# Definition of Assignment Model

Personalized homework help for all major subjects.

Order confidently with our risk free, 14-day money-back guarantee.

• ✔️ No sign-up required
• | 🔒 100% Confidential

## Our Expert Writers

We proudly boast a team of expert professionals with verified academic credentials, selected for their proven skills and flexibility through a strict process.

Engage with experts from the top universities across the globe.

## Get Homework Help Instantly

Say goodbye to homework stress! 📚 Just share your details and we’ll whip up an affordable quote in no time – often within 15 minutes.

Let us consider one assignment problem that includes ‘n’ resources for ‘n’ destinations. The objective of finding the solution is to determine the maximization or minimization. It means the maximization of total profit and minimization of total time taken to complete each and every task (‘n’ tasks).

For the formulating of assignment models, following assumptions should be considered:

1. Each resource should be assigned to only one task
2. Each task should be assigned to one resource
• To find out the solution, the available number of resources must be equal to total numbers of tasks to be performed.

Let ijbe any variable then;

Xij        =         (1 if resource I is assigned to task j @0 if resource I is not assigned to task j)

Cij        =          Objective function contribution if resource is assigned to task j

n          =          Number of resources and the number of tasks

Now, As only one job is assigned to one resource then, it can be written as,

ij= 1                   and                  ij= 1

And the total assignment cost is given by,

Z = ijCij

Hence, the mathematical formulation assumes this following form;

Determine ij 0 (i, j = 1, 2, …..n) so as to minimize, Z = ijCij subject to following constraints, i.e.;

ij= 1       where, j = 1, 2, 3, …..n and ij= 0 or 1

Thus,

The general assignment model can be written as,

Maximize or Minimize,

Z = C1111 + C1212 + …………+ C1n1n + C2121 + ………Cnnnsubject to,

11 + 12 + …………+ 1n                 =          1

21 + 22 + …………+ 2n                 =          1

:           :                       :

:           :                       :

n1 + n2 + …………+ nn                 =          1

11 + 21 + …………+ n1                 =          1

12 + 22 + …………+ n2                 =          1

:           :                       :

:           :                       :

1n + 2n + …………+ nn                 =          1

ij= 0 or, 1 for all values of i and j

Students should notice that the variables are restricted to only two values i.e. 0 and 1 for this model. Here, 0 means non-assignment of resources and 1 means assignment of resources. This restriction is different from other Linear Programming (LP) models that we have seen so far.

Theorem 1:

The optimum assignment schedules remain unaltered if we subtract or add ant constant to/ from all the elements of row/ column of the assignment cost matrix.

Theorem 2:

For assignment problems where all Cij 0, the assignment schedule (ij) that satisfy ijCij= 0 should be optimal.

These two theorems mentioned above are the basis of assignment algorithm. If we add/ subtract any suitable constant to/ from the elements of cost matrix, then the new Cij 0 should produce at least one new Cij= 0 at each row and column. And, it should try to make the assignments from these 0 positions. Thus, the assignment schedule becomes optimal if there is only one assignment in each row and column (It means exactly one should be assigned to 0).

Pricing may change based on requirements

l

## FAQ - Frequently Asked Questions

Discover quick answers in our FAQ, covering the most common customer questions about our homework help service.

### Is your homework service confidential?

M
L

Absolutely! Confidentiality is one of the basic guarantees of our service at MyHomeworkHelp.com.

When our customers make their homework orders, they know their information remains 100% confidential.

Even your homework writer will not be provided with your personal details. So, when you hire a professional homework helper on our website, rest assured that your information will remain private and safe.

### Who will help me with my homework?

M
L

We work with subject experts from all over the world. We hire them with the help of complex tests in the disciplines of their expertise. We also verify the IDs and academic transcripts of our homework writers to be sure that our experts have a bachelor's or master’s or a PhD degree. This is how we can be sure of the proficiency of our panel of experts who will help you with your homework.

### Is it legal to ask for help with homework?

M
L

Seeking homework help is perfectly fine and shows your proactive approach to overcoming challenges. But it's important to use our homework service to enhance your understanding, not to replace your own efforts.

Our homework service offers original solutions for personal use, including:

• Generating ideas or arguments for your research.
• Direct citation, with proper referencing.

However, it's crucial to avoid plagiarism by not submitting our work as your own. Make sure to check your institution's academic integrity policies before using our services. Our goal is to support your educational journey in a responsible and beneficial way. Refer our honor code for more details.

### Is myhomeworkhelp.com legit?

M
L

Yes, myhomeworkhelp.com is completely legitimate. We've been successfully connecting students with top experts worldwide since 2012, offering direct, secure communication for a seamless learning experience. With over thousands of students helped and a commitment to innovative, effective education tools, we're dedicated to making learning easier and more accessible for everyone.

You can read our reviews here on Trustpilot and Sitejabber (Independent, verified reviews from buying customers) like you!

### Is there a possibility of plagiarism in my completed order?

M
L

Unlike our competitors who use cheap and ineffective in -house plagiarism software, MyHomeworkHelp.com uses credible software to check your homework solution originality. We guarantee that your paper will pass TurnItIn checks with a low percentage of similarity. In addition, we also check submitted papers for ai-content using Originality.ai.

You will receive a complemantary plagiarism free report with your completed order.

### What makes you one of the best homework help website?

M
L

We are not number 1 (yet!). We're an independent, bootstrapped business standing up to Big EdTech for last 12 years. So it means a lot that folks like you are willing to consider our services for your educational needs.

Myhomework Help is recognized as one of the premier websites for homework answers for three key reasons.

1. Firstly, we pride ourselves on the expertise and qualifications of our tutors/experts, who are selected through a rigorous vetting process to ensure they can provide best academic assistance across a wide range of subjects.
2. Secondly, our response time to student inquiries is fast (as early as few minutes), reflecting our understanding of the importance of timely support in an academic setting.
3. Lastly, we keep our pricing very student friendly. Our aim is to provide the best learning experience to students like yourself without burning a hole in your pockets.