Transportation Problems

Assignment II  (Part – D)

Transshipment Problems

Q1.      Consider the following transshipment problem with two sources and two destination, the costs for shipment in rupees one given below. Determine the shipping schedule:

	S1	S2	D1	D2	Supply
S1	4	3	1	2	5
S2	5	2	3	4	25
D1	3	5	6	3
D2	2	4	4	5
Demand			20	10

Q2.      Consider a firm having two factories. The firm is to ship its products form the factory to three-retail stores. The number of units available at factories X and Y are 200 & 300 respectively. While those demanded at retail stores A B & C are 100, 150 & 250 respectively. Rather than shipping directly form factories to retail stores, it is asked to investigate the possibility of transshipment. The transportation cost per unit is given in the table

	Factory			Retail Store
Factory		X	Y	A	B	C	Available
	X	0	8	7	8	9	200
	Y	6	0	5	4	3	300
Retail Store	A	7	2	0	5	1
	B	1	5	1	0	4
	C	8	9	7	8	0
	Requirement			100	150	250

Answer: XX-500, XA-100, XB-100, YY-500, YB-50, YC-250, AA-500, BB-500, CC-500

Q3.      Consider the following transshipment problem with two sources and three destinations, the cost for shipments is given below. Determine the optimal shipping schedule.

Sources	Source			Destination
		S1	S2	D1	D2	D3	Supply
	S1	0	80	10	20	30	100+300
	S2	10	0	20	50	40	200+300
Destination	D1	20	30	0	4	10	300
	D2	40	20	10	0	20	300
	D3	60	70	80	20	0	300
	Demand	300	300	100 + 300	100 + 300	100 + 300

Transportation Problems

Assignment II  (Part – D)

Maximization Problems

Q1.      Solve the transportation problem to maximize profit & give criterion for optimality

	I	II	III	IV	Supply
A	40	25	22	33	100
B	44	35	30	30	30
C	38	38	28	30	70
Demand	40	20	60	30

Answer: Total Optimal Cost for transportation =5,130

Q2.      Solve the transportation problem to maximize profit & give criterion for optimality

	I	II	III	IV	Supply
A	40	25	22	33	100
B	44	35	30	30	30
C	38	38	28	30	70
Demand	90	20	60	40

Answer: Total Optimal Cost for transportation =7,200

Q3.      A departmental store whishes to purchase the following quantities of sarees:

Types of sarees	A	B	C	D	E
Quantity	150	100	75	250	200

Tenders are submitted by 4 different manufacturers who undertake to supply not more than the quantities mentioned below (all types of sarees combined):

Manufacturers	W	X	Y	Z
Total Quantity	300	250	150	200

The store estimates that its profit per saree will vary with the manufacturers as shown in the following matrix

Manufactures	Sarees
	A	B	C	D	E
W	275	350	425	225	150
X	300	325	450	175	100
Y	250	350	475	200	125
Z	325	275	400	250	175

            How should the order be placed?

Answer: Total Optimal Cost for transportation =775

Q4.      Solve the transportation problem to maximize profit & give criterion for optimality

	I	II	III	IV	Supply
A	12	18	6	25	200
B	8	7	10	18	500
C	14	3	11	20	300
Demand	180	320	100	400

Answer: Total Optimal Cost for transportation =15,400

Q5.      Solve the transportation problem to maximize profit & give criterion for optimality

	I	II	III	IV	Supply
A	40	25	22	33	200
B	44	35	30	30	60
C	38	38	28	30	140
Demand	80	40	120	60

Answer: Total Optimal Cost for transportation =10,260