LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE
FIFTH SEMESTER – APRIL 2008
CS 5503 – RESOURCE MANAGEMENT TECHNIQUES
Date : 030508 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PARTA
Answer all the questions: (10×2=20 marks)
 Define a general linear programming problem.
 Write the dual of the following problem:
 What is an assignment problem?
 Define degeneracy in a transportation problem.
 Define total elapsed time in a sequencing problem.
 What is meant by ‘activity’ and ‘event’ in network analysis?
 Explain economic order quantities in inventory problems.
 What are quantity discounts?
 Give an example of replacement situation.
 Define present worth of money in replacement models.
PARTB
Answer all the questions: (5×8=40 marks)
 a) Explain basic solution, basic feasible solution and optimal solution in a linear programming problem.
(OR)
 b) Use graphical method to solve the linear programming problem:
 a) Give the mathematical formulation of a transportation problem.
(OR)
 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 
 a) Mention the assumptions made in a sequencing problem.
(OR)
 b) A project schedule has the following characteristics:
Activity  Time
(in weeks) 
Activity  Time
(in weeks) 
12  4  56  4 
13  1  57  8 
24  1  68  1 
34  1  78  2 
35  6  810  5 
49  5  910  7 
 a) Explain the costs involved in inventory models.
(OR)
 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.
 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)
 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 
PARTC
Answer any TWO questions (2×20=40 marks)
 a) Solve by simplex method:
 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 
 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  a_{i} 
1  8  10  7  6  50 
2  12  9  4  7  40 
3  9  11  10  8  30 
b_{j}  25  32  40  23  120 
 b) The time estimates (in months) for the activities of a PERT network are given
below:
Activity:  12  13  14  25  35  46  56 
t_{o}:  1  1  2  1  2  2  3 
t_{m}:  1  4  2  1  5  5  6 
t_{p}:  7  7  8  1  14  8  15 
 Draw the network and determine the project length.
 Calculate the variance of the project.
 Find the probability that the project will be completed in 20 weeks:
 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
 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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