Transportation Problems

Prof. Vinay Pandit

TRANSPORTATION PROBLEMS Solve the following transportation problem for the total transportation cost 1) O1 O2 O3 Demand

D1 6 4 6 70

D2 5 8 3 90

D3 1 7 9 80

D4 3 2 3 60

capacity 100 125 75

O1 O2 O3 Demand

D1 3 2 5 50

D2 1 6 1 60

D3 3 1 4 90

D4 5 3 8 100

capacity 120 95 85

O1 O2 O3 Demand

D1 4 3 1 50

D2 5 6 4 40

D3 3 7 1 90

D4 6 3 2 20

capacity 50 70 80

2)

3)

4) A distribution system has the following constraints Factory Capacity (units) A 45 B 15 C 40

Warehouse I II III

Demand (units) 25 55 20

The transportation cost per unit (in Rs.) associated with each route are as follows: From I II III A 10 7 8 B 15 12 9 C 7 8 12 Find the transportation cost

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Prof. Vinay Pandit 5) Solve the transportation problem for the total transportation cost Source A B C Demand

D1 15 15 13 20

Destination D2 18 19 16 20

D3 22 20 23 25

D4 16 14 17 35

supply 30 40 30 100

Is the optimal solution obtained by you is a unique one? If not, why? What is an alternate optimum then? 6) National oil company (NOC) has three refineries and four depots. Transportation cost per ton, Capacities and requirements are as follows: D1 R1 5 R2 8 R3 12 Requirements (tons) 300 Determine the allocation of output.

D2 7 6 10 600

D3 13 14 9 700

D4 10 13 11 400

Capacity (tons) 700 400 800

7) Cement manufacturing company wishes to transport cement from its three factories P, Q and to five distribution depots situated at A, B, C, D and E The quantities produced at the factories per week, requirements at the depots per week and respective transportation cost per tone are given in the table below: Depots Factories A B C D E Tones available P 4 1 3 4 4 60 Q 2 3 2 2 3 35 R 3 5 2 4 4 40 Tones required 22 45 20 18 30 135 Determine the cost distribution programme for the company.

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Prof. Vinay Pandit 9) A plastic modeling company produces homogeneous molding in its three factories X, Y and Z. These have to be distributed to the three wholesale outlets A, B and C. Data regarding unit transportation cost, capacity and demand are given below Factories

A

B

C

Factory capacity (units)

X Y Z

7 11 8

8 3 5

5 6 7

200 150 350

150

175

425

Outlet demand (units)

Find the allocation of factory outputs to the wholesale outlets and asses the total cost 10) A company has factories at F1, F2and F3 which manufactures and supplies the same commodity to sales depots at D1, D2, D3 and D4. Production capacity of factories in any month is 1600, 1500 and 1900 units respectively. Sales depots have standardized their requirement over a period of time and have a constant in- takes month after month. Their demand in any month is 800, 900, 1700 and 1600 units respectively. Depending on the location of the factories and the process involved, the manufacturing costs vary from factory to factory as given below: MANUFACTURING COST PER UNIT F1 14

F2 10

F3 13

Depending on the relative location, the unit transportation cost also varies. Details of the same are given below: D1 D2 D3 D4 F1 2 6 3 7 F2 1 5 4 5 F3 4 4 3 6 Depots are distributed all over the country. Depending on the demand, competition and the factory of origin (quality difference) the unit sale realization varies in a factory depot combination basis, as reproducer below:

F1 F2 F3

Sales Realisation (Rs. /unit) D1 D2 40 38 30 32 50 45

D3 45 28 42

D4 50 30 40

The product in chare wants to draw out a schedule of manufacturing/transportation/sale which would maximize overall profits to the company. Use a transportation model to arrive at the profits maximization allocation.

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Prof. Vinay Pandit 11) A company has three plants located at different places put producing an identical product. The cost of production distribution cost for each plant to the three different warehouses, the sale price at each warehouse and the individual capacities for the plant and warehouse are given below: Plant Raw material Other expenses

F1 15 10

F2

F3

18

14

9

12

Distribution cost to Warehouse W1 W2 W3 Capacity of the plant

F1

F2

F3

S.P

Warehouse capacity

3

9

5

34

80

1

7

4

32

110

5

8

3

31

150

150

100

130

a) Establish a suitable table giving net profit/loss for a unit produced at different plants and distributed at different warehouses. b) Introduced a suitable dummy warehouse/ plant so as to match the capacities of the plants and warehouses. c) Find a distribution pattern to find profit/ loss.

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Prof. Vinay Pandit 12) A company manufactures a certain product at two factories and distributes it to three warehouses. Each factory runs both a regular shift and when necessary, an over time shift for any remaining production requirement. Production costs differ between factories and the selling price of the product varies at the different warehouse locations. The pertinent information is given in the table I Table I Weekly production capability (units) Regular Overtime 100 40 150 30

Factory 1 2

Warehouse 1 2 3

Unit Production Cost Regular Overtime Rs. 17 Rs. 24 Rs. 18 Rs.23

Weekly requirement unit 80 120 70

Unit selling price Rs. 35 Rs. 37 Rs. 34

Transportation cost (Rs. per unit) Warehouse Factory 1 2

1 6 4

2 7 2

3 6 8

The object is to select that combination of regular and overtime production which when allocated to shipping in an optimal fashion will maximize profit. • •

Questions: Set up the transportation table for an initial solution Obtain an IBFS

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