Q7/13O/03-14 Reg. No

St. Joseph’s College of Arts & Science (Autonomous) St. Joseph’s College Road, Cuddalore – 607001 EPMT705S - OPERATION RESEARCH

Time : 3 hrs

Max Marks :75 SECTION – A (5X2=10) Answer ALL Questions

1. Write the significance of using PERT and CPM. 2. Define set-up cost. 3. Explain transient state. 4. Define progressive failure. 5. Write any two advantages of simulation. SECTION – B (3X5=15) Answer any THREE Questions 6. Write basic difference between PERT and CPM. 7. The production department for a company requires 3600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs.36 and the cost of carrying Inventory is 25 per cent of the investment in the inventories. The price is Rs10 per kg .The purchase Manager wishes to determine an ordering policy for raw material. 8. Write the classification of queuing models. 9. A firm is considering replacement of a machine, whose cost price is Rs.12200 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 8

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Q7/13O/03-14 Running 200 500 800 1200 1800 2500 3200 4000 cost When should the machine be replaced? 10. A company manufactures 200 motor cycles per day. Depending upon the availability of Raw materials and other conditions the daily production has been varying from 196 motor cycles to 204 motor cycles, whose probability distribution is as given below: Production/day 196 probability 0.05

197 0.09

198 0.12

199 0.14

200 0.20

201 0.15

202 0.11

203 0.08

204 0.06

The motor cycles are transported in specially designed threestoreyed lorry that can accommodate only 200 motor cycle. Using the following random number 82,89,78,24,52,53,61,18,45,04,23,50,77,27,54,10, simulate the process to find out: a) The average number of motor cycles waiting in the factory? b) The average number of empty space in the lorry? SECTION - C (5X10=50) Answer ALL Questions 11. a) An established company has decided to add a new product to its line. It will buy the product from a manufacturing concern, package it, and sell it to a number of distributor selected in geographical basis. Market research has indicated the volume expected and the size of sales force required. The steps shown in the following table are to be planned. Activity A B Predecessor - A Duration(days) 6 4

C D E F G H I J B A D E - G J,H 7 2 4 10 2 10 6 13

K A 9

L M C,K I,L 3 3

(or) b) The data for a PERT network is displayed in the table below.

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Q7/13O/03-14 Determine the critical path and expected duration of complition of the entire project. What is the probability that the project duration will exceed 60 days. Activity sequence t0 tm tp

1-2 1-3 1-4 2-3 2-5 3-4 3-6 4-6 5-6 2 4 6

6 6 6

6 12 24

2 5 8

11 14 23

15 24 45

3 6 9

9 15 27

4 10 16

12. a) A chemical company holds its inventory of raw materials in special containers with each container occupying 10 sq. feet of space. There are only 5000sq. feet of storage space available. Each year this company uses 9000 special containers of raw materials, paying Rs.8 per container of raw material. If odering cost is Rs.40 per order and annual holding cost are Rs.20 percent of the average inventory value, how much is it worth for this company to increase its container of raw material storage area? (or) b) The demand for an item in a company is 18000 units per year, and the company can produce the item at a rate of 3000 per month. The cost of one setup is Rs.500 and the holding cost of one unit per month is 15 paise. The shortage cost of 1 unit is Rs.240 per year. Determine the optimum manufacturing quantity and the number of shortages. Also determine the manufacturing time and the time between setups. 13. a) Consider a self service store with one cashier. Assume poisson arrivals and exponential service times. Suppose that 9 customers arrive on average every 5 min and the cashier can serve 10 in 5 min. calculate the following i) Average number of customers queueing for service. ii) Probability of having 10 customers in the system. (or) b) An insurance company has 3 claims adjusters in its branch office. People with claims against the company are found to arrive in poisson fashion, at an average rate of 20 per 8hour day.

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Q7/13O/03-14 The amount of time an adjusters spends with a claimant is found to have a negative exponential with mean service time 40 mins. i) How many hours a week can an adjuster expect to spend with claimants? ii) Find the average time a claimant spend in the branch office? 14. a) Let the value of the money be assumed to be 10%per year and suppose that machine A is replaced after every 3 years where as machine B is replaced every 6 years. The yearly cost(in Rs) of both the machines are given below. Year Machine A Machine B

1 1000 1700

2 200 100

3 400 200

4 1000 300

5 200 400

6 400 500

Determine which machine should be purchased. (or) b) An engineering company is offered a material handling equipment A. It is priced at Rs.60000 including cost of installation and cost for operation and maintenance are estimated to be Rs.10000 for each of the first five years. increasing every year by Rs.3000 in the sixth and subsequent years. The company expects a return of 10% on all its investment. What is the optimal replacement period? 15. a) XYZ spare parts company wishes to determine the levels of stock it should carry for the items in its range. Demand is not certain and there is a lead time for stock replenishment. For one item X the following information is obtained : Demand (units/day) probability

3

4

0.10 0.20

5 0.30

6

7

0.30 0.10

Carrying cost (per unit/day) is Rs 2 , ordering cost (per order) is Rs 50, lead time for replenishment is 3 days. Stock on hand at the beginning run over a period of 10days with the objective of evaluating the inventory rule:

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Q7/13O/03-14 Order 15 units when present inventory plus any outstanding order falls below 15 units. The sequence of random numbers to be used is 0,9,1,1,5,1,8,6,3,5,7,1,2,9 using the first number for day one. (or) b) The automobile company manufactures around150 scooters. The daily production varies from 146 to 154 depending upon the availability of raw materials and other working conditions. Production 146 147 148 149 150 151 152 153 154 /day probability 0.04 0.09 0.12 0.14 0.11 0.10 0.20 0.12 0.08 The finished scooters are transported in a specially arranged lorry accommodating 150 scooters. Using following random numbers : 80,81,76,75,64,43,18,26,10,12,65,68,69,61,47. simulate the process to find out: i) What will be the average number of scooters waiting in the factory? ii) What will be the average number of empty space on the lorry?

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