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Total no. of Pages:
Register Number: 7196
Name of the Candidate:
P.G.Diploma EXAMINATION, 2013
(APPLIED OPERATIONS RESEARCH)
(PAPER-III)
130. INVENTORY, QUEING AND SIMULATION MODELS
May) (Time: 3 Hours
Maximum: 100 Marks
Answer any five questions (5×20=100)
All questions carry equal marks
1. i) State the different types of approach in inventory models used in OR . (5)
ii) Derive the EOQ formula of the inventory model with out shortages. (5)
iii) An air craft company uses rivets at an approximate customer rate of 2 500 kg per year. The rivets cost `. 30 per kg and the company personnel estimate that it costs Rs.130 to place an order and the inventory carrying cost is 10% per year. How frequently should orders for rivets be placed and what quantities should be ordered. (10)
2. i) The probability distribution of monthly sales of a certain item is as follows:
The cost of carrying inventory is `.30 per unit per month and the cost of unit shortage is `.70 per month. Determine the optimum stock level with minimized the total expected cost. (10)
ii) A manufacturer of water filters purchases components in EOQ of 850 units per order. Total demand averages 12000 components per year and MAD is 32 units. If the manufacturer carries a safety stock of units 80 units, what service level is provided by him. (10)
3. i) The uniform annual demands for two bulky items are 90 units and 160 units
respectively. The carrying costs are ` .250 and ` .200 per ton per year, and
setup costs are `. 50 and `. 40 per production respectively. No shortages are allowed. Space considerations restrict the average amount inventory of both items to 4000c.ft. A ton of the first item occupies 1000 c. ft., and a ton of second item occupies 500 c.ft. Find the optimal lot size. (10)
ii) A baking company sells cake by the pound. It makes a profit of 50 paisa a pound on every pound sold on the day it baked. It disposes of all cakes not sold on the date it is baked at a loss of 12 paisa a pound. If the demand is known to be rectangular between 2000 and 3000 pounds determine the optimum daily amount baked. (10)
4. i) Explain using the flow chart about the operation of event increment simulation
model of a single server queuing system. (10)
ii) A printing press receives a different number of orders each day. The time required for composing and printing varies from order to order. There is sufficient number of printing machines and the orders usually do not have to wait for printing. The critical time is that of composing. The manger of the press is interested in knowing the number of composers he should have so that the sum of the cost of composer idle time and the cost of orders is minimized, the following data regarding the number of orders per day and the composing times are available.
The press works for eight hours per day, but a composer can work effectively for only seven hours a day. An order is accepted only if it can be processes within two days. The wages of the composer are `.3 per hour, while the cost of orders back order comes to `. 5 per hour. (10)
5. i) Enumerate the derivation results of M/M/1:FCFS/Infinite — queuing model
problem. (10)
ii) A mechanic repairs four machines. The mean time between service requirements is 5 hours for each machine and forms an exponential distribution. The mean repair time is 1 hour and also follows the same distribution pattern. Machine
down time costs `. 25 per hour and the mechanic cost `.55 per day.
a) Find the expected number of operating machines. (5)
b) Determine the expected down time cost per day. (5)
6. i) Briefly explain the Erlang family distribution.
ii) A firm is engaged in both shipping and receiving activities. The management is always interested in improving the efficiency of new innovations in loading and unloading procedure. The arrival distribution of trucks is found to be Poisson with the arrival rate of 4 trucks per hour. The service time distribution is exponential with unloading rate of 4 trucks per hour. Determine
a)Expected number of trucks in the queue (3)
b) Probability that the loading and unloading dock and workers will be idle. (3)
c) What reductions in waiting time are possible if loading and unloading is standardized. (4)
7. i) In a certain bank, the customers arrive according to Poisson distribution with a
mean of 4 per hour. From observations on the teller’s performance, the mean service time is estimated to be 10 minutes, with a variance of 25 minutes. It is felt that the Erlng would be reasonable assumption for the distribution of the teller’s service time. Also it is assumed that there is no limit on the number of customers. Bank officials wish to know, on the average, how long a customer must wait until he gets the service, and how many customers are waiting for service. (12)
ii) Differentiate the Q system and P system models with numerical examples. (8)
8. i) How the evaluation of spare inventory models differ from the conventional
material storage models like XYZ, YOS. (4)
ii) Explain the reason for measuring the safety stock in the purchasing model with example. (8)
iii) Explain the application of Monte Carlo simulation technique. (8)
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