1. A firm has 2 factories X & Y & 3 retail stores A, B & C. The number of units of a product available at factories X & Y are 200 & 300 respectively, while demanded at retail stores are 100, 150 & 250 respectively. Rather than shipping directly from sources to destinations, it is decided to investigate the possibility of trans-shipment. Find the optimal shipping schedule. The transportation costs in rupees per unit are given below. FactoryRetail store X YA B C 6 0

6 0 7 8 9

5 4 3

7 2

1 5

8 9 0 5 1

1 0 4

7 6 0

Factory X YReatil store A B C

Solution: For this trans-shipment problem, buffer stock = total supply = total demand = 500 units. Adding 500 units to each supply/demand point,we get table below. I.B.F.S obtained by VAM is also shown.To X Y A B C Supply0 (500)67 (200)89700

60 (500)54 (50)3 (250) 800

720 (400)5 (100)1500

1510 (500)4500

99760 (500)500

5005006006507503000

From X Y A B CDemand

The the diagonal allocations in this table may be ignored since they have no physical meaning. The remaining allocations may be interpreted as follows: To

X Y A B C 0 (500)67 (100)8 (100)9

60 (500)54 (50)3 (250)

720 (500)51

1510 (500)4

99760 (500)

500500600650750

From X Y A B C

Factory X supplies 10units each to retail stores A & B. Factory Y supplies 50 units to retail store B & 250 units to C.

2. Table below represents the supply from the plants, the requirement at the distribution centres & the unit transportation costs. Distribution Centres A B C Supply111325150

131535300

150150150450

Plant 1 2 Requirement

when each plant is also considered a destination & each distribution centre is also considered as origin, some additional cost data are necessary, which are given in the tables below:

To plant 1 2 075

110

From Plant 1 2

To distribution centres A B C03311

11013

75130

From Distribution Centre A B C

To plant 1 2 1325

3513

5565

From Distribution centre A B C

Find the optimal shipping schedule for the transhippment problem.

Solution: From the given 4 tables we get the following transportation formulation of the trans-shipment problem:

To 1 2 A B C Supply0 (150)7511 (300)13 (150)25600

11 (300)0 (450)1315 35 750

13250 (300)33 11 (150)450

3513110 (450)13450

556575130 (450)450

450450600600600

From 1 2 A B CDemand

A buffer stock of 450 units, which is the total supply as well as total requirement in the original transportation problem, is added to each row a& column of the trans-shipment problem. The opyimal solution is also given in above table. The diagonal allocations in the table may be igonred since they have no physical meaning. The remaining allocations may be interpreted as follows:a) Plant 2 supplies 300units to plant 1. This increases the supply capacity of plant 1 to 450 units including the 150 units originally available in it.b) Plant 1 transports 300 units to distribution centre A & 150 units to B.c) Distribution centre A sends 150 units to C out of 300 units available in it.The total cost of trans-shipment = 11 300 + 13 150 + 11 300 + 11 150 = 10,200.