The document discusses transportation problems and their optimization using linear programming. It begins by explaining that transportation problems aim to optimally transport goods from supply origins to demand destinations at minimum cost while satisfying supply and demand constraints. The document then discusses how balanced transportation problems have equal total supply and demand, while unbalanced problems introduce dummy variables to balance totals. It provides examples of unbalanced problems where supply exceeds demand and vice versa, and how dummy columns/rows are added to balance the problems and find optimal solutions.
the major theories of industrial location were developed by the economists. some of them which we consider pioneering and useful in understanding the locational behaviour of firm are explained here.
Two major theories namely :(1) Weber's Theory. (2) The market area theory of Tord Palander.
the major theories of industrial location were developed by the economists. some of them which we consider pioneering and useful in understanding the locational behaviour of firm are explained here.
Two major theories namely :(1) Weber's Theory. (2) The market area theory of Tord Palander.
this presentations help students to understand meaning of location of industries. factors that affecting industrial location and Alfred Weber's theory of location...
The transportation problem is a special type of linear programming problem where the objective is to minimize the cost of distributing a product from a number of sources or origins to a number of destinations.
Because of its special structure, the usual simplex method is not suitable for solving transportation problems. These problems require a special method of solution.
this presentations help students to understand meaning of location of industries. factors that affecting industrial location and Alfred Weber's theory of location...
The transportation problem is a special type of linear programming problem where the objective is to minimize the cost of distributing a product from a number of sources or origins to a number of destinations.
Because of its special structure, the usual simplex method is not suitable for solving transportation problems. These problems require a special method of solution.
The Least Cost Method is another method used to obtain the initial feasible solution for the transportation problem. Here, the allocation begins with the cell which has the minimum cost. The lower cost cells are chosen over the higher-cost cell with the objective to have the least cost of transportation.
The European Unemployment Puzzle: implications from population agingGRAPE
We study the link between the evolving age structure of the working population and unemployment. We build a large new Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economy, we quantify the extent to which demographic changes over the last three decades have contributed to the decline of the unemployment rate. Our findings yield important implications for the future evolution of unemployment given the anticipated further aging of the working population in Europe. We also quantify the implications for optimal monetary policy: lowering inflation volatility becomes less costly in terms of GDP and unemployment volatility, which hints that optimal monetary policy may be more hawkish in an aging society. Finally, our results also propose a partial reversal of the European-US unemployment puzzle due to the fact that the share of young workers is expected to remain robust in the US.
What website can I sell pi coins securely.DOT TECH
Currently there are no website or exchange that allow buying or selling of pi coins..
But you can still easily sell pi coins, by reselling it to exchanges/crypto whales interested in holding thousands of pi coins before the mainnet launch.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and resell to these crypto whales and holders of pi..
This is because pi network is not doing any pre-sale. The only way exchanges can get pi is by buying from miners and pi merchants stands in between the miners and the exchanges.
How can I sell my pi coins?
Selling pi coins is really easy, but first you need to migrate to mainnet wallet before you can do that. I will leave the telegram contact of my personal pi merchant to trade with.
Tele-gram.
@Pi_vendor_247
Turin Startup Ecosystem 2024 - Ricerca sulle Startup e il Sistema dell'Innov...Quotidiano Piemontese
Turin Startup Ecosystem 2024
Una ricerca de il Club degli Investitori, in collaborazione con ToTeM Torino Tech Map e con il supporto della ESCP Business School e di Growth Capital
BONKMILLON Unleashes Its Bonkers Potential on Solana.pdfcoingabbar
Introducing BONKMILLON - The Most Bonkers Meme Coin Yet
Let's be real for a second – the world of meme coins can feel like a bit of a circus at times. Every other day, there's a new token promising to take you "to the moon" or offering some groundbreaking utility that'll change the game forever. But how many of them actually deliver on that hype?
This presentation poster infographic delves into the multifaceted impacts of globalization through the lens of Nike, a prominent global brand. It explores how globalization has reshaped Nike's supply chain, marketing strategies, and cultural influence worldwide, examining both the benefits and challenges associated with its global expansion.
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1. Elemental Economics - Introduction to mining.pdfNeal Brewster
After this first you should: Understand the nature of mining; have an awareness of the industry’s boundaries, corporate structure and size; appreciation the complex motivations and objectives of the industries’ various participants; know how mineral reserves are defined and estimated, and how they evolve over time.
How to get verified on Coinbase Account?_.docxBuy bitget
t's important to note that buying verified Coinbase accounts is not recommended and may violate Coinbase's terms of service. Instead of searching to "buy verified Coinbase accounts," follow the proper steps to verify your own account to ensure compliance and security.
Yes of course, you can easily start mining pi network coin today and sell to legit pi vendors in the United States.
Here the telegram contact of my personal vendor.
@Pi_vendor_247
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how to sell pi coins effectively (from 50 - 100k pi)DOT TECH
Anywhere in the world, including Africa, America, and Europe, you can sell Pi Network Coins online and receive cash through online payment options.
Pi has not yet been launched on any exchange because we are currently using the confined Mainnet. The planned launch date for Pi is June 28, 2026.
Reselling to investors who want to hold until the mainnet launch in 2026 is currently the sole way to sell.
Consequently, right now. All you need to do is select the right pi network provider.
Who is a pi merchant?
An individual who buys coins from miners on the pi network and resells them to investors hoping to hang onto them until the mainnet is launched is known as a pi merchant.
debuts.
I'll provide you the Telegram username
@Pi_vendor_247
The secret way to sell pi coins effortlessly.DOT TECH
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Abhay Bhutada Leads Poonawalla Fincorp To Record Low NPA And Unprecedented Gr...Vighnesh Shashtri
Under the leadership of Abhay Bhutada, Poonawalla Fincorp has achieved record-low Non-Performing Assets (NPA) and witnessed unprecedented growth. Bhutada's strategic vision and effective management have significantly enhanced the company's financial health, showcasing a robust performance in the financial sector. This achievement underscores the company's resilience and ability to thrive in a competitive market, setting a new benchmark for operational excellence in the industry.
2. The basic transportation problem was developed in 1941 by F.I.
Hitchaxic. However it could be solved for optimally as an answer to
complex business problem only in 1951,when Geroge B. Dantzig
applied the concept of Linear Programming in solving the
Transportation models.
Transportation problems are primarily concerned with the optimal
(best possible) way in which a product produced at different factories
or plants (called supply origins) can be transported to a number of
warehouses (called demand destinations).
INTRODUCTION
3. Transportation problem is a special kind of LP
problem in which goods are transported from a set
of sources to a set of destinations subject to the
supply and demand of the source and the
destination respectively, such that the total cost of
transportation is minimized.
The objective in a transportation problem is:-To
fully satisfy the destination requirements within
the operating production capacity constraints at
the minimum possible cost.
4. Whenever there is a physical movement of goods from
the point of manufacture to the final consumers through
a variety of channels of distribution (wholesalers,
retailers, distributors etc.), there is a need to minimize
the cost of transportation so as to increase the profit on
sales. Transportation problems arise in all such cases.
.
5. It aims at providing assistance to the top
management in ascertaining how many units of a
particular product should be transported from each
supply origin to each demand destinations to that
the total prevailing demand for the company’s
product is satisfied, while at the same time the
total transportation costs are minimized
6. i.e.; The total supply available at the plants exactly matches
the total demand at the destinations. Hence, there is neither
excess supply nor excess demand.
Such type of problems where supply and demand are
exactly equal are known as Balanced Transportation
Problem.
Supply (from various sources) are written in the rows,
while a column is an expression for the demand of different
warehouses. In general, if a transportation problem has m
rows an n columns, then the problem is solvable if there are
exactly (m + n –1) basic variables
7. .UNBALANCED TRANSPORTATION PROBLEM :
A transportation problem is said to be unbalanced if the
supply and demand are not equal.
Two situations are possible:-
1. If Supply < demand, a dummy supply variable is
introduced in the equation to make it equal to demand.
2. If demand < supply, a dummy demand variable is
introduced in the equation to make it equal to supply.
8. Then before solving we must balance the demand & supply.
When supply exceeds demand, the excess supply is assumed to go to
inventory. A column of slack variables is added to the transportation
table which represents dummy destination with a requirement equal to
the amount of excess supply and the transportation cost equal to zero.
When demand exceeds supply, balance is restored by adding a dummy
origin. The row representing it is added with an assumed total
availability equal to the difference between total demand & supply and
with each cell having a zero unit cost.
9. Demand Less Than Supply
Suppose that a plywood factory increases its rate of
production from 100 to 250 desks
The firm is now able to supply a total of 850 desks each
period
Warehouse requirements remain the same (700) so the
row and column totals do not balance
We add a dummy column that will represent a fake
warehouse requiring 150 desks
This is somewhat analogous to adding a slack variable
We use the northwest corner rule and either vogel’s
approximation method or MODI to find the optimal
solution
10. FROM
TO
A B C TOTAL
AVAILABLE
I 5 4 3 250
II 8 4 3 300
III 9 7 5 300
WAREHOUSE
REQUIREMENTS
300 200 200 850
700
11. FROM
TO
A B C D TOTAL
AVAILABLE
I 5 4 3 0 250
II 8 4 3 0 300
III 9 7 5 0 300
WAREHOUSE
REQUIREMENTS
300 200 200 150
850= 850
12. FROM
TO
A B C D TOTAL
AVAILABLE
I
5 4 3 0
250
II
8 4 3 0
300
III
9 7 5 0
300
WAREHOUSE
REQUIREMENTS
300 200 200 150
(1)
(1)
(2)
(3) (0) (0) (0)
250
300-250=50
13. FROM
A B C D
TOTAL
AVAILABLE
II
8 4 3 0 300
III 9 7 5 0 300
WAREHOUSE
REQUIREMENTS
50 200 200 150
TO
(1)
(2)
(1) (3) (2) (0)
200
300-200=100
14. FROM
A C D
TOTAL
AVAILABLE
II 8 3 0 100
III 9 5 0 300
WAREHOUSE
REQUIREMENTS
50 200 150
TO
100 (5)
(4)
(1) (2) (0)
200-100=100
18. FROM
A B C D
I 5 4 3 0
II 8 4 3 0
III 9 7 5 0
TO
WAREHOUSE
REQUIREMENTS
TOTAL
AVAILABLE
300 200 200 150
250
300
300
250
200 100
50 100 150
m+n-1 = 3+4-1= 6
19. FROM
A B C D
I 5 4 3 0
II 8 4 3 0
III 9 7 5 0
TO
WAREHOUSE
REQUIREMENTS
TOTAL
AVAILABLE
300 200 200 150
250
300
300
250
200 100
50 100 150
u1
u2
U3
v1 v2 v3 v4
24. Total cost = 250*5+200*4+100*3+50*9+100*5+150*0
1250+800+300+450+500+0 = 3,300
Initial basic feasible solution
Here all the dij values are positive, therefore the solution is
optimal.
25. Demand Greater than Supply
The second type of unbalanced condition
occurs when total demand is greater than
total supply
In this case we need to add a dummy row
representing a fake factory
The new factory will have a supply exactly
equal to the difference between total
demand and total real supply
26. FROM
A B C
PLANT
SUPPLY
W 6 4 9 200
X 10 5 8 175
Y 12 7 6 75
WAREHOUSE
DEMAND 250 100 150
450
TO
500
Totals do not
balance
27. FROM
A B C
PLANT
SUPPLY
W 6 4 9 200
X 10 5 8 175
Y 12 7 6 75
Z 0 0 0 50
WAREHOUSE
DEMAND 250 100 150
500
TO
500
28. FROM
A B C
PLANT
SUPPLY
W 6 4 9 200
X 10 5 8 175
Y 12 7 6 75
Z 0 0 0 50
WAREHOUSE
DEMAND 250 100 150
TO
200
0 100 75
50
75
32. Here, all the dij values are positive, therefore the
solution is optimal.
TC= 200*6+0*10+100*5+75*8+75*6+50*0
1200+500+600+450= 2750
33. CONCLUSION
In real-life problems, total demand is frequently not
equal to total supply
These unbalanced problems can be handled easily by
introducing dummy sources or dummy destinations
If total supply is greater than total demand, a dummy
destination (warehouse), with demand exactly equal to
the surplus, is created
If total demand is greater than total supply, we introduce
a dummy source (factory) with a supply equal to the
excess of demand over supply
34. Any units assigned to a dummy destination represent
excess capacity
Any units assigned to a dummy source represent unmet
demand