LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc.
|
DEGREE EXAMINATION –COMPUTER SCIENCE
FIFTH SEMESTER – APRIL 2007
CS 5503 – RESOURCE MANAGEMENT TECHNIQUES
Date & Time: 30/04/2007 / 1:00 – 4:00 Dept. No. Max. : 100 Marks
Section A
Answer ALL the questions. (10 x 2 = 20)
- Define feasible solution.
- What is a slack variable?
- Define basic variable.
- Find the Dual for the following
Maximize
Subject to
- Define immediate predessor and immediate successor.
- Define critical path and free float.
- Define total elapsed time.
- Explain indirect cost with an example.
- What do you mean by lot-size inventory?
- Define depreciation value.
Section B
Answer ALL the questions. (5 x 8 = 40)
- (a) A firm manufactures three types of products A, B and C and sells them at a profit of Rs.2 on type A, Rs.3 on type B and Rs.4 on type C. Each product is processed on three machines M1, M2 and M3. Type A requires 1 minute of processing time on M1, 2 minutes on M2 and 1 minute on M3. Type B requires 1 minute on each machine M1, M2 and M3. Type C requires 2 minutes on M1, 1 minute on M2 and 2 minutes on M3. Machine M1 is available for not more than 6 hrs 40 minutes, machine M2 is available for 10 hrs while machine M3 is available for 4 hrs 20 minutes during any working day. Formulate the mathematical model for the problem.
(or)
(b) Apply graphical method to solve LPP.
Maximize
Subject to
- (a) Find the initial basic feasible solution for the following transportation problem by,
(i) Least Cost method (ii) Vogel’s Approximation method.
Distribution Centers
| D1 | D2 | D3 | D4 | Availability | |
| S1 | 11 | 13 | 17 | 14 | 250 |
| S2 | 16 | 18 | 14 | 10 | 300 |
| S3 | 21 | 24 | 13 | 10 | 400 |
| Demand | 200 | 225 | 275 | 250 | 950 |
Origin
(or)
(b) Solve the following travelling salesman problem.
To
| A | B | C | D | |
| A | – | 46 | 16 | 40 |
| B | 41 | – | 50 | 40 |
| C | 82 | 32 | – | 60 |
| D | 40 | 40 | 36 | – |
From
- (a) Find the sequence that minimizes the total elapsed time required to complete the following task on the machines M1 and M2 in the order M1M2. Find also the minimum total elapsed time (days).
| Task | A | B | C | D | E | F | G | H | I |
| M1 | 2 | 5 | 4 | 9 | 6 | 8 | 7 | 5 | 4 |
| M2 | 6 | 8 | 7 | 4 | 3 | 9 | 3 | 8 | 11 |
(or)
(b) Write the algorithm for forward pass calculation.
- (a) A project has the following time schedule:
| Activity | Duration (months) |
| 1-2 | 2 |
| 1-3 | 2 |
| 1-4 | 1 |
| 2-5 | 4 |
| 3-6 | 8 |
| 3-7 | 5 |
| 4-6 | 3 |
| 5-8 | 1 |
| 6-9 | 5 |
| 7-8 | 4 |
| 8-9 | 3 |
Construct the network and compute
(i) Total float for each activity.
(ii) Critical path and its duration.
(or)
(b) The annual demand for an item is 3200 units. The unit cost is Rs.6/- and inventory carrying charges 25% per annum. If the cost of one procurement is Rs.150/- determine (i) Economic order quality (ii) time between two consecutive orders (iii) number of order per year (iv) the optimal total cost.
- (a) The demand for an item is 18,000 units per year. The holding cost per unit time is Rs. 1.20 and the cost of shortage is Rs. 5.00, the production cost is Rs. 400. Assuming that replenishment rate is instantaneous, determine the optimal order quality.
(or)
(b) Let the value of the money be 10% per year and suppose that machine A is replaced after every 3 years whereas machine B is replaced after every 6 years. The yearly cost of both the machines is given as under:
| Age | 1 | 2 | 3 | 4 | 5 | 6 |
| Machine A | 1000 | 200 | 400 | 1000 | 200 | 400 |
| Machine B | 1700 | 100 | 200 | 300 | 400 | 500 |
Determine which machine should be purchased?
Section C
Answer any TWO questions. (2 x 20 = 40)
- (a) A firm produces an alloy having the following specification,
(i) Specific gravity £ 0.98
(ii) Chromium ³ 8%
(iii) Melting point ³
Raw materials A, B and C having the properties shown in the table can be used to make the alloy.
Raw material
| Property | A | B | C |
| Specific gravity | 0.92 | 0.97 | 1.04 |
| Chromium | 7% | 13% | 16% |
| Melting point |
Cost of the various raw material per unit ton are: Rs.90 for A, Rs.280 for B and Rs.40 for C. Find the proportions in which A, B and C be used to obtain an alloy of desired properties while the cost of raw materials is minimum.
(b) Solve the following by simplex method.
Maximize
Subject to
and then find its dual. (6 + 14)
- (a) Five workers are available to work with the machines and the respective costs (in rupees) associated with each worker-machine assignment is given below. A sixth machine is available to replace one of the existing machines and the associated costs are also given below:
| Machines | ||||||
| Workers | M1 | M2 | M3 | M4 | M5 | M6 |
| W1 | 12 | 3 | 6 | – | 5 | 8 |
| W2 | 4 | 11 | – | 5 | – | 3 |
| W3 | 8 | 2 | 10 | 9 | 7 | 5 |
| W4 | – | 7 | 8 | 6 | 12 | 10 |
| W5 | 5 | 8 | 9 | 4 | 6 | – |
- Determine whether the new machine can be accepted?
- Determine also optimal assignment.
(b)We have four jobs of which have to go through the machines M1, M2… M6 in the
order M1, M2… M6. Processing time (in hrs) is given below:
| Machines | ||||||
| M1 | M2 | M3 | M4 | M5 | M6 | |
| A | 18 | 8 | 7 | 2 | 10 | 25 |
| B | 17 | 6 | 9 | 6 | 8 | 19 |
| C | 11 | 5 | 8 | 5 | 7 | 15 |
| D | 20 | 4 | 3 | 4 | 8 | 12 |
Determine a sequence of these four jobs that minimizes the total elapsed time.
(12 + 8)
- (a) A small project is composed of seven activities whose time estimates are listed in the table
as follows.
| Activity | 1-2 | 1-3 | 2-4 | 2-5 | 3-5 | 4-6 | 5-6 |
| t0 | 1 | 1 | 2 | 1 | 2 | 2 | 3 |
| tm | 1 | 4 | 2 | 1 | 5 | 5 | 6 |
| tp | 7 | 7 | 8 | 1 | 14 | 8 | 15 |
You are required to
- Draw the project network.
- Find the expected duration and variance of each activity.
- Calculate the early and late occurrence for each event and the expected project length.
- Calculate the variance and standard deviation of the project length.
(b) A newspaper boy buys paper for 30 paise each and sells them for 70 paise. He cannot return
unsold newspaper. Daily demand has the following distribution.
| No of customers | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 |
| Probability | 0.01 | 0.03 | 0.06 | 0.10 | 0.20 | 0.25 | 0.15 | 0.10 | 0.05 | 0.05 |
If each boy’s demand is independent of the previous day’s how many papers should he order each day?
(c) The cost of a machine is Rs. 6100 and its scrap value is Rs. 100. The maintenance costs
found from experience are as follows:
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Main cost (Rs) | 100 | 250 | 400 | 600 | 900 | 1200 | 1600 | 2000 |
When should the machine be replaced? (10 + 4 + 6)
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