Second Topic Transportation Model Problems discussed in the class Q.1 A dairy firm has their plants located in a state. The daily milk production at each plant is as follows: PLANT MILK SUPPLY 1 6 2 1 3 10

Each day, the firm must fulfill the needs of its four distribution centers. Minimum requirement at each center is as follows: CENTER MILK SUPPLY 1 7 2 5 3 3 4 2

Cost in the hundreds of rupees of shipping one million litre from each plant to each distribution center is given in the following table: Distribution center D1 P1 2 P2 1 P3 5

D2 3 0 8

D3 11 6 15

D4 7 1 9

Find initial basic feasible solution for given problem by using: (a)North – West corner rule (b) Least cost method and (c) Vogel’s approximation method If the objective is to minimize the total transportation cost. Q.2 A Company has factories at F1, F2, and F3 which supply to warehouses at W1, W2, and W3. Weekly factory capacities are 200,160,and 90 units, respectively. Weekly warehouse requirement are 180,120and 150 units respectively. Unit shipping costs (in rupees) are as follows: Ware house W1 W2 W3 SUPPLY F1 16 20 12 200 F2 14 8 18 160 F3 26 24 16 90 DEMAND 180 120 150 450

Determined the optimal distribution for this company to minimize total shipping cost.

Second Topic Transportation Model Problems for Practice

Q.1 A company has four manufacturing plants and five warehouses. Each plant manufactures the same product which is sold at different prices in each warehouse area. The cost of manufacturing and cost of raw material are different in each plant to various factors. The capacities of the plants are also different. The data are given in the following table: PLANT ITEM Manufacturing cost (RS) per unit Raw material cost (RS)per unit Capacity per unit time 1 12 08 100 2 10 07 200 3 08 07 120 4 08 05 80

The company has five warehouses. The sales prices, transportation costs and demands are given in the following table: ware house transportation cost per unit sale price demand per unit(Rs.)

1

2

3

4

A 4 7 4 3 30 80 B 8 9 7 8 32 120 C 2 7 6 10 28 150 D 10 7 5 8 34 70 E 2 5 8 9 30 90 (a) Formulate this problem as a transportation problem to maximize profit. (b) Find the solution using VAM method. Q.2 Obtain an optimal solution to the transportation problem by UV method. Use VAM method for obtaining initial feasible solution D1 19 70 40 5 D2 30 30 8 8 D3 50 40 70 7 D4 10 60 20 14 CAPACITY 7 9 18 34

S1 S2 S3 DEMAND

Q.3 Consider a firm having 2 factories. The firm is to ship its products from the factories to three- retail stores. The number of units available at factories X and Y are 200 and 300, respectively while those demanded at retail stores A ,B and C are 100,150 and 250, respectively. Rather than shipping directly from factories to retail stores, it is asked to investigate the possibility of Trans- shipment. The transportation cost (in Rupees) per unit is given in the table . FACTORY X Factory X Y 0 6 y 8 0 RETAIL STORE A 7 11 B 8 9 C 9 10

Retail store A B C

7 1 8

2 5 9

0 1 7

5 0 8

1 4 0

Find out the optimal shipping schedule. Q.4 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 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 given below: Ware house III 4 7 6 85

A B C DEMAN D

I 6 5 3 60

II 4 6 4 80

IV 7 4 3 105

V 5 8 4 70

SUPPLY 100 125 175 400

The Cost Of Manufacturing The Product At Different Production Shop Is shop A B C Variable cost 14 16 15 Fixed cost 7000 4000 5000

Find the optimum quantity to be supplied from each shop to different warehouses at minimum total cost.

Third Topic Assignment Model Problems discussed in the class Q.1 A job production unit has four jobs A,B,C,D which can be...