Application of Transportation Model in Business MAIN
Transcript of Application of Transportation Model in Business MAIN
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Application of Transportation Model in
Business/IndustriesPRESENTED BY:-GROUP 3
ARKA PRBHA GHOSH(09DF011)ARNAB DAS(09DF012)
ARUN KUMAR(09DF013)ARUNJYOTI MUKHERJEE(09DF014)
ASHRAF ANSARI(09DF015)
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INTRODUCTION• Transportation problem is to
transport various amount of a single homogeneous commodity, that are initially stored at various origins, to different destinations in such way that the total transportation cost is minimum.
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METHODS OF TRANSPORTATION
• North-West Corner Rule(NWCR)
• Lowest Cost Entry Method(LCEM)
• Vogel’s Approximation Method(VAM)
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North West Corner Method
W1 W2 W3 W4
6 10 12 15
F1 11
F2 13
F3 19
Requirement(Demand) 43
Capacity(Supply)
21 16 25 13
23
41
14
18
18
27
17
32
6
5 8
4 15
WarehouseFactory
5
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• X11=6• X12=5• X22=5• x23=8• X33=4• X34=15
Total Transportation Cost=(6*21)+(5*16)+(5*18)+(8*14)+(4*18)+(15*41)
=Rs1055
Initial Basic Feasible Solution
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Applications of NWCM
The main areas of applications of NWCM are:• It is used for transportation within the campus
of an organization as costs are not significant.• It is used for transportation to satisfy such
obligations where cost is not the criteria.
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VOGEL’S APPROXIMATION METHOD
W1 W2 W3 W4
150 100 200 150
F1 100
F2 300
F3 200
Demand 600
CapacityFrom
To
19 7 3 21
6
22
18
15
21
14
15
11
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Initial basic feasible solutionx13=100x21=50x23=100x24=150x31=100x32=100TTC= (100*3)+(50*15)+(100*18)+(150*6)+(100*11)+(100*14) =300+750+1800+900+1100+1400
=6250
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LEAST COST METHODW1 W2 W3 W4 CAPACITY
F1 19 30 50 10 7
F2 70 30 40 60 9
F3 40 8 70 20 18
REQUIREMENT
5 8 7 14 43
FROM
TO
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LCM OR MATRIX-MINIMA METHOD
STEP 1 :-• DETERMINE THE SMALLEST COST IN THE COST MATRIX OF THE
TRANSPORTATION TABLE.LET IT BE CIJ. ALLOCATE XIJ =MIN(AI ,BJ) IN THE CELL.
STEP 2 :-• IF ITH ROW GETS EXHAUSTED CROSS IT OUT ,AS A RESULT THE
TRANSPORTATION TABLE GETS REDUCED.• IF JTH COLUMN GETS EXHAUSTED CROSS IT OUT ,AS A RESULT THE
TRASPORTATION TABLE GETS REDUCED.
STEP 3 :-• REPEAT STEPS 1 AND 2 UNTIL THE ALL THE REQUIREMENTS ARE
SATISFIED.
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APPLICATION:- LCM OR MATRIX MINIMA METHOD IS CERTAINLY AN
IMPROVEMENT OVER THE NWCR(NORTH-WEST CORNER RULE) ,BUT IS NOT YET THE LOWEST POSSIBLE SHIPPING
SCHEDULE. IT IS USED TO COMPUTE TRANSPORTAION ROUTE IN SUCH A
WAY SO AS TO MINIMISE COST BUT NOT IN AN OPTIMUM WAY.
IN LCM METHOD REDUCTION OF TOTAL COST IS DEFINTELY THE PRIMARY CRITERIA BUT IT IS NOT DEALT IN A OPTIMUM WAY,WHICH CAN BE DERIVED THROUGH VAM METHOD.
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APPLICATIONS OF VAM
•It is used to compute transportation routes in such a way as to minimize transportation cost for finding out locations of warehouses.•It is used to find out locations of transportation corporations depots where insignificant total cost difference may not matter.
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APPLICATIONS-TRANSPORTATION METHOD
Minimize shipping costs from factories to warehouses(or from warehouses to retail outlets).
Determine lowest cost location for new factory,warehouse,office,or other outlet facility.
Find minimum cost production schedule that satisfies firm’s demand and production limitations.
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CONCLUSION
The transportation problem is one of the most frequently encountered application in real life situations and is a special type of linear programming problem.
The transportation problem indicates the amount of consignment to be transported from various origins to different destinations so that the total transportation cost is minimized without violating the availability constraints and the requirement constraints.
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THANK YOU