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)

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.

METHODS OF TRANSPORTATION

• North-West Corner Rule(NWCR)

• Lowest Cost Entry Method(LCEM)

• Vogel’s Approximation Method(VAM)

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

• 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

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.

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

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

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

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.

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.

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.

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.

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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