8/18/2019 Mid Semester Examination Solution to Question 1

1/1

1

2  7

3

4

6   5

203

40

8

4

2

10

9   30

50,000 liters/d   60,000 liters/d

90,000 liters/d

20,000 liters/d

1 3

2 4

56

7

60,000

60,000

60,000

40,000

20,000

20,00

50,000

50,000

40,000

90,000

Problem 1 (5 Marks)

The schematic of an oil pipeline network is shown below. The nodes represent pumping/receiving stations. The

distances between the nodes are given in the figure (not to scale). The cost of transportation is proportional to

the distance between the nodes.

As shown in the figure, the oil supply to the network is through nodes 1 and , while the demand is at node !and ". #onstruct a transshipment model for the least cost transportation of oil from nodes 1 and to nodes !

and ". $o not solve the resulting %&&.

&rovide the probable optimal solution to the problem through visual inspection and without resorting to any

calculations.

'ariables

1!, 1*, ", *, +", +, -, *!, *+

#osts

#1!, #1*, #", #*, #+", #+, #-, #*!, #*+

inimie

(1!.#1!) 0 (1*.#1*) 0 (".#") 0

(*.#*) 0 (+".#+") 0 (+.#+) 0(-.#-) 0 (*!.#*!) 0 (*+.#*+)

#onstraints

1! 0 1* 21 +3333* 0 " 2 3333

1!0!0*! $! 43333

" 0 +" $" !3333+ !

*+ 0 *! * 0 1*

*+ +" 0 +