LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE
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FIFTH SEMESTER – NOV 2006
CS 5503 – RESOURCE MANAGEMENT TECHNIQUES
(Also equivalent to CSC 509)
Date & Time : 30-10-2006/9.00-12.00 Dept. No. Max. : 100 Marks
SECTION A
Answer ALL the questions. (10 x 2 = 20)
- Define Basic Variables.
- Define an optimal solution.
- Find the Dual for the following
Maximize
Subject to
- Write down the route condition for the traveling salesman problem.
- Define total elapsed time and idle time.
- Explain planning and scheduling.
- Define critical path and total float.
- Explain optimistic time estimate.
- Define shortage cost and setup cost.
- Define present worth factor.
SECTION B
Answer ALL the questions. (5 x 8 = 40)
- (a) A firm produces three products. These products are processed on three different machines. The time required to manufacture one unit of each of the three products and the daily capacity of the three machines are given in the table below:
| Time per unit (minutes) | ||||
| Machine | Product 1 | Product 2 | Product 3 | Machine capacity(min/day) |
| M1 | 2 | 3 | 2 | 440 |
| M2 | 4 | – | 3 | 470 |
| M3 | 2 | 5 | – | 430 |
It is required to determine the number of units to be manufactured for each product daily. The profit per unit for product 1, 2, and 3 is Rs.4, Rs.3, and Rs.6 respectively. It is assumed that all the amount produced are consumed in the market. Formulate the mathematical model for the problem and find it’s dual.
(or)
(b)Solve the following LPP by graphical method
Maximize
Subject to
- (a) The owner of a small machine shop has four mechanics available to assign jobs for the day. Five jobs are offered with expected profit for each mechanic on each job which are as follows:
Job
| Mechanic | A | B | C | D | E |
| 1 | 62 | 78 | 50 | 101 | 82 |
| 2 | 71 | 84 | 61 | 73 | 59 |
| 3 | 87 | 92 | 111 | 71 | 81 |
| 4 | 48 | 64 | 87 | 77 | 80 |
Find by using the assignment method, the assignment of mechanics to the job that will result in a maximum profit. Which job should be declined?
(or)
(b) (i) Write the algorithm for processing n jobs on 3 machines.
(ii) Find the sequence that minimizes the total elapsed time required to complete the following task on the machines in the order 1-2-3. Find also the minimum total elapsed time (hrs) and the idle time on the machines.
| Task | A | B | C | D | E | F | G |
| Machine 1 | 3 | 8 | 7 | 4 | 9 | 8 | 7 |
| Machine 2 | 4 | 3 | 2 | 5 | 1 | 4 | 3 |
| Machine 3 | 6 | 7 | 5 | 11 | 5 | 6 | 12 |
- (a) Construct the network for the project whose activities are given below and compute the total, free and independent float for each activity and hence determine the critical path and the project duration.
| Activity | 1-2 | 1-3 | 1-5 | 2-3 | 2-4 | 3-4 | 3-5 | 3-6 | 4-6 | 5-6 |
| Duration (days) | 8 | 7 | 12 | 4 | 10 | 3 | 5 | 10 | 7 | 4 |
(or)
(b) The following table shows the job of a network along with their time estimates.
| Job | 1-2 | 1-6 | 2-3 | 2-4 | 3-5 | 4-5 | 5-8 | 6-7 | 7-8 |
| t0 | 1 | 2 | 2 | 2 | 7 | 5 | 3 | 5 | 8 |
| tm | 7 | 5 | 14 | 5 | 10 | 5 | 3 | 8 | 17 |
| tp | 13 | 14 | 26 | 8 | 19 | 17 | 9 | 29 | 32 |
Draw the project network and find the probability that the project is completed in 40 days. [given that].
- (a) The following time cost applies to a project. Use it to arrive at the network associated with completing the project in the minimum time at minimum cost.
| Normal Crash | ||||
| Activity | Time (days) | Cost (Rs) | Time (days) | Cost (Rs) |
| 1-2 | 2 | 800 | 1 | 1400 |
| 1-3 | 5 | 1000 | 2 | 2000 |
| 1-4 | 5 | 1000 | 3 | 1800 |
| 2-4 | 1 | 500 | 1 | 500 |
| 2-5 | 5 | 1500 | 3 | 2100 |
| 3-4 | 4 | 2000 | 3 | 3000 |
| 3-5 | 6 | 1200 | 4 | 1600 |
| 4-5 | 3 | 900 | 2 | 1600 |
(or)
(b) (i) The demand for an item is 12,000 per year and shortages are allowed. If the unit cost is Rs. 15 and the holding cost is Rs. 20 per year per unit. Determine the optimum total yearly cost. The cost of placing one order is Rs. 6000 and the cost of one shortage is Rs. 100 per year (ii) Define lot-size inventories.
- (a) (i) 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 boys demand is independent of the previous days how many papers should he order each day?
(ii) State the reasons for maintaining inventory.
(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 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) Use simplex method to solve the LPP
Maximize
Subject to
(b) Find the optimal solution for the following transportation problem using Modi method. Destination
| 1 | 2 | 3 | 4 | Supply | |
| 1 | 14 | 56 | 48 | 27 | 70 |
| 2 | 82 | 35 | 21 | 81 | 47 |
| 3 | 99 | 31 | 71 | 63 | 93 |
| Demand | 70 | 35 | 45 | 60 | 210 |
Origin
(10 + 10)
- (a) We have five jobs, each of which must go through the two machines A and B in the order AB. Processing times in hours are given in the table below.
| Job | 1 | 2 | 3 | 4 | 5 |
| Machine A | 3 | 8 | 5 | 7 | 4 |
| Machine B | 4 | 10 | 6 | 5 | 8 |
(c) the following data is pertaining to a project with normal time and crash time.
| Normal Crash | ||||
| Activity | Time (hrs) | Cost (Rs) | Time (hrs) | Cost (Rs) |
| 1-2 | 8 | 100 | 6 | 200 |
| 1-3 | 4 | 150 | 2 | 350 |
| 2-4 | 2 | 50 | 1 | 90 |
| 2-5 | 10 | 100 | 5 | 400 |
| 3-4 | 5 | 100 | 1 | 200 |
| 4-5 | 3 | 80 | 1 | 100 |
(i) If the indirect cost is Rs.100 per day find the least cost schedule.
(ii) What is the minimum duration? (7 + 13)
- (a) Define Lead time and Reorder level.
(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.
(c) A taxi owner estimates from his past records that the costs per year for operating a taxi whose purchase price when new is Rs. 60,000 are as given below:
| Age | 1 | 2 | 3 | 4 | 5 |
| Operating Cost (Rs) | 10,000 | 12,000 | 15,000 | 18,000 | 20,000 |
After 5 years, the operating cost is Rs.6000k where k = 6, 7, 8, 9, 10 (k denoting age in years). If the resale value decreases by 10% of purchase price each year, what is the best replacement policy? Cost of the money is zero. (4 + 8 + 8)