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The Assignment Model

The linear programming formulation of the assignment model is similar to the formulation of the transportation model, except all the supply values for each source equal one, and all the demand values at each destination equal one. Thus, our example is formulated as follows :

This is a balanced assignment model. An unbalanced model exists when supply exceeds demand or demand exceeds supply.

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Assignment Model | Linear Programming Problem (LPP) | Introduction

What is assignment model.

→ Assignment model is a special application of Linear Programming Problem (LPP) , in which the main objective is to assign the work or task to a group of individuals such that;

i) There is only one assignment.

ii) All the assignments should be done in such a way that the overall cost is minimized (or profit is maximized, incase of maximization).

→ In assignment problem, the cost of performing each task by each individual is known. → It is desired to find out the best assignments, such that overall cost of assigning the work is minimized.

For example:

Suppose there are 'n' tasks, which are required to be performed using 'n' resources.

The cost of performing each task by each resource is also known (shown in cells of matrix)

• 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

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Education Lessons

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Home Blog Education How to Present a Lesson Plan

How to Present a Lesson Plan

First days are always exciting, and expectation builds up about the contents of the task ahead, especially if you’re starting a class as a student or professor. This interaction will be significant because it will establish and define the subjects to be covered and the set of expectations flowing from the instructor towards the audience. 

Perhaps you are ready to begin your career as a teacher and need some guidance; otherwise, you are a seasoned instructor searching for a refresher in your program. No matter which of the above you represent, the truth of the matter is that you are probably seeking a better way to introduce the subjects you’ll be teaching to your students. 

What is a lesson plan? 

A lesson plan will be the set of subject matter materials you will be teaching during a specific timeframe. The lesson plan should be an index that students can constantly consult to understand better the parts of the learning journey they will go through during each session. 

Teachers and professors should have a lesson plan template that happens in every session. This is different from a syllabus because, in the latter case, the whole curriculum of the program will be laid out; however, for each lesson, there should be one individual lesson plan example to guide the instructor in the set timeframe. 

When building the materials for the class or lesson’s attention, it’s always essential to share elements like the purpose or rules that guide the learning process . This article will explore the best way to present a lesson plan and drive a learning session successfully from the instructor or professor’s view. 

How to write a lesson plan 

Education nowadays guides different sorts of students and target specific learning needs. Therefore, it’s important and relevant to understand how lesson plans can change and be varied to truly implement the best learning path for your students. Once you have this part figured out, the next step is to understand how you will transmit the information and use a PowerPoint Presentation to simplify creating and presenting a lesson plan to your students. 

Lesson plans will comprise several different sections that will clarify the first questions students can have: How long will the course be? Will it be an online course ? What will be the main objectives? Which subjects will be discussed along with the class? 

1. Introduction 

As the lesson begins, it’s essential to place a brief yet descriptive introduction about what the session will cover. A good practice is to create a catchy title for each lesson to have an overall understanding of the information they will be receiving.

Example: Digital Marketing Basics: Industry background, historical review years 1980-2010. In this session, we will cover the birth of digital marketing, including all the touchpoints that shaped today’s industry. 

2. Audience

If your class is a one-time-only or recurring session, or even a blended learning journey, it’s essential to explain to your students who this class is for; this will allow them to calibrate their expectations about the matter to be taught ahead. 

Example: This lesson is directed to professionals who work in traditional marketing, business owners, or communication specialists seeking to have a profound understanding of how digital marketing came to be. 

3. Lesson Objectives 

This piece is critical because it will allow the students to assess the intention of each lesson. When thinking about the objectives, it’s vital to consider the acquired skills we expect our students to have at the end of the class. Like any other goals in life or business, each one should be actionable and measurable, meaning after each class, students should be able to use what they have learned and put into action the concepts. 

Example : Understand and be able to create a timeline framework of reference to explain the story of the Internet.

4. Materials 

Suppose the lesson requires using any specific materials, physical or not, including any software or hardware necessary. In that case, it´s important to list or include within the lesson plan so students can set clear expectations on what they might require. This is particularly important if the session you will be delivering requires them beforehand to bring anything. 

Example : 

• Computer 
• Scratch paper 

5. Learning Activities 

We´ve covered all the logistics by this point; however, now we need to start sharing the actual activities during the lesson. Ideally, this is a play-by-play of how each activity will guide the lesson towards the already established objectives. To add the list of learning activities that will be helpful for your students, take into account how all of them align with each goal and the requirements students need. 

Make sure that you add variety to the activities that you are proposing, go ahead and research trends of how many other teachers or professors, students will appreciate your search to engage them in learning. 

Also, consider how much time they will take so that you can note it in the next section. 

• Create a timeline on the wall with the most important moments of digital marketing history, including creation of social media, mainstream of email, etc.

Time periods

Pairing each learning activity with a specific timeframe will be useful both for instructors and students. Make sure you calculate a reasonable amount of time for each activity and list it within the lesson plan so everyone can set correct expectations. Assigning time slots for each exercise will also help students and teachers stay on track with the lesson and not waste valuable time invested in learning.

Example : Creation of a timeline – 45 min

How to present a lesson plan 

We have now listed the components of the lesson plan structure, everything looks beautiful in the draft, but now we need to start planning how we will present the program to the students. This part is challenging because you have to choose a template that makes sense for you and will be helpful for your students to understand.

A PowerPoint presentation is a great way to showcase all the contents of the lesson plan, however, the trick is to decide how you want to structure it.

Lesson Plan Design

By this point, you’ve structured a lesson plan template that can go through any test. Nevertheless, creating the materials to accompany it can be a key in the commitment generates between the students and the professor.

Design and Style

Before adding any text to your presentation template , think about the requirements you have: Does the academic institution where you work require the use of logos? Do you have to follow any visual guidelines? This might be important for the cohesiveness of your presentation.

It’s essential to think about how you would like to present the lesson plan. You may want to keep it simple and have a 1 pager and talk through it to understand your students fully, or perhaps you need to create one full presentation where every slide will be a relevant piece of information. Let’s explore this a bit further. 

One Pager Lesson Plan 

If your style is more towards simplicity, this is a great solution: succinct, minimalistic, and straight to the point. You can complete a one-page lesson plan with bullets of the relevant data and send it out to students. A great advantage of this format is that you can either send it as a PDF or even as a single image (JPG or PNG), exporting it directly from PowerPoint. 

One significant advantage is that your students will only have to check for one source by choosing this simple format when revising the lesson during the class or afterward. 

Several pages lesson plan 

Almost like a syllabus, a more extended presentation will include several slides so you can include the information in different formats. 

For example, you can use the first slide to include the lesson title; afterward, a new slide can define the purpose or introduction of the lesson. In the upcoming slides, you can include materials, contents, and even ad charts or similar to explain how grades will be affected by each lesson’s assignments on the upcoming slides. 

Text in the presentation 

It’s always good to follow the reliable practices of presentations and include the necessary information without overwhelming students. Don’t add an excessive amount of text to one slide; actually, make sure that every piece of data is helpful for students to plan their time both during and after class. 

However, if you will be sending out the presentation to your students before reviewing it, consider that they will be using it for their reference to follow through with your lesson. So make sure all the information is easy to read and accessible. 

Additional elements 

Learners of all sorts have become increasingly visual, so don’t be afraid to add infographics, images, photographs, icons or any other elements to make your lesson plan presentation more appealing visually. 

Final Words 

Remember the lesson plan presentation will be the first approach your students will have with the subject matter. Take your time, enjoy the process, and create comprehensive and attractive lesson plan slides that will inspire your students to have thoughtful and deep learning. 

1. 1-Slide Lesson Plan PowerPoint Template

Create a simple and minimalist one-pager lesson plan for your academic uses, course planning, and even as student handouts, with this eye-catching PowerPoint template. 

Use This Template

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Bus 480 – Lecture 2 Transportation and Assignment models

Mar 12, 2019

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Bus 480 – Lecture 2 Transportation and Assignment models. Transportation Model. Product is transported from location to location minimum cost Each source able to supply a fixed number of units Each destination has a demand for a fixed number of units

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• minimum cost
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Bus 480 – Lecture 2Transportation and Assignment models

Transportation Model • Product is transported from location to location minimum cost • Each source able to supply a fixed number of units • Each destination has a demand for a fixed number of units • Can have multiple solutions, but the same minimum cost

Transportation Model • Let Xij = amount of product from point i to point j • We will minimize cost • The constraints will be the amount that is shipped out of point i to point j • Supply Constraints • Demand Constraints • Each row will be its own constraint • Each column will be its own constraint

Example #4 • Each cell represents the cost of shipping one unit from site i to site j • The cost of sending one unit of product from site A to site 1 is $6 • Site 1 has a demand of 80 units • Site A can supply 130 units

Example #4 Let XA1=amount shipped from site A to site 1 XA2=amount shipped from site A to site 2 XA3=amount shipped from site A to site 3 XB1=amount shipped from site B to site 1 XB2=amount shipped from site B to site 2 XB3=amount shipped from site B to site 3 XC1=amount shipped from site C to site 1 XC2=amount shipped from site C to site 2 XC3=amount shipped from site C to site 3

Demand/Supply Check • Check to see if total supply equals total demand. • If yes, then constraints are equality • If no, then if supply > demand then supply constraints are <= and demand is = • if supply < demand then supply constraints are = and demand is <=

Example 4 • Total demand : 80 + 110 + 60 = 250 • Total supply : 130 + 70 + 100 = 300 • Supply is greater than demand. • Cannot ship more product than is demanded • Supply constraints will be <= • Can meet all the demand • Demand constraints will be =

Example 4 • Objective Function • Min 6XA1 + 9XA2 + 11XA3 + 12XB1 + 3XB2 + 5XB3 + 4XC1 + 8XC2 + 11XC3 • Note the structure. It’s the same as the table

Example 4 • Supply Constraints XA1 + XA2 + XA3 ≤ 130 XB1 + XB2 + XB3 ≤ 70 XC1 + XC2 + XC3 ≤ 100 Why are the signs ≤ ? • Demand Constraints XA1 + XB1 + XC1 = 80 XA2 + XB2 + XC2 = 110 XA3 + XB3 + XC3 = 60 Why are the signs =?

Example 4 Hint : Copy the table twice. Once for the decision variables and one for costs Each row will be a sum. Each column will be a sum. Objective function will be sumproduct

Example 4 - Solution Site A : Ship 80 units to site 2 Site B : Ship 10 units to site 2 and 60 units to site 3 Site C : Ship 80 units to site 1 and 20 units to site 2 Minimum cost = $1530 Check All constraints to verify the results

Transshipment Problems • Have intermediate sites • If an intermediate site cannot hold product then everything going into the site must equal that going out of the site • Still have supply and demand constraints • One extra constraint for each site

A F D B G E C H Transshipment Diagram • Site D and E are intermediary Sites • Sites A, B, C are supply sites • Sites F, G, H are demand sites

Transshipment Constraints • Everything going into site d must equal everything leaving site d Xad + Xbd + Xcd = Xdf + Xdg + Xdh • In Excel, move all variables to the left side of the equation Xad + Xbd + Xcd - Xdf - Xdg - Xdh = 0

Example 41 • Ship from European port to US port • Once product gets to US port, it is immediately shipped to the inland port • This makes the transshipment constraints=0 • If the port can hold product, then 0 will change to the amount of product the port can hold, typically ≤ . Why?

Example 41- Solution

Example 41- Solution Cost function is the addition of multiple sumproducts

Assignment Problem • Set up identical the transportation problem • All constraints are equal to 1 • Xij will be binary = 1 if selected, 0 otherwise

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Transportation Systems Analysis pp 259–347 Cite as

Basic Static Assignment to Transportation Networks

• Ennio Cascetta 2  
• First Online: 01 January 2009

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 29))

Traffic assignment models simulate the interaction of demand and supply on a transportation network. These models allow calculation of performance measures and user flows for each supply element (network link), resulting from origin–destination (O-D) demand flows, path choice behavior, and the mutual interactions between supply and demand.

• Assignment Model
• User Equilibrium
• Short Path Tree
• Stochastic User Equilibrium

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