LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

AK 1

           B.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

FIFTH SEMESTER – APRIL 2008

CS 5503 – RESOURCE MANAGEMENT TECHNIQUES

 

 

 

Date : 03-05-08                  Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART-A

Answer all the questions:                                                                  (10×2=20 marks)

1. Define a general linear programming problem.
2. Write the dual of the following problem:

1. What is an assignment problem?
2. Define degeneracy in a transportation problem.
3. Define total elapsed time in a sequencing problem.
4. What is meant by ‘activity’ and ‘event’ in network analysis?
5. Explain economic order quantities in inventory problems.
6. What are quantity discounts?
7. Give an example of replacement situation.
8. Define present worth of money in replacement models.

 

PART-B

Answer all the questions:                                                                  (5×8=40 marks)

1. a) Explain basic solution, basic feasible solution and optimal solution in a linear programming problem.

(OR)

1. b) Use graphical method to solve the linear programming problem:

1. a) Give the mathematical formulation of a transportation problem.

(OR)

1. b) A computer centre has three expert programmers. The centre wants three

application programs to be developed. The computer time in minutes required by

the experts for the application programs is given below. Assign the programmers to the programs in such a way that the total computer time is minimum.

Programs

Programmers		A	B	C
	1	120	100	80
	2	80	90	110
	3	110	140	120

1. a) Mention the assumptions made in a sequencing problem.

(OR)

1. b) A project schedule has the following characteristics:

Activity	Time (in weeks)	Activity	Time (in weeks)
1-2	4	5-6	4
1-3	1	5-7	8
2-4	1	6-8	1
3-4	1	7-8	2
3-5	6	8-10	5
4-9	5	9-10	7

 

 

 

 

1. a) Explain the costs involved in inventory models.

(OR)

1. b) A stockist has ot supply 12,000 units of a product per year to his customer. The

demand is fixed and known and shortages are not allowed. The inventory holding cost is Re 0.20 per unit per month and the ordering cost per order is Rs.350. Determine i) the optimal lot size and ii) the time between the orders.

 

1. a)  A firm is considering replacement of a machine, whose cost price is Rs.12,200 and the scrap value Rs.200. The running costs are found from experience to be as follows:

Year:	1	2	3	4	5	6	7
Running cost (Rs.):	200	500	800	1200	1800	2500	3200

When should be the machine be replaced?

(OR)

1. b) The yearly cost of two machines A and B when money value is neglected is

given below. Find their cost patterns if money value is 10% per year and hence find which machine is more economical.

Year:	1	2	3
Machine A (Rs):	1800	1200	1400
Machine B (Rs):	2800	200	1400

 

PART-C

Answer any TWO questions                                                            (2×20=40 marks)

1. a) Solve by simplex method:

1. b) Find the sequence that minimises the total time required in performing the following jobs on three machines in the order ABC. Processing times (in hours) are given in the following table:

Jobs:	1	2	3	4	5
Machine A :	8	10	6	7	11
Machine B :	5	6	2	3	4
Machine C:	4	9	8	6	5

1. a) The following table gives the unit cost matrix with supplies a_i, i=1,2,3 and demands b_j, j=1,2,3,4. Find the optimal solution to minimise the cost.

Destination

Source	1	2	3	4	ai
1	8	10	7	6	50
2	12	9	4	7	40
3	9	11	10	8	30
bj	25	32	40	23	120

1. b) The time estimates (in months) for the activities of a PERT network are given

below:

Activity:	1-2	1-3	1-4	2-5	3-5	4-6	5-6
to:	1	1	2	1	2	2	3
tm:	1	4	2	1	5	5	6
tp:	7	7	8	1	14	8	15

1. Draw the network and determine the project length.
2. Calculate the variance of the project.

• Find the probability that the project will be completed in 20 weeks:

1. a) A person is considering to purchase a machine for his factory. The related data about the alternative machines are as follows:

	Machine A	Machine B	Machine C
Present investment (Rs):	1000	12000	15000
Total annual cost (Rs):	2000	1500	1200
Salvage value(Rs):	500	1000	1200
Life (years):	10	10	10

As an advisor of the company, you have been asked to select the best machine considering 12% normal rate of return per year, given, present with factor at 12% for 10 years = 5.65 present worth factor at 12% for 10^th year = .322

1. b) The demand for a commodity is 100 units per day. Every time an order is

placed, a fixed cost of Rs.400 is incurred. Holding cost is Re .08 per unit per day.

If the lead time is 13 days, determine the economic lot size and the reorder point.

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

NA 14

FIFTH SEMESTER – November 2008

CS 5503 – RESOURCE MANAGEMENT TECHNIQUES

 

 

 

Date : 10-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION – A   ( 10 x 2 = 20 Marks)

Answer ALL questions.

 

1. Discuss the slack and surplus variables.
2. What are basic feasible solution and the unbounded solution?
3. Write the dual of the following LPP.

Minimize : z = 3x + 2y

Subject to :     x + y ≥  4;         3x+y ≥20;         x, y ≥ 0.

1. When is an artificial variable introduced in the constraints? Explain with illustration.
2. Obtain the initial solution of the following transportation problem by the north-west corner rule given that (i) the requirements are 40, 90 and 100 units and (ii) the supply are 90, 70  and 70.

 

	Source
Destination	S1	S2	S3
D1	15	28	27
D2	24	24	25
D3	22	25	20

 

1. When is transportation problem said to be unbalanced?  Given an example.
2. What does PERT stand for? What is the objective of PERT?
3. State job sequencing problem.
4. What are reorder level and reorder point?
5. What are the three replacement policies?

 

SECTION – B   ( 5 x 8 = 40 Marks)

Answer ALL questions.

1. (a). Solve the following LPP graphically.

 

Maximize z = 3x₁ + 2 x₂

Subject to       5x₁ +   x₂ ≥10

x₁ +   x₂ ≥6

x₁ + 4x₂ ≥12

x₁ , x₂ ≥ 0

(OR)

(b). Show that the LPP given below has unbounded solution.

 

Maximize z = 2x₁ + x₂

Subject to     x₁ – x₂ ≤ 10

2x₁ – x₂ ≤ 40

x₁ , x₂ ≥ 0

 

 

1. (a). Solve the following transportation problem.

 

Destination	Origin				Requirement
	A	B	C	D
I	7	4	3	4	15
II	3	2	7	5	25
III	4	4	3	7	20
IV	9	7	5	3	40
	12	28	35	25	100

 

(OR)

 

(b). The following table gives the profit earned by doing certain jobs on different machines.  Only one job is permitted on a machine.  Assign the jobs to the machines so as to maximize the profit.

 

Machines
Jobs		M1	M2	M3	M4
	J1	210	84	120	35
	J2	180	168	560	105
	J3	210	120	168	42
	J4	63	84	112	28

 

1. (a). Draw the network diagram, find the critical path and the Expected project duration for the project details given below.

 

Activity	1-2	1-3	1-4	2–4	2-5	3-5	4-5
Optimistic Time	2	3	4	8	6	2	2
Most likely Time	4	4	5	9	8	3	5
Pessimistic Time	5	6	6	11	12	4	7

 

(OR)

 

(b). The time required for printing and binding of books on respective machines are given below.  Determine the order in which the jobs to be processed in order to minimize the total time required to complete the job.

 

Book	1	2	3	4	5	6
Printing time on machine A	5	7	2	6	3	4
Binding time on machine B	2	5	4	9	1	3

 

1. (a). The annual demand for an item is 3200 units.  The unit cost is Rs.6 and the inventory carrying cost is 25% per annum.  If the cost of one procurement is Rs. 150, determine (i) economic order quantity (ii) Number of orders per year and (iii) the optimal cost.

 

(OR)

 

(b).  A company buys 500 boxes which is a three month supply.  The cost per box is Rs.125 and the ordering cost is Rs.150.  The inventory carrying cost is estimated at 20% of unit value.  (i)  What is the total annual cost of the existing inventory policy?  (ii)  How much money could be saved by employing the economic order quantity?

 

 

 

1. (a). Derive the replacement policy of an item whose maintenance cost increases with time when the money value is not changed, on the assumption the time is continuous.

 

(OR)

 

(b). Obtain the replacement policy of an item whose maintenance cost increases with time when the money value is not changed, on the assumption the time is discrete.

 

SECTION – C   (2x 20 = 40 Marks)

Answer TWO questions.

 

1. Using the simplex method, solve the following problem.

 

Maximize  z = 2x₁ + 3x₂

Subject to the constraints

-x₁ + 2x₂   ≤ 4

x₁ +  2x₂  ≤ 6

x₁ + 3x₂   ≤ 9

x_1, x₂ ≥ 0.

 

1. The transportation costs of items per unit manufactured by Glass Company from four different locations to four different warehouses are given below.  Find the allocation of items from locations to warehouses in order to minimize the transportation cost.

 

		Locations of Company				Requirement
		L1	L2	L3	L4
Warehouses	W1	20	36	10	28	10
	W2	40	20	45	20	4
	W3	75	35	45	50	6
	W4	30	35	40	25	5
	Availability	13	10	6	6

 

1. Machine X costs Rs.9000. The annual operating costs are Rs.200 for the first year and the increase by Rs.2000 every year.  Determine the best age at which to replace the machine. If the optimum replacement policy is followed, what will be the average yearly cost of owning and operating the machine?  When the machine X is one year old, machine Y is available at the cost of Rs.10000 and the annual operating costs of Y are Rs.400 for the first year and then increases by Rs.800 every year. Is it necessary to replace X by Y? If so, when?

 

 

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