The document discusses the assignment problem and provides examples of solving it using different methods. It can be summarized as:
1) The assignment problem involves allocating tasks or jobs to workers or machines in the most efficient way, often to minimize costs. It has special characteristics as each job can only be assigned to one worker.
2) The document provides examples of solving assignment problems using methods like the least cost method, stepping stone method, and the Hungarian method.
3) It also discusses how to model assignment problems as transportation problems and how to solve maximization versions by converting to minimization problems.
This presentation covers the problems and solutions of North West Corner Method, Least cost Method and Vogels Approximation Method in Transportation Problem
The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized.
This presentation covers the problems and solutions of North West Corner Method, Least cost Method and Vogels Approximation Method in Transportation Problem
The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized.
This is a special type of LPP in which the objective function is to find the optimum allocation of a number of tasks (jobs) to an equal number of facilities (persons). Here we make the assumption that each person can perform each job but with varying degree of efficiency. For example, a departmental head may have 4 persons available for assignment and 4 jobs to fill. Then his interest is to find the best assignment which will be in the best interest of the department.
this ppt is helpful for BBA/B.tech//MBA/M.tech students.
the ppt is on simulation topic...its covers -
Meaning
Advantages & Disadvantages
Uses
Process
Monte Carlo SImulation
Advantages & Disadvantages
Its example
Assignment Chapter - Q & A Compilation by Niraj ThapaCA Niraj Thapa
My name is Niraj Thapa. I have compiled Assignment Chapter including SM, PM & Exam Questions of AMA.
You feedback on this will be valuable inputs for me to proceed further.
This is a special type of LPP in which the objective function is to find the optimum allocation of a number of tasks (jobs) to an equal number of facilities (persons). Here we make the assumption that each person can perform each job but with varying degree of efficiency. For example, a departmental head may have 4 persons available for assignment and 4 jobs to fill. Then his interest is to find the best assignment which will be in the best interest of the department.
this ppt is helpful for BBA/B.tech//MBA/M.tech students.
the ppt is on simulation topic...its covers -
Meaning
Advantages & Disadvantages
Uses
Process
Monte Carlo SImulation
Advantages & Disadvantages
Its example
Assignment Chapter - Q & A Compilation by Niraj ThapaCA Niraj Thapa
My name is Niraj Thapa. I have compiled Assignment Chapter including SM, PM & Exam Questions of AMA.
You feedback on this will be valuable inputs for me to proceed further.
Since a feasible solution exists only for balanced problem, it is necessary that the total availability be made equal to the total demand. To solve an unbalanced transportation problem, first of all it is converted into balance transportation problem by introducing a fictitious origin or destination which will provide the surplus supply or demand
A.Consider the transportation problem where costs are to be minimi.docxransayo
A.Consider the transportation problem where costs are to be minimized from locations (rows) 1, 2 and 3 to destinations (columns) A, B, C, and D according to the following cost and requirements table, where M is a very large number:
Destination
A
B C D
Supply
Location 1
9
8 6 7
25
2
M
9 15 8
15
3
6
12 10 M
10
Demand:
5
20 15 10
Solve for the optimal solution using the transportation simplex method and the northwest corner rule to obtain an initial basic feasible solution. Be sure to identify the shipping assignments and compute total shipping costs for your solution. (15 points)
B.Consider the following network problem:
O
T
5
8
3
4
8
5
8
7
6
4
3
6
7
5
4
3
6
5
4
8
3
5
6
5
9
7
a. Display the final solution and compute the shortest path.
(5 points)
O
T
5
8
3
4
8
5
8
7
6
4
3
6
7
5
4
3
6
5
4
8
3
5
6
5
9
7
b. If the arc values represent distances, find the minimal spanning tree that would connect all the nodes. (Disregard the arc direction.) Display the final solution and compute the distance of the minimal spanning tree.
(5 points)
O
T
5
8
3
4
8
5
8
7
6
4
3
6
7
5
4
3
6
5
4
8
3
5
6
5
9
7
c. If the arc values represent maximum capacities, find the maximum flow from the beginning arrow to the ending arrow. Display the final solution and compute the maximum flow through the network.
(5 points)
O
T
5
8
3
4
8
5
8
7
6
4
3
6
7
5
4
3
6
5
4
8
3
5
6
5
9
7
C. Consider the following nonlinear programming problem:
max Z = 54(x1) - 9(x1)2 + 78(x2) - 13(x2)2
s. t. x1 <= 4 2x2 <= 12 3x1 + 2x2 <= 18
x1, x2 >= 0
a. List the KKT conditions. 10 pts.
b. Derive the optimal solution. 5 pts.
D.Consider the assignment problem having the following cost and requirements table. Solve for the optimal solution, using the Northwest
Corner Rule as the initial starting solution. (15 points)
Assign
A B C D
1 4 6 8 7
2 7 M 2 6
3 8 5 6 7
4 5 2 3 4
E.Four new products are being considered for production. The start-up costs and marginal revenues are shown below.
Product 1 2 3 4 Start-up costs $30,000 $35,000 $40,000 $50,000 Marginal revenue $20 $25 $35 $30
Let x1, x2, x3, and x4 denote the continuous variables associated with the production levels of the four products. Formulate this problem as a mathematical programming problem, including the following additional constraints.
15 pts
· No more than three of the prod.
In this paper an innovative method named MM method is proposed for finding an optimal solution directly. A new algorithm in MM method is discussed in this paper which gives optimal solution. Some example are provided to illustrate the proposed algorithm and result is compared to MOD I (modified distribution) method. The most attractive feature of this method is that it requires very simple arithmetical and logical calculation.
Is the practice of predicting something that will happen or come to be in the future. It is not, however, like horoscope or tarot reading or other practices carried out by the likes of psychics. Forecasting relies on solid evidence to predict future events. It is used in a number of areas today, most commonly in the process of predicting the future weather and the imminent economic climate.
VAT Registration Outlined In UAE: Benefits and Requirementsuae taxgpt
Vat Registration is a legal obligation for businesses meeting the threshold requirement, helping companies avoid fines and ramifications. Contact now!
https://viralsocialtrends.com/vat-registration-outlined-in-uae/
RMD24 | Debunking the non-endemic revenue myth Marvin Vacquier Droop | First ...BBPMedia1
Marvin neemt je in deze presentatie mee in de voordelen van non-endemic advertising op retail media netwerken. Hij brengt ook de uitdagingen in beeld die de markt op dit moment heeft op het gebied van retail media voor niet-leveranciers.
Retail media wordt gezien als het nieuwe advertising-medium en ook mediabureaus richten massaal retail media-afdelingen op. Merken die niet in de betreffende winkel liggen staan ook nog niet in de rij om op de retail media netwerken te adverteren. Marvin belicht de uitdagingen die er zijn om echt aansluiting te vinden op die markt van non-endemic advertising.
Tata Group Dials Taiwan for Its Chipmaking Ambition in Gujarat’s DholeraAvirahi City Dholera
The Tata Group, a titan of Indian industry, is making waves with its advanced talks with Taiwanese chipmakers Powerchip Semiconductor Manufacturing Corporation (PSMC) and UMC Group. The goal? Establishing a cutting-edge semiconductor fabrication unit (fab) in Dholera, Gujarat. This isn’t just any project; it’s a potential game changer for India’s chipmaking aspirations and a boon for investors seeking promising residential projects in dholera sir.
Visit : https://www.avirahi.com/blog/tata-group-dials-taiwan-for-its-chipmaking-ambition-in-gujarats-dholera/
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
Discover the innovative and creative projects that highlight my journey throu...dylandmeas
Discover the innovative and creative projects that highlight my journey through Full Sail University. Below, you’ll find a collection of my work showcasing my skills and expertise in digital marketing, event planning, and media production.
RMD24 | Retail media: hoe zet je dit in als je geen AH of Unilever bent? Heid...BBPMedia1
Grote partijen zijn al een tijdje onderweg met retail media. Ondertussen worden in dit domein ook de kansen zichtbaar voor andere spelers in de markt. Maar met die kansen ontstaan ook vragen: Zelf retail media worden of erop adverteren? In welke fase van de funnel past het en hoe integreer je het in een mediaplan? Wat is nu precies het verschil met marketplaces en Programmatic ads? In dit half uur beslechten we de dilemma's en krijg je antwoorden op wanneer het voor jou tijd is om de volgende stap te zetten.
What is the TDS Return Filing Due Date for FY 2024-25.pdfseoforlegalpillers
It is crucial for the taxpayers to understand about the TDS Return Filing Due Date, so that they can fulfill your TDS obligations efficiently. Taxpayers can avoid penalties by sticking to the deadlines and by accurate filing of TDS. Timely filing of TDS will make sure about the availability of tax credits. You can also seek the professional guidance of experts like Legal Pillers for timely filing of the TDS Return.
Implicitly or explicitly all competing businesses employ a strategy to select a mix
of marketing resources. Formulating such competitive strategies fundamentally
involves recognizing relationships between elements of the marketing mix (e.g.,
price and product quality), as well as assessing competitive and market conditions
(i.e., industry structure in the language of economics).
3.0 Project 2_ Developing My Brand Identity Kit.pptxtanyjahb
A personal brand exploration presentation summarizes an individual's unique qualities and goals, covering strengths, values, passions, and target audience. It helps individuals understand what makes them stand out, their desired image, and how they aim to achieve it.
Enterprise Excellence is Inclusive Excellence.pdfKaiNexus
Enterprise excellence and inclusive excellence are closely linked, and real-world challenges have shown that both are essential to the success of any organization. To achieve enterprise excellence, organizations must focus on improving their operations and processes while creating an inclusive environment that engages everyone. In this interactive session, the facilitator will highlight commonly established business practices and how they limit our ability to engage everyone every day. More importantly, though, participants will likely gain increased awareness of what we can do differently to maximize enterprise excellence through deliberate inclusion.
What is Enterprise Excellence?
Enterprise Excellence is a holistic approach that's aimed at achieving world-class performance across all aspects of the organization.
What might I learn?
A way to engage all in creating Inclusive Excellence. Lessons from the US military and their parallels to the story of Harry Potter. How belt systems and CI teams can destroy inclusive practices. How leadership language invites people to the party. There are three things leaders can do to engage everyone every day: maximizing psychological safety to create environments where folks learn, contribute, and challenge the status quo.
Who might benefit? Anyone and everyone leading folks from the shop floor to top floor.
Dr. William Harvey is a seasoned Operations Leader with extensive experience in chemical processing, manufacturing, and operations management. At Michelman, he currently oversees multiple sites, leading teams in strategic planning and coaching/practicing continuous improvement. William is set to start his eighth year of teaching at the University of Cincinnati where he teaches marketing, finance, and management. William holds various certifications in change management, quality, leadership, operational excellence, team building, and DiSC, among others.
Memorandum Of Association Constitution of Company.pptseri bangash
www.seribangash.com
A Memorandum of Association (MOA) is a legal document that outlines the fundamental principles and objectives upon which a company operates. It serves as the company's charter or constitution and defines the scope of its activities. Here's a detailed note on the MOA:
Contents of Memorandum of Association:
Name Clause: This clause states the name of the company, which should end with words like "Limited" or "Ltd." for a public limited company and "Private Limited" or "Pvt. Ltd." for a private limited company.
https://seribangash.com/article-of-association-is-legal-doc-of-company/
Registered Office Clause: It specifies the location where the company's registered office is situated. This office is where all official communications and notices are sent.
Objective Clause: This clause delineates the main objectives for which the company is formed. It's important to define these objectives clearly, as the company cannot undertake activities beyond those mentioned in this clause.
www.seribangash.com
Liability Clause: It outlines the extent of liability of the company's members. In the case of companies limited by shares, the liability of members is limited to the amount unpaid on their shares. For companies limited by guarantee, members' liability is limited to the amount they undertake to contribute if the company is wound up.
https://seribangash.com/promotors-is-person-conceived-formation-company/
Capital Clause: This clause specifies the authorized capital of the company, i.e., the maximum amount of share capital the company is authorized to issue. It also mentions the division of this capital into shares and their respective nominal value.
Association Clause: It simply states that the subscribers wish to form a company and agree to become members of it, in accordance with the terms of the MOA.
Importance of Memorandum of Association:
Legal Requirement: The MOA is a legal requirement for the formation of a company. It must be filed with the Registrar of Companies during the incorporation process.
Constitutional Document: It serves as the company's constitutional document, defining its scope, powers, and limitations.
Protection of Members: It protects the interests of the company's members by clearly defining the objectives and limiting their liability.
External Communication: It provides clarity to external parties, such as investors, creditors, and regulatory authorities, regarding the company's objectives and powers.
https://seribangash.com/difference-public-and-private-company-law/
Binding Authority: The company and its members are bound by the provisions of the MOA. Any action taken beyond its scope may be considered ultra vires (beyond the powers) of the company and therefore void.
Amendment of MOA:
While the MOA lays down the company's fundamental principles, it is not entirely immutable. It can be amended, but only under specific circumstances and in compliance with legal procedures. Amendments typically require shareholder
Attending a job Interview for B1 and B2 Englsih learnersErika906060
It is a sample of an interview for a business english class for pre-intermediate and intermediate english students with emphasis on the speking ability.
Kseniya Leshchenko: Shared development support service model as the way to ma...Lviv Startup Club
Kseniya Leshchenko: Shared development support service model as the way to make small projects with small budgets profitable for the company (UA)
Kyiv PMDay 2024 Summer
Website – www.pmday.org
Youtube – https://www.youtube.com/startuplviv
FB – https://www.facebook.com/pmdayconference
Kseniya Leshchenko: Shared development support service model as the way to ma...
Assignment problem
1.
2. 19-Mar-20 Dr. Abdulfatah Salem 2
Assignment problem as a special transportation case
Special form of transportation model is the assignment model where.
Supply at each source and demand at each destination limited to one unit.
In a balanced model supply equals demand.
In an unbalanced model supply does not equal demand.
3. 19-Mar-20 Dr. Abdulfatah Salem 3
A B C
X 1 0
Y 1 0
Z 1 0
0 0 0
Total cost = 6 + 5 + 11 = 22
A B C
X 1 0 0
Y 1 0
Z 1 0 0 0
0 0 0
A B C
X 1 0 0 0
Y 0 0 1 0
Z 0 1 0 0
0 0 0
Least cost Stepping stone Optimal case
Ex. Solve the following transportation model using:
•The least cost method to determine the initial feasible solution.
•The stepping stone method to find the optimal solution
Sol.
1
1
1
4. 19-Mar-20 Dr. Abdulfatah Salem 4
The assignment problem refers to the class of linear programming problems
that involve determining the most efficient assignment of :
people to Tasks
salespeople to territories
contracts to bidders
jobs to machines, etc.
The objective is most often to minimize total costs or total time of
performing the tasks at hand.
One important characteristic of assignment problems is that only one job or worker is assigned to one machine or Task.
An example is the problem of a taxi company with 4 taxis and 4 passengers. Which taxi should collect which passenger in order
to minimize costs?
An assignment problem can be viewed as a transportation problem in which:
The capacity from each source (or person to be assigned) is 1.
The demand at each destination (or job to be done) is 1.
5. 19-Mar-20 Dr. Abdulfatah Salem 5
1) Find the opportunity cost table by
a) Subtracting the smallest number in each row of the original cost table or matrix
from every number in that row.
b) Then subtracting the smallest number in each column of the table obtained in
part (a) from every number in that column.
2) Test the table resulting from step 1
to see whether an optimal assignment can be made. The procedure is to draw the
minimum number of vertical and horizontal straight lines necessary to cover all zeros in
the table. If the number of lines equals either the number of rows or columns, an optimal
assignment can be made. If the number of lines is less than the number of rows or
columns, we proceed to step 3.
3) Revise the present opportunity cost table
This is done by subtracting the smallest number not covered by a line from every other
uncovered number. This same smallest number is also added to any number(s) lying at
the intersection of the horizontal and vertical lines. We then return to step 2 and
continue the cycle until an optimal assignment is possible.
6. 19-Mar-20 Dr. Abdulfatah Salem 6
A B C
X 6 8 10
Y 7 11 11
Z 4 5 12
Ex.
Three computer systems needs to be
installed in the same time by three different
companies, bids for each system are to be
solicited from each company.
Required :
To which company should each system be
assigned.
7. 19-Mar-20 Dr. Abdulfatah Salem 7
A B C
X 6 8 10
Y 7 11 11
Z 4 5 12
Sol.
A B C
X 6 8 10
Y 7 11 11
Z 4 5 12
A B C
X 6 8 10
Y 7 11 11
Z 4 5 12
A B C
X 6 8 10
Y 7 11 11
Z 4 5 12
A B C
X 6 8 10
Y 7 11 11
Z 4 5 12
A B C
X 6 8 10
Y 7 11 11
Z 4 5 12
Total cost = 29
Total cost = 25Total cost = 22Total cost = 22
Total cost = 23Total cost = 27
8. 19-Mar-20 Dr. Abdulfatah Salem 8
A B C
X 6 8 11
Y 7 11 11
Z 4 5 12
Solution using The Hungarian method
Column
Reduction
Row
Reduction
A B C
X 0 2 5
Y 0 4 4
Z 0 1 8
A B C
X 0 2 5
Y 0 4 4
Z 0 1 8
A B C
X 0 1 1
Y 0 3 0
Z 0 0 4
9. 19-Mar-20 Dr. Abdulfatah Salem 9
Using The Hungarian method
Optimal case
A B C
X 0 1 1
Y 0 3 0
Z 0 0 4
Assignment
A B C
X 0 1 1
Y 0 3 0
Z 0 0 4
A B C
X 6 8 10
Y 7 11 11
Z 4 5 12
Labor Task Cost T.Cost
X A 6
22Y C 11
Z B 5
10. 19-Mar-20 Dr. Abdulfatah Salem 10
Task 1 Task 2 Task 3
Ahmed 11 14 6
Mustafa 8 10 11
Ali 9 12 7
Ex.
Assign
• Three tasks (Task1, Task2, Task3)
to
• Three labors (Ahmed, Mustafa, Ali)
in a way
• That will minimize total costs.
11. 19-Mar-20 Dr. Abdulfatah Salem 11
Task. 1 Task. 2 Task. 3
Ahmed 11 14 6
Mustafa 8 10 11
Ali 9 12 7
Using The Hungarian method
Task. 1 Task. 2 Task. 3
Ahmed 5 8 0
Mustafa 0 2 3
Ali 2 5 0
Column
Reduction
Task. 1 Task. 2 Task. 3
Ahmed 5 8 0
Mustafa 0 2 3
Ali 2 5 0
Task. 1 Task. 2 Task. 3
Ahmed 5 6 0
Mustafa 0 0 3
Ali 2 3 0
Row
Reduction
Sol.
12. 19-Mar-20 Dr. Abdulfatah Salem 12
Task. 1 Task. 2 Task. 3
Ahmed 5 6 0
Mustafa 0 0 3
Ali 2 3 02
Task. 1 Task. 2 Task. 3
Ahmed 3 4 0
Mustafa 0 0 5
Ali 0 1 0
Task. 1 Task. 2 Task. 3
Ahmed 3 4 0
Mustafa 0 0 5
Ali 0 1 0
The no. of lines covering all zeros are 3
Which is equals to the no. of rows
So, the optimality is made
The no. of lines covering all zeros are 2
Which is less than the no. of rows
So, the optimality is not made
13. 19-Mar-20 Dr. Abdulfatah Salem 13
Task. 1 Task. 2 Task. 3
Ahmed 3 4 0
Mustafa 0 0 5
Ali 0 1 0
i. Find a row or column with only one zero cell.
ii. Make the assignment corresponding to that zero cell.
iii. Eliminate that row and column from the table.
iv. Continue until all the assignments have been made.
0
0
0
Ahmed Task. 3
Mustafa Task. 2
Ali Task. 1
Task. 1 Task. 2 Task. 3
6
10
9
Total Cost 9 + 10 + 6 2525
14. 19-Mar-20 Dr. Abdulfatah Salem 14
Ex.
Careem Taxi company has four taxis locating at Smouha area and there are four passengers, A, B,
C and D requiring taxis. The distance between the taxis and the passengers are given in the table
below, in Kilometers'. The Taxi company wishes to assign a taxis to each passenger so that the
distance traveled is a minimum.
A B C D
Renault 3 4 6 5
Toyota 4 1 5 3
Lanos 8 3 2 1
Optra 11 5 3 9
16. 19-Mar-20 Dr. Abdulfatah Salem 16
Cst. km T.km
Renault A 3
8
Toyota B 1
Lanos D 1
Optra C 3
A B C D
Renault 3 4 6 5
Toyota 4 1 5 3
Lanos 8 3 2 1
Optra 11 5 3 9
0
0
0
0
17. 19-Mar-20 Dr. Abdulfatah Salem 17
Maximization of the assignment problem :
Some assignment problems are phrased in terms of maximizing the payoff, profit, or
effectiveness of an assignment instead of minimizing costs.
It is easy to obtain an equivalent minimization problem by converting all numbers in the
table to opportunity costs.
This is brought about by subtracting every number in the original payoff table from the
largest single number in that table.
The transformed entries represent opportunity costs:
It turns out that minimizing opportunity costs produces the same assignment as the
original maximization problem.
Once the optimal assignment for this transformed problem has been computed, the total
payoff or profit is found by adding the original payoffs of those cells that are in the optimal
assignment.
18. 19-Mar-20 Dr. Abdulfatah Salem 18
A law firm maintains a large staff of young lawyer who hold the title of junior partner. The firm
concerned with the effective utilization of this personnel resources, seeks some objective means
of making lawyer-to-client assignments. On march 1, four new clients seeking legal assistance
came to the firm. While the current staff is overloads and identifies four junior partners who,
although busy, could possibly be assigned to the cases. Each young lawyer can handle at most
one new client. Furthermore each lawyer differs in skills and specialty interests.
Seeking to maximize the overall effectiveness of the new client assignment, the firm draws up the
following table, in which he rates the estimated effectiveness (of a scale of 1 to 9) of each lawyer
on each new case.
Client case
Lawyer Divorce
Corporate
merger
Embezzlement Exhibitionism
Adam 6 2 8 5
Brook 9 3 5 8
Carter 4 8 3 4
Darwin 6 7 6 4
Ex.