Least Cost Cell Method | In case of Tie | Transportation Problem in Operations research | Kauserwise
Summary
TLDRThis video tutorial focuses on solving a balanced transportation problem using the least cost cell method. The presenter guides viewers through the process of finding an initial basic feasible solution by selecting the least cost cell and allocating resources based on supply and demand. The video includes a step-by-step demonstration using a cost matrix with three sources and four destinations, and it concludes with the calculation of the total transportation cost. Viewers are encouraged to explore more videos on the topic and on handling unbalanced transportation problems.
Takeaways
- ๐ The video is a tutorial on solving transportation problems using the least cost cell method.
- ๐ The presenter begins by ensuring the transportation problem is balanced, confirming that the total supply equals the total demand.
- ๐ A cost matrix with three sources and four destinations is provided, with specific supply and demand figures.
- ๐ The least cost cell method involves selecting the cell with the lowest cost to start the allocation process.
- โ๏ธ After allocating, cells that are fully utilized are 'deleted' from further consideration.
- ๐ In case of a tie in the lowest cost, the presenter explains how to choose the cell that allows for the maximum allocation.
- ๐ The term 'Thai' is mentioned to describe a situation where the same cost value appears in multiple cells.
- ๐ The process is iterative, with the presenter repeatedly selecting the least cost cell and allocating resources until all cells are utilized.
- ๐ The video concludes with a calculation of the total transportation cost based on the allocations made.
- ๐ฅ A follow-up video is teased, which will cover solving unbalanced transportation problems using the same method.
Q & A
What is the main topic of the video?
-The main topic of the video is solving the Transportation Problem using the least cost cell method.
What is the first step in solving a Transportation Problem as described in the video?
-The first step in solving a Transportation Problem is to check whether the problem is balanced or unbalanced by comparing the total supply with the total demand.
How is a balanced Transportation Problem defined in the video?
-A balanced Transportation Problem is defined as one where the total supply equals the total demand.
What is the total supply and demand in the given problem according to the video?
-The total supply is 600 units (150 + 200 + 250) and the total demand is also 600 units (125 + 175 + 200 + 100), making the problem balanced.
What is the least cost cell method as explained in the video?
-The least cost cell method is a technique used to solve Transportation Problems by selecting the cell with the lowest cost in the cost matrix and allocating the minimum of the corresponding supply and demand to that cell.
What is the procedure when a tie occurs in the least cost cell method, as described in the video?
-When a tie occurs, meaning the same lowest cost is found in multiple cells, the procedure is to select the cell that allows for the maximum allocation based on the remaining supply and demand.
How does the video demonstrate the allocation of the least cost cell?
-The video demonstrates the allocation by comparing the demand and supply for the selected cell, allocating the minimum of the two, and then updating the matrix by cancelling the row or column if the supply or demand is met.
What is the total transportation cost calculated at the end of the video?
-The total transportation cost calculated at the end of the video is 900 rupees.
What is the next topic the video series will cover according to the video?
-The next topic the video series will cover is how to solve unbalanced Transportation Problems using the least cost cell method.
How can viewers find more videos on this topic as mentioned in the video?
-Viewers can find more videos on this topic by looking in the description box of the video for links to additional related content.
Outlines
๐ Introduction to Solving Transportation Problems with Least Cost Cell Method
This paragraph introduces the video's focus on solving transportation problems using the least cost cell method. The presenter explains that this video is a continuation of a series on transportation problems and provides links to previous videos in the description box. The video aims to find an initial basic feasible solution to a given transportation problem with a cost matrix that includes three sources and four destinations, along with their respective demands and supplies. The presenter checks if the problem is balanced by comparing the total supply with the total demand, confirming that it is a balanced problem. The solution process involves selecting the least cost cell and allocating the minimum of the demand and supply to that cell, then repeating the process until all cells are allocated or canceled. The paragraph concludes with the allocation of 150 units to the least cost cell, leaving a balance of 25 in the supply.
๐ Allocating Maximum Values in Case of Ties Using Least Cost Cell Method
This paragraph continues the explanation of the least cost cell method by addressing ties in the cost matrix. When two cells have the same least cost, the presenter advises selecting the cell that allows for the maximum allocation. The process involves comparing the remaining demand and supply for each cell and choosing the one that maximizes allocation. The presenter demonstrates this by allocating 125 units to one cell and then canceling the column. The process is repeated, and another tie occurs with two cells having the same cost. The presenter again selects the cell that allows for the maximum allocation, which is 150 units, and cancels the row. The video concludes with the final allocation of 25 units to the last undeleted cell, resulting in all cells being canceled and the total transportation cost being calculated as 900 rupees. The presenter thanks the viewers and encourages them to like, comment, subscribe, and share the video, promising to cover unbalanced transportation problems in the next video.
Mindmap
Keywords
๐กTransportation Problem
๐กLeast Cost Cell Method
๐กCost Matrix
๐กInitial Basic Feasible Solution
๐กBalanced Transportation Problem
๐กSupply and Demand
๐กDummy Column/Row
๐กAllocation
๐กTie
๐กTotal Transportation Cost
๐กUnbalanced Transportation Problem
Highlights
Introduction to solving Transportation problems using the least cost cell method.
Providing a list of videos on the topic of Transportation problems.
Explaining the importance of checking whether a Transportation problem is balanced or unbalanced.
Demonstrating how to find the total supply and demand to determine if the problem is balanced.
Discussing the necessity of adding dummy columns or rows for unbalanced problems.
Guiding viewers on how to select the least cost in the cost Matrix.
Allocating the minimum value between demand and supply to the selected cell.
Deleting the row or column once all cells in it have been allocated.
Handling ties in the cost Matrix by selecting the cell that allows for maximum allocation.
Comparing demand and supply to decide on allocation amounts in case of ties.
Allocating the maximum possible amount to the selected cell in case of a tie.
Continuing the allocation process until all cells are canceled.
Calculating the total transportation cost using the allocated values.
Providing the final transportation cost as 900 rupees.
Announcing the next video's focus on solving unbalanced Transportation problems using the least cost cell method.
Encouraging viewers to like, comment, subscribe, and share the video.
Transcripts
hi welcome to kauser wise Channel this
is the continuation video of
Transportation problem I have already
uploaded list of videos on this topic
you can find the links in the
description box in this video we are
going to see how to solve Transportation
problem by using least cost cell method
in case of Thai look at the problem find
the initial basic feasible solution to
the following Transportation Problem by
least cost cell method see the cost
Matrix here we have three rows and four
columns a b c these are the three source
and one two three four these are the
destination okay and demand 125 175 200
100 Supply 150 200 250 okay so with this
information they allows you to solve
Transportation problem by using least
cost cell method okay so before you
solve the problem problem the first step
is we need to check whether the problem
is balanced or unbalanced Transportation
problem for balanced Transportation
problem we'll be getting equal demand
and Supply now let us see whether the
problem is balanced or unbalanced
see Supply 150 200 250 total 600 now
check the demand 125 plus 175 plus 200
plus 100 total 600 so this problem is
balanced one okay so in case of
unbalanced Transportation problem we
need to add either dummy column of dummy
row accordingly that we will see in a
separate video okay so this one is
balanced one now let us see the solution
how to solve this problem by using least
cost cell method say according to least
cost cell method we need to select the
least cost in the cost Matrix okay among
these values which one is least cost 2
is the least cost okay so I am going to
allocate this particular cell in order
to allocate the value we need to compare
demand and Supply with respect to this
this particular cell okay so for this
particular cell the demand is 175 and
Supply is 150. now we need to allocate
minimum value which one is minimum 150
or 175 150 so allocate 150 here
so after allocating this here you'll be
getting 0 and here you will be getting
25 as balance okay so here's 0 no so
delete this particular row
okay now repeat the same procedure until
we delete all the cells okay now among
the undeleted cells which one is list
value 4 is the least value right but
here we have 2 4 so 4 occurs in two
different cells so this is called Thai
in case of tie we need to select which
cell is going to get maximum allocation
I'll just explain if I select this
particular cell just compare the demand
and Supply 100 to 50. the least value is
100 no so I can allocate 100 here okay
so in case if I select this particular
cell what is the demand and Supply 125
and 200 the least value is 125 no so I
can select 125 now compare these two
values here I can allocate 125 and here
I can allocate 100 so which one is
maximum allocation 125 is a maximum
allocation okay so I have to select this
particular 4 instead of this particular
cell so this is the procedure in case of
type so I have allocated this particular
cell which is having maximum allocation
okay so 125
balance 75 so here I am getting 0 no
just cancel this particular column
okay again repeat the same thing so out
of the undeleted cell which one is least
value 4 so now compare demand and Supply
100 to 50 100 is the least value so
enter 100 so balance 150 here here 0 so
cancel this particular colon again I
have to select the least cell so again I
am getting Thai okay 6 6 now I have to
select the maximum allocation see if I
select this particular cell 200 150 the
least value is 150 no suppose if I
select this particular cell 25 150 so
least value is 25 so if I select this
particular cell I'll be getting maximum
allocation
so select this particular cell 200 150
so put 150 here balance 50 here 0 so
cancel this particular row okay now out
of these two undulated value 10 is the
least value so I can select this
particular cell 50 75 so least amount is
50
0 balance
25 so 0 no cancel this particular column
finally I'm getting only one undeleted
cell so I can allocate 25 25 equal value
so enter 25 okay
so cancel this so all the cells are get
canceled now you can calculate the
transportation cost
150 into 2.
plus 125 into 4.
plus 25 into 12.
plus 50 into 10.
thank you
plus 150 into 6.
plus 100 into 4
900 rupees
this is the total transportation cost
according to least cost cell method so
this is the way to solve Transportation
problem by using least cos cell method
in the next video we are going to see
how to solve unbalanced Transportation
problem by using least cost cell method
you can find the links in the
description box hope you like this video
please hit the like comment subscribe
and share with your friends thank you
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