behind The Letter Grades
• How to Write an Article Review: Tips, Outline, Format
• Explanatory Essay Writing Guide
• Poem Analysis Essay Guide: Outline, Template, Structure

Securing Higher Grades is no more expensive!

We can help you boost your grades at best price., get exclusive 20% off.

[email protected] | (+1)617-933-5480

187 Wolf Road, Albany, New York, 12205, USA

100% Secure Payment

We offer assignment writing services in :

• Los Angeles

Disclaimer: Any material such as academic assignments, essays, articles, term and research papers, dissertations, coursework, case studies, PowerPoint presentations, reviews, etc. is solely for referential purposes. We do not encourage plagiarism in any form. We trust that our clients will use the provided material purely as a reference point in their own writing efforts.

GoAssignmentHelp Rated 4.4/5 based on 123 Reviews Copyright © 2010-2024 | www.goassignmenthelp.com | All rights reserved.

Tap to Chat

Get instant assignment help