Transportation

solution and find

1. Use North - West Cormer method to obtai.a an initial basic feasible
out the optimal solution by using MODI method.
G Availability
13 17 14 250
A
B 16 18 14 10 300
24 13 10 400
21
200 225 275 250 950/950
Demand

solution of the
2. Use.ogel's approxination method toobtain an initial basic feasible
transpiration probiem of below example, and find out the optimal solution by MODI
muhod.

G Availability
13 17 14 250
6 18 14 10 300
B
24 13 10 400
21
225 275 250 950/950
Demand 200

have a surplus
3A company has four warehouses and six stores. The warehouses together
of 22 units of a givencommodity, divided among thcm as follows:
3
Ware house
6 2
Surplus
The six tore togcther need 22 units of the commodity. Individual requirements unitsat stores
one of
1,2.3, 4, 5 and 6 are 4, 4, 6, 2, 4 and 2 units respectively. Cost of shipping
commodity from warehouse ito stores jin rupees is given in the matrix below:

Store
Ware house
3 4
12 10
3 7 7
3 6 5
8 2 10
4 6
How should the products be shipped from the warehouse to the stores so that the
transportation cost is the minimum? Alsoexplain degeneracy in transportation technique
in thecontext of this example.
4. Find the basic feasible solution of the following transportation problem by NWC
method. Also find the optimal transportation plan.
5 Available
2 6 80
A 3
B 5 2 3 4 5 60
C 6 3 2 40
D 2 4 5 3 20
60 40 J0 200/200
Required 60 30

5. A product is produced by four factories A, B,C andD. The unit production costs in
them are Rs. 2,Rs. 3, Rs. I and Rs.5 respectively. Their production capacities are in the
factories A-50 units, B-70 units, C-30 units and D-50 units. These factories supply the
product to four stores, demands of whichare 25, 35, 105 and 20 units respectively. Unit
transportation cost in rupees from each sores is given the table below:
Factory Store
2 4
A 2 4 6 11
B 10 7 5
C 13 9 12
D 4 6 8 3

Determine the extent of deliveries from each of the factories to each of the
the total production and transportation cost is stores so that
minimum.
6. A conpany has three plants and four
warehouses. The supply and demand in units and
the corresponding transportation costs are given below
Plants Ware house
2 3
A
B
5 10 4 Supply
10
6
C 4 25
2 5
Demand 7
25 10 20
15
55 /55
The allocation in different cells
has been talken from the
transportation problem as follows. solution procedure of
XA3 = 10,
XB]=20, XB4=5
XC1=5, XC2=10, XC3=5
Answer the following questions, giving brief reasons
(a) Is this solution
(b) ls this solution feasible?
(c) Is this solution degenerate?
optimum?
(d) Docs this problem
have more than one optimum
solution? If so, show all of them.
7. Solve the following transportation problem
From To
3 4 Supply
1 12
2 6 9 7
10 15 6 3 10
6 6
5 11 10 11 13
6 8 14 5 12 6
Demand 10 8 14 41 /41

8. ABC Limited has three production shops supplying a product to five warehouses. The
cost of production varies from shop to shop and cost of transportation varies from one
shop to a warehouse also varies. Each shop has a specific production capacity and each
warehouse has certain amount of requirement.
The cost of transportation are as given below:

Shop Warehouse Supply

III IV >0
A
< 6 4 4 7 100
B 6 125
3 4 6 4 175
Demand 60 80 85 105 70 400/400

The cost of manufacturing the product at different production shops are

Shop
Warehouse
A
14
B
16
C
15

(i) Finsthe optimal distribution pattern so as to minimize the cost.

(ii) Identify alternate solution(s) if any.

9. Consider the following datafor the transportation problem

Factory Destination Supply
1 3
A 7 10
B 6 4 6 80
C 3 2 15
Demand 75 20 50

Since there is not enough supply, some of the demands at the three destinations may not
be satisfied. For the unsatisfied demands let the penalty costs be rupees 1,2 and 3 for
destinations (1), (2) and (3) respectively. Find the initial basic feasible solution by using
Vogel's approximation method.
10.Atransportation problem has the supplies at four sources and requirements at five
destinations. The following table shows the cost of shipping one unit from a particular
source to a particular destination

Source Destination
2 3 4 5
12 4 5 9
2 8 1 6 6
12 4
10 15

The following feasible transportation pattern is proposed X1 | =25, X14=30, X22-20,

X23-25, X31=15, X33=15, X43=10and X45=40 and all other Xij=0
Test whether this allocation has the least possible transportation cost. If so how? If not,
determine the optimal transportation pattern.

I1.The following table shows all necessary information on the availability of supply to
each warehouse, the requirement of each market and the unit transportation cost from
each warehouse to each market.

Warehouse Market Supply

P R
A 6 5 4 22
B 9 2 7 15
7 8 6
Requirement 7 12 17 45/
45

The shipping check has worked out the following schedule from experience.
12 unit from A to Q
1units from A to R
9 unitsfrom A to S
15units from B to R
7units from C to P
Iunits from C to R
() Check and see if the clerk has the optimal schedule.
(ii) Find the optimal schedule and minimum transportation cost
(ii1) It the clerk is approached by a courier to route Cto Q, who offers to reduce his rate
in the hope of getting some business, by how much the rate should be reduced that the
clerk will offer him the business.
 ASteel company has three open hearth furnaces and five rolling mills. Transportation
cOst (Rs. Per quintal) for shipping steel from furnace to rolling mills is shown in the
following table.
Furnace Rolling mills Supply
MI M2 M3 M4 M5
F1 4 3 2 6 8
F2 4 5 12
F3 6 5 4 7 14
Demand 4 4 6 8 34/30

() Find the initial basic feasible solution by using Vovel's approximation method
(i1) Also find optimal solution by using MODImethod.
then
13. A cement company has three factoriess which manufacture cement which is
transported to four distribution centers.
The quantity of monthly production of each factory, the demand of each distribution
centre and the associated transportation cost per quintal are given as follows:

Factories Distribution centers Monthly

W X Z production
(in quintal)
10 5 4 7000
A
B 7 9 15 8000
6 10 14 10000
C
6000 8000 5000 25000 /
Monthly 6000
25000
demand (in
quintals)

() Suggest the optimal transportation schedule.

(ii)
Is there any other transportation schedule which is equally attractive? If, so write
that.
(ii) If the company wants at least 5000 quintal of cement is transported from factory
Cto distribution centre Y, will the transportation schedule be any different? If so,
what will be the new optimal schedule and the effect on cost?
(iv) Suppose the conpany desires to send at most 500 quintals of cement from factory
Cto distribution centre Y, what will the optimal schedule is? Also, obtain the
total transportation cost in such a case.