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
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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
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- 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
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One of the most well-known combinatorial optimization problems is the assignment problem . Here's an example: suppose a group of workers needs to perform a set of tasks, and for each worker and task, there is a cost for assigning the worker to the task. The problem is to assign each worker to at most one task, with no two workers performing the same task, while minimizing the total cost.
You can visualize this problem by the graph below, in which there are four workers and four tasks. The edges represent all possible ways to assign workers to tasks. The labels on the edges are the costs of assigning workers to tasks.
An assignment corresponds to a subset of the edges, in which each worker has at most one edge leading out, and no two workers have edges leading to the same task. One possible assignment is shown below.
The total cost of the assignment is 70 + 55 + 95 + 45 = 265 .
The next section shows how solve an assignment problem, using both the MIP solver and the CP-SAT solver.
Other tools for solving assignment problems
OR-Tools also provides a couple of other tools for solving assignment problems, which can be faster than the MIP or CP solvers:
- Linear sum assignment solver
- Minimum cost flow solver
However, these tools can only solve simple types of assignment problems. So for general solvers that can handle a wide variety of problems (and are fast enough for most applications), we recommend the MIP and CP-SAT solvers.
Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4.0 License , and code samples are licensed under the Apache 2.0 License . For details, see the Google Developers Site Policies . Java is a registered trademark of Oracle and/or its affiliates.
Last updated 2023-01-02 UTC.
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Assignment problem
The problem of optimally assigning $ m $ individuals to $ m $ jobs. It can be formulated as a linear programming problem that is a special case of the transport problem :
maximize $ \sum _ {i,j } c _ {ij } x _ {ij } $
$$ \sum _ { j } x _ {ij } = a _ {i} , i = 1 \dots m $$
(origins or supply),
$$ \sum _ { i } x _ {ij } = b _ {j} , j = 1 \dots n $$
(destinations or demand), where $ x _ {ij } \geq 0 $ and $ \sum a _ {i} = \sum b _ {j} $, which is called the balance condition. The assignment problem arises when $ m = n $ and all $ a _ {i} $ and $ b _ {j} $ are $ 1 $.
If all $ a _ {i} $ and $ b _ {j} $ in the transposed problem are integers, then there is an optimal solution for which all $ x _ {ij } $ are integers (Dantzig's theorem on integral solutions of the transport problem).
In the assignment problem, for such a solution $ x _ {ij } $ is either zero or one; $ x _ {ij } = 1 $ means that person $ i $ is assigned to job $ j $; the weight $ c _ {ij } $ is the utility of person $ i $ assigned to job $ j $.
The special structure of the transport problem and the assignment problem makes it possible to use algorithms that are more efficient than the simplex method . Some of these use the Hungarian method (see, e.g., [a5] , [a1] , Chapt. 7), which is based on the KönigâEgervary theorem (see König theorem ), the method of potentials (see [a1] , [a2] ), the out-of-kilter algorithm (see, e.g., [a3] ) or the transportation simplex method.
In turn, the transportation problem is a special case of the network optimization problem.
A totally different assignment problem is the pole assignment problem in control theory.
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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:
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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:
- For each row of the matrix, find the smallest element and subtract it from every element in its row.
- Do the same (as step 1) for all columns.
- Cover all zeros in the matrix using minimum number of horizontal and vertical lines.
- Test for Optimality: If the minimum number of covering lines is n, an optimal assignment is possible and we are finished. Else if lines are lesser than n, we havenât found the optimal assignment, and must proceed to step 5.
- Determine the smallest entry not covered by any line. Subtract this entry from each uncovered row, and then add it to each covered column. Return to step 3.
Try it before moving to see the solution
Explanation for above simple example:
An example that doesn’t lead to optimal value in first attempt: In the above example, the first check for optimality did give us solution. What if we the number covering lines is less than n.
Time complexity : O(n^3), where n is the number of workers and jobs. This is because the algorithm implements the Hungarian algorithm, which is known to have a time complexity of O(n^3).
Space complexity : O(n^2), where n is the number of workers and jobs. This is because the algorithm uses a 2D cost matrix of size n x n to store the costs of assigning each worker to a job, and additional arrays of size n to store the labels, matches, and auxiliary information needed for the algorithm.
In the next post, we will be discussing implementation of the above algorithm. The implementation requires more steps as we need to find minimum number of lines to cover all 0’s using a program. References: http://www.math.harvard.edu/archive/20_spring_05/handouts/assignment_overheads.pdf https://www.youtube.com/watch?v=dQDZNHwuuOY
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Assignment Problem: Linear Programming
The assignment problem is a special type of transportation problem , where the objective is to minimize the cost or time of completing a number of jobs by a number of persons.
In other words, when the problem involves the allocation of n different facilities to n different tasks, it is often termed as an assignment problem.
The model's primary usefulness is for planning. The assignment problem also encompasses an important sub-class of so-called shortest- (or longest-) route models. The assignment model is useful in solving problems such as, assignment of machines to jobs, assignment of salesmen to sales territories, travelling salesman problem, etc.
It may be noted that with n facilities and n jobs, there are n! possible assignments. One way of finding an optimal assignment is to write all the n! possible arrangements, evaluate their total cost, and select the assignment with minimum cost. But, due to heavy computational burden this method is not suitable. This chapter concentrates on an efficient method for solving assignment problems that was developed by a Hungarian mathematician D.Konig.
"A mathematician is a device for turning coffee into theorems." -Paul Erdos
Formulation of an assignment problem
Suppose a company has n persons of different capacities available for performing each different job in the concern, and there are the same number of jobs of different types. One person can be given one and only one job. The objective of this assignment problem is to assign n persons to n jobs, so as to minimize the total assignment cost. The cost matrix for this problem is given below:
The structure of an assignment problem is identical to that of a transportation problem.
To formulate the assignment problem in mathematical programming terms , we define the activity variables as
for i = 1, 2, ..., n and j = 1, 2, ..., n
In the above table, c ij is the cost of performing jth job by ith worker.
Generalized Form of an Assignment Problem
The optimization model is
Minimize c 11 x 11 + c 12 x 12 + ------- + c nn x nn
subject to x i1 + x i2 +..........+ x in = 1 i = 1, 2,......., n x 1j + x 2j +..........+ x nj = 1 j = 1, 2,......., n
x ij = 0 or 1
In Σ Sigma notation
x ij = 0 or 1 for all i and j
An assignment problem can be solved by transportation methods, but due to high degree of degeneracy the usual computational techniques of a transportation problem become very inefficient. Therefore, a special method is available for solving such type of problems in a more efficient way.
Assumptions in Assignment Problem
- Number of jobs is equal to the number of machines or persons.
- Each man or machine is assigned only one job.
- Each man or machine is independently capable of handling any job to be done.
- Assigning criteria is clearly specified (minimizing cost or maximizing profit).
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WHAT IS ASSIGNMENT PROBLEM
Assignment Problem is a special type of linear programming problem where the objective is to minimise the cost or time of completing a number of jobs by a number of persons.
The assignment problem in the general form can be stated as follows:
âGiven n facilities, n jobs and the effectiveness of each facility for each job, the problem is to assign each facility to one and only one job in such a way that the measure of effectiveness is optimised (Maximised or Minimised).â
Several problems of management has a structure identical with the assignment problem.
Example I A manager has four persons (i.e. facilities) available for four separate jobs (i.e. jobs) and the cost of assigning (i.e. effectiveness) each job to each ...
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Generalized Assignment Type Goal Programming Problem: Application to Nurse Scheduling
- Published: July 2001
- Volume 7 , pages 391â413, ( 2001 )
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- Jacques A. Ferland 1 ,
- Ilham Berrada 2 ,
- Imene Nabli 3 ,
- B. Ahiod 4 ,
- Philippe Michelon 5 ,
- Viviane Gascon 6 &
- Ăric GagnĂ© 7 Â
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The notion of the Generalized Assignment Type Goal Programming Problem is introduced to consider the additional side constraints of an Assignment Type problem as goal functions. A short term Tabu Search method together with diversification strategies are used to deal with this model. The methods are tested on real-world Nurse Scheduling Problems.
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Home » Assignment – Types, Examples and Writing Guide
Assignment – Types, Examples and Writing Guide
Table of Contents
Definition:
Assignment is a task given to students by a teacher or professor, usually as a means of assessing their understanding and application of course material. Assignments can take various forms, including essays, research papers, presentations, problem sets, lab reports, and more.
Assignments are typically designed to be completed outside of class time and may require independent research, critical thinking, and analysis. They are often graded and used as a significant component of a student’s overall course grade. The instructions for an assignment usually specify the goals, requirements, and deadlines for completion, and students are expected to meet these criteria to earn a good grade.
History of Assignment
The use of assignments as a tool for teaching and learning has been a part of education for centuries. Following is a brief history of the Assignment.
- Ancient Times: Assignments such as writing exercises, recitations, and memorization tasks were used to reinforce learning.
- Medieval Period : Universities began to develop the concept of the assignment, with students completing essays, commentaries, and translations to demonstrate their knowledge and understanding of the subject matter.
- 19th Century : With the growth of schools and universities, assignments became more widespread and were used to assess student progress and achievement.
- 20th Century: The rise of distance education and online learning led to the further development of assignments as an integral part of the educational process.
- Present Day: Assignments continue to be used in a variety of educational settings and are seen as an effective way to promote student learning and assess student achievement. The nature and format of assignments continue to evolve in response to changing educational needs and technological innovations.
Types of Assignment
Here are some of the most common types of assignments:
An essay is a piece of writing that presents an argument, analysis, or interpretation of a topic or question. It usually consists of an introduction, body paragraphs, and a conclusion.
Essay structure:
- Introduction : introduces the topic and thesis statement
- Body paragraphs : each paragraph presents a different argument or idea, with evidence and analysis to support it
- Conclusion : summarizes the key points and reiterates the thesis statement
Research paper
A research paper involves gathering and analyzing information on a particular topic, and presenting the findings in a well-structured, documented paper. It usually involves conducting original research, collecting data, and presenting it in a clear, organized manner.
Research paper structure:
- Title page : includes the title of the paper, author’s name, date, and institution
- Abstract : summarizes the paper’s main points and conclusions
- Introduction : provides background information on the topic and research question
- Literature review: summarizes previous research on the topic
- Methodology : explains how the research was conducted
- Results : presents the findings of the research
- Discussion : interprets the results and draws conclusions
- Conclusion : summarizes the key findings and implications
A case study involves analyzing a real-life situation, problem or issue, and presenting a solution or recommendations based on the analysis. It often involves extensive research, data analysis, and critical thinking.
Case study structure:
- Introduction : introduces the case study and its purpose
- Background : provides context and background information on the case
- Analysis : examines the key issues and problems in the case
- Solution/recommendations: proposes solutions or recommendations based on the analysis
- Conclusion: Summarize the key points and implications
A lab report is a scientific document that summarizes the results of a laboratory experiment or research project. It typically includes an introduction, methodology, results, discussion, and conclusion.
Lab report structure:
- Title page : includes the title of the experiment, author’s name, date, and institution
- Abstract : summarizes the purpose, methodology, and results of the experiment
- Methods : explains how the experiment was conducted
- Results : presents the findings of the experiment
Presentation
A presentation involves delivering information, data or findings to an audience, often with the use of visual aids such as slides, charts, or diagrams. It requires clear communication skills, good organization, and effective use of technology.
Presentation structure:
- Introduction : introduces the topic and purpose of the presentation
- Body : presents the main points, findings, or data, with the help of visual aids
- Conclusion : summarizes the key points and provides a closing statement
Creative Project
A creative project is an assignment that requires students to produce something original, such as a painting, sculpture, video, or creative writing piece. It allows students to demonstrate their creativity and artistic skills.
Creative project structure:
- Introduction : introduces the project and its purpose
- Body : presents the creative work, with explanations or descriptions as needed
- Conclusion : summarizes the key elements and reflects on the creative process.
Examples of Assignments
Following are Examples of Assignment templates samples:
Essay template:
I. Introduction
- Hook: Grab the reader’s attention with a catchy opening sentence.
- Background: Provide some context or background information on the topic.
- Thesis statement: State the main argument or point of your essay.
II. Body paragraphs
- Topic sentence: Introduce the main idea or argument of the paragraph.
- Evidence: Provide evidence or examples to support your point.
- Analysis: Explain how the evidence supports your argument.
- Transition: Use a transition sentence to lead into the next paragraph.
III. Conclusion
- Restate thesis: Summarize your main argument or point.
- Review key points: Summarize the main points you made in your essay.
- Concluding thoughts: End with a final thought or call to action.
Research paper template:
I. Title page
- Title: Give your paper a descriptive title.
- Author: Include your name and institutional affiliation.
- Date: Provide the date the paper was submitted.
II. Abstract
- Background: Summarize the background and purpose of your research.
- Methodology: Describe the methods you used to conduct your research.
- Results: Summarize the main findings of your research.
- Conclusion: Provide a brief summary of the implications and conclusions of your research.
III. Introduction
- Background: Provide some background information on the topic.
- Research question: State your research question or hypothesis.
- Purpose: Explain the purpose of your research.
IV. Literature review
- Background: Summarize previous research on the topic.
- Gaps in research: Identify gaps or areas that need further research.
V. Methodology
- Participants: Describe the participants in your study.
- Procedure: Explain the procedure you used to conduct your research.
- Measures: Describe the measures you used to collect data.
VI. Results
- Quantitative results: Summarize the quantitative data you collected.
- Qualitative results: Summarize the qualitative data you collected.
VII. Discussion
- Interpretation: Interpret the results and explain what they mean.
- Implications: Discuss the implications of your research.
- Limitations: Identify any limitations or weaknesses of your research.
VIII. Conclusion
- Review key points: Summarize the main points you made in your paper.
Case study template:
- Background: Provide background information on the case.
- Research question: State the research question or problem you are examining.
- Purpose: Explain the purpose of the case study.
II. Analysis
- Problem: Identify the main problem or issue in the case.
- Factors: Describe the factors that contributed to the problem.
- Alternative solutions: Describe potential solutions to the problem.
III. Solution/recommendations
- Proposed solution: Describe the solution you are proposing.
- Rationale: Explain why this solution is the best one.
- Implementation: Describe how the solution can be implemented.
IV. Conclusion
- Summary: Summarize the main points of your case study.
Lab report template:
- Title: Give your report a descriptive title.
- Date: Provide the date the report was submitted.
- Background: Summarize the background and purpose of the experiment.
- Methodology: Describe the methods you used to conduct the experiment.
- Results: Summarize the main findings of the experiment.
- Conclusion: Provide a brief summary of the implications and conclusions
- Background: Provide some background information on the experiment.
- Hypothesis: State your hypothesis or research question.
- Purpose: Explain the purpose of the experiment.
IV. Materials and methods
- Materials: List the materials and equipment used in the experiment.
- Procedure: Describe the procedure you followed to conduct the experiment.
- Data: Present the data you collected in tables or graphs.
- Analysis: Analyze the data and describe the patterns or trends you observed.
VI. Discussion
- Implications: Discuss the implications of your findings.
- Limitations: Identify any limitations or weaknesses of the experiment.
VII. Conclusion
- Restate hypothesis: Summarize your hypothesis or research question.
- Review key points: Summarize the main points you made in your report.
Presentation template:
- Attention grabber: Grab the audience’s attention with a catchy opening.
- Purpose: Explain the purpose of your presentation.
- Overview: Provide an overview of what you will cover in your presentation.
II. Main points
- Main point 1: Present the first main point of your presentation.
- Supporting details: Provide supporting details or evidence to support your point.
- Main point 2: Present the second main point of your presentation.
- Main point 3: Present the third main point of your presentation.
- Summary: Summarize the main points of your presentation.
- Call to action: End with a final thought or call to action.
Creative writing template:
- Setting: Describe the setting of your story.
- Characters: Introduce the main characters of your story.
- Rising action: Introduce the conflict or problem in your story.
- Climax: Present the most intense moment of the story.
- Falling action: Resolve the conflict or problem in your story.
- Resolution: Describe how the conflict or problem was resolved.
- Final thoughts: End with a final thought or reflection on the story.
How to Write Assignment
Here is a general guide on how to write an assignment:
- Understand the assignment prompt: Before you begin writing, make sure you understand what the assignment requires. Read the prompt carefully and make note of any specific requirements or guidelines.
- Research and gather information: Depending on the type of assignment, you may need to do research to gather information to support your argument or points. Use credible sources such as academic journals, books, and reputable websites.
- Organize your ideas : Once you have gathered all the necessary information, organize your ideas into a clear and logical structure. Consider creating an outline or diagram to help you visualize your ideas.
- Write a draft: Begin writing your assignment using your organized ideas and research. Don’t worry too much about grammar or sentence structure at this point; the goal is to get your thoughts down on paper.
- Revise and edit: After you have written a draft, revise and edit your work. Make sure your ideas are presented in a clear and concise manner, and that your sentences and paragraphs flow smoothly.
- Proofread: Finally, proofread your work for spelling, grammar, and punctuation errors. It’s a good idea to have someone else read over your assignment as well to catch any mistakes you may have missed.
- Submit your assignment : Once you are satisfied with your work, submit your assignment according to the instructions provided by your instructor or professor.
Applications of Assignment
Assignments have many applications across different fields and industries. Here are a few examples:
- Education : Assignments are a common tool used in education to help students learn and demonstrate their knowledge. They can be used to assess a student’s understanding of a particular topic, to develop critical thinking skills, and to improve writing and research abilities.
- Business : Assignments can be used in the business world to assess employee skills, to evaluate job performance, and to provide training opportunities. They can also be used to develop business plans, marketing strategies, and financial projections.
- Journalism : Assignments are often used in journalism to produce news articles, features, and investigative reports. Journalists may be assigned to cover a particular event or topic, or to research and write a story on a specific subject.
- Research : Assignments can be used in research to collect and analyze data, to conduct experiments, and to present findings in written or oral form. Researchers may be assigned to conduct research on a specific topic, to write a research paper, or to present their findings at a conference or seminar.
- Government : Assignments can be used in government to develop policy proposals, to conduct research, and to analyze data. Government officials may be assigned to work on a specific project or to conduct research on a particular topic.
- Non-profit organizations: Assignments can be used in non-profit organizations to develop fundraising strategies, to plan events, and to conduct research. Volunteers may be assigned to work on a specific project or to help with a particular task.
Purpose of Assignment
The purpose of an assignment varies depending on the context in which it is given. However, some common purposes of assignments include:
- Assessing learning: Assignments are often used to assess a student’s understanding of a particular topic or concept. This allows educators to determine if a student has mastered the material or if they need additional support.
- Developing skills: Assignments can be used to develop a wide range of skills, such as critical thinking, problem-solving, research, and communication. Assignments that require students to analyze and synthesize information can help to build these skills.
- Encouraging creativity: Assignments can be designed to encourage students to be creative and think outside the box. This can help to foster innovation and original thinking.
- Providing feedback : Assignments provide an opportunity for teachers to provide feedback to students on their progress and performance. Feedback can help students to understand where they need to improve and to develop a growth mindset.
- Meeting learning objectives : Assignments can be designed to help students meet specific learning objectives or outcomes. For example, a writing assignment may be designed to help students improve their writing skills, while a research assignment may be designed to help students develop their research skills.
When to write Assignment
Assignments are typically given by instructors or professors as part of a course or academic program. The timing of when to write an assignment will depend on the specific requirements of the course or program, but in general, assignments should be completed within the timeframe specified by the instructor or program guidelines.
It is important to begin working on assignments as soon as possible to ensure enough time for research, writing, and revisions. Waiting until the last minute can result in rushed work and lower quality output.
It is also important to prioritize assignments based on their due dates and the amount of work required. This will help to manage time effectively and ensure that all assignments are completed on time.
In addition to assignments given by instructors or professors, there may be other situations where writing an assignment is necessary. For example, in the workplace, assignments may be given to complete a specific project or task. In these situations, it is important to establish clear deadlines and expectations to ensure that the assignment is completed on time and to a high standard.
Characteristics of Assignment
Here are some common characteristics of assignments:
- Purpose : Assignments have a specific purpose, such as assessing knowledge or developing skills. They are designed to help students learn and achieve specific learning objectives.
- Requirements: Assignments have specific requirements that must be met, such as a word count, format, or specific content. These requirements are usually provided by the instructor or professor.
- Deadline: Assignments have a specific deadline for completion, which is usually set by the instructor or professor. It is important to meet the deadline to avoid penalties or lower grades.
- Individual or group work: Assignments can be completed individually or as part of a group. Group assignments may require collaboration and communication with other group members.
- Feedback : Assignments provide an opportunity for feedback from the instructor or professor. This feedback can help students to identify areas of improvement and to develop their skills.
- Academic integrity: Assignments require academic integrity, which means that students must submit original work and avoid plagiarism. This includes citing sources properly and following ethical guidelines.
- Learning outcomes : Assignments are designed to help students achieve specific learning outcomes. These outcomes are usually related to the course objectives and may include developing critical thinking skills, writing abilities, or subject-specific knowledge.
Advantages of Assignment
There are several advantages of assignment, including:
- Helps in learning: Assignments help students to reinforce their learning and understanding of a particular topic. By completing assignments, students get to apply the concepts learned in class, which helps them to better understand and retain the information.
- Develops critical thinking skills: Assignments often require students to think critically and analyze information in order to come up with a solution or answer. This helps to develop their critical thinking skills, which are important for success in many areas of life.
- Encourages creativity: Assignments that require students to create something, such as a piece of writing or a project, can encourage creativity and innovation. This can help students to develop new ideas and perspectives, which can be beneficial in many areas of life.
- Builds time-management skills: Assignments often come with deadlines, which can help students to develop time-management skills. Learning how to manage time effectively is an important skill that can help students to succeed in many areas of life.
- Provides feedback: Assignments provide an opportunity for students to receive feedback on their work. This feedback can help students to identify areas where they need to improve and can help them to grow and develop.
Limitations of Assignment
There are also some limitations of assignments that should be considered, including:
- Limited scope: Assignments are often limited in scope, and may not provide a comprehensive understanding of a particular topic. They may only cover a specific aspect of a topic, and may not provide a full picture of the subject matter.
- Lack of engagement: Some assignments may not engage students in the learning process, particularly if they are repetitive or not challenging enough. This can lead to a lack of motivation and interest in the subject matter.
- Time-consuming: Assignments can be time-consuming, particularly if they require a lot of research or writing. This can be a disadvantage for students who have other commitments, such as work or extracurricular activities.
- Unreliable assessment: The assessment of assignments can be subjective and may not always accurately reflect a student’s understanding or abilities. The grading may be influenced by factors such as the instructor’s personal biases or the student’s writing style.
- Lack of feedback : Although assignments can provide feedback, this feedback may not always be detailed or useful. Instructors may not have the time or resources to provide detailed feedback on every assignment, which can limit the value of the feedback that students receive.
About the author
Muhammad Hassan
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The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment.
The problem is to assign each worker to at most one task, with no two workers performing the same task, while minimizing the total cost. Since there are more workers than tasks, one worker will not be assigned a task. MIP solution. The following sections describe how to solve the problem using the MPSolver wrapper. Import the libraries
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 ...
In an assignment problem, we must find a maximum matching that has the minimum weight in a weighted bipartite graph. The Assignment problem. Problem description: ... We can exploit the structure to improve the performance of the Simplex Algorithm for some special type of problem. Some specially adapted Simplex Algorithms: ...
Step 3. Cover all the zeros of the matrix with the minimum number of horizontal or vertical lines. Step 4. Since the minimal number of lines is 3, an optimal assignment of zeros is possible and we are finished. Since the total cost for this assignment is 0, it must be. Step 3.
The total cost of the assignment is 70 + 55 + 95 + 45 = 265. The next section shows how solve an assignment problem, using both the MIP solver and the CP-SAT solver. Other tools for solving assignment problems. OR-Tools also provides a couple of other tools for solving assignment problems, which can be faster than the MIP or CP solvers:
First, we give a detailed review of two algorithms that solve the minimization case of the assignment problem, the Bertsekas auction algorithm and the Goldberg & Kennedy algorithm. It was previously alluded that both algorithms are equivalent. We give a detailed proof that these algorithms are equivalent. Also, we perform experimental results comparing the performance of three algorithms for ...
The assignment problem is one of the special type of transportation problem for which more efficient (less-time consuming) solution method has been devised by KUHN (1956) and FLOOD (1956). The justification of the steps leading to the solution is based on theorems proved by Hungarian mathematicians KONEIG (1950) and EGERVARY (1953), hence the ...
The assignment problem arises when $ m = n $ and all $ a _ {i} $ and $ b _ {j} $ are $ 1 $. If all $ a _ {i} $ and $ b _ {j} $ in the transposed problem are integers, then there is an optimal solution for which all $ x _ {ij } $ are integers (Dantzig's theorem on integral solutions of the transport problem). In the assignment problem, for such ...
Assignment problems involve optimally matching the elements of two or more sets, where the dimension of the problem refers to the number of sets of elements to be matched. ... One type of problem that allows or requires assigning the same agent to more than one task, the multiple bottleneck assignment problem [2], was discussed in Section 2.10 ...
This problem is called the generalized assignment problem with special ordered sets of type 2 (GAPS2). In other words, GAPS2 is the problem of allocating tasks to time-periods, where each task must be assigned to a time-period, or shared between two consecutive time-periods.
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 ...
The generalized assignment problem is an assignment problem (15.7) with the complicating constraint that the jobs j assigned to each resource i satisfy ... We call this latter type of problem a constraint-satisfaction problem. A prominent member of this class involves assigning values to variables subject to constraints.
Time complexity : O(n^3), where n is the number of workers and jobs. This is because the algorithm implements the Hungarian algorithm, which is known to have a time complexity of O(n^3). Space complexity : O(n^2), where n is the number of workers and jobs.This is because the algorithm uses a 2D cost matrix of size n x n to store the costs of assigning each worker to a job, and additional ...
The assignment problem is a special type of transportation problem, where the objective is to minimize the cost or time of completing a number of jobs by a number of persons.. In other words, when the problem involves the allocation of n different facilities to n different tasks, it is often termed as an assignment problem.
The Assignment Problem is a special type of Linear Programming Problem based on the following assumptions: However, solving this task for increasing number of jobs and/or resources calls forâŠ
ASSIGNMENT PROBLEM Introduction: Assignment Problem is a special type of linear programming problem where the objective is to minimise the cost or time of completing a number of jobs by a number of persons. The assignment problem in the general form can be stated as follows:
Assignment Problem is a special type of linear programming problem where the objective is to minimise the cost or time of completing a number of jobs by a number of persons. The assignment problem in the general form can be stated as follows: "Given n facilities, n jobs and the effectiveness of each facility for each job, the problem is to ...
solving an assignment problem. It is shorter and easier compared to any method of finding the optimal solution of a transportation problem. In this unit, we discuss various types of assignment problems, including travelling salesman problem and apply the Hungarian method for solving these problems.
The organization of this paper is given as follows: Section 2 discusses the definition and the mathematical formulation of general assignment problem. Next, the types of assignment problem within the education domain, along with their approaches, are presented in Section 3. In fact, this section is divided into subsections that elaborate in ...
The notion of the Generalized Assignment Type Goal Programming Problem is introduced to consider the additional side constraints of an Assignment Type problem as goal functions. A short term Tabu Search method together with diversification strategies are used to deal with this model. The methods are tested on real-world Nurse Scheduling Problems.
An Assignment Problem is a special type of Transportation Problem in Operational Research that deals with assigning n origins (workers or instances) to n destinations (jobs or machines). The goal of the assignment problem is to determine the minimum cost of the assignment.
Assignment is a task given to students by a teacher or professor, usually as a means of assessing their understanding and application of course material. Assignments can take various forms, including essays, research papers, presentations, problem sets, lab reports, and more. Assignments are typically designed to be completed outside of class ...
Proposal of solutions: Unlike other types of writing that may focus solely on analysis, problem solution essays require the writer to propose practical methods to address the identified challenge. Logical structure: It typically follows a logical problem solution essay structure, progressing from identifying the difficulty to offering the ways ...