WAITING LINE NUMERICALS (A)

Qs.1 : A bank is opening a window for customer service. It is estimated that customer will arrive at the rate of 15 per hour. The staff at the window can service 1 customer in 3 minutes. Assuming Poissons arrivals & exponential service, find the following –

1.1 Utilization of the window. 1.2 Average number in waiting line.1.3 Average number in the system. 1.4 Average waiting time in line.1.5 Average waiting time in the system including service. 1.6 Present level of service for 3 customers limit in the system.

------------------------------------------------------------------------------------------------Qs.2 : A departmental store has only 1 cashier. Customers arrive at a rate of 20 per hour. The average number of customers that can be handled by the cashier is 24 per hour. Assume conditions of single channel model. Find –

2.1 Probability that cashier is idle.2.2 Average number of customers in the system.2.3 Average time a customer spends in the system. 2.4 Average number of customers in the queue.2.5 Average time a customer spends in the queue.

------------------------------------------------------------------------------------------------Qs.3 The customers in a tailoring house follow Poissons distribution with mean arrival rate of 12 per hour. Customers are attended by tailor on First come First served basis. The time taken by tailor to attend a customer is exponentially distributed with a mean of 4 minutes. Find –

3.1 The utilization parameter.3.2 Probability that queuing system is idle.3.3 Average time tailor is free on 8 hours working day.3.4 Probability of having 5 customers in the shop at a point of time.3.5 What is the number of customers in the shop ?3.6 Expected number of customers waiting for tailor’s services.3.7 Expected waiting time in the queue.3.8 Expected time in the shop by a customer.

Qs.4 Mean rate of arrival of planes at an airport is 20 per hour & the actual number of arrivals follows a Poissons distribution. The airport can land on an average 60 planes per hour in good weather & 30 planes per hour in bad weather. During congestion planes circle in the air awaiting clearance for landing after the planes arrived earlier.

4.1 How many planes shall be circling on an average in good & in bad weather?4.2 How much time a plane shall be taking for circling and in landing in good & in bad weather ?

-----------------------------------------------------------------------------------------------------Qs. 5 BBA – IP : 12 / 2006 & 12 / 2005

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INVENTORY MANAGEMENT NUMERICALS (B)

Qs.1 Find the economic order quantity, reorder point & total annual cost from the Data furnished below: Annual demand = 1000 units ; Ordering cost = Rs. 5 per order ; Holding cost=Rs.1.25 per unit per year; Lead time=5 days; Cost=Rs. 12.5 per unit

Qs. 2 A company uses 12000 units of raw materials annually costing Rs. 1.25 per unit. Placing each order costs Rs. 15 & the carrying cost is 15 % per year per unit of inventory cost. Find the economic order quantity.---------------------------------------------------------------------------------------------------Qs. 3 An organization requires 1000 units per month. Ordering cost is estimated to be Rs. 50 per order. In addition to Re. 1 the carrying costs are 10 % per unit of inventory cost. The purchase price is Rs. 10 per unit. Find the economic lot size to be ordered & the total cost.

Qs. 4 The following information is available about an enterprise:Annual requirement=24000 units; Lead time=10 days; Working days=240per year In the past 2 years the demand has gone to 140 units per day. Calculate the required reorder level with normal and increased demand. -----------------------------------------------------------------------------------------------------Qs. 5 A company uses annually 48000 units of a raw material costing Rs. 1.25 per unit. Placing each order costs Rs. 45 & carrying cost is 15 % of the inventory cost. Find the economic order quantity. Suppose the company follows economic order quantity purchasing policy & it operates for 300 days a year and the procurement time is 12 days with safety stock of 500 units. Find the reorder point, maximum, minimum & average inventory. -----------------------------------------------------------------------------------------------------Qs. 6 A factory is manufacturing an item in batches. The following details are available :- Cost of setting-up of machine & tools : Rs. 1400 /- Annual rate of depreciation, interest, etc. : 18 % Consumption of parts in assembly shop : 120 per month Processing of each part : 6 hours on the machine Labour rate : Rs. 20 per day for 8 hours Material cost : Rs. 5 per kg ; Weight of each item : 4 kg Overhead on each item is allocated at 120 % of prime cost. Find

(a) Economic batch size for machining(b) Duration of machine run, assuming machine loading factor as 90 % .

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Qs. 7 Perform ABC analysis on the following items of inventory :

Item Annual Consumption, Units Price per unit, Rs.A 300 0.10B 2800 0.15C 30 0.10D 1100 0.05E 40 0.05F 220 1.00G 150 0.05H 800 0.05I 600 0.15J 80 0.10

CONTROL CHARTS NUMERICALS :

Qs. 1 - The normal diameter of a shaft is 1.5” with standard deviation of 0.02”. The sample size was 10. Construct the control chart showing the central line and 2 control limits.---------------------------------------------------------------------------------------------------

Qs. 2- Ten samples each of size 50 were inspected, the results of the inspection are furnished below. Draw a fraction defective chart (p-chart) and state your conclusion.

Sample No. 1 2 3 4 5 6 7 8 9 10No. of Defects 2 3 2 0 2 3 2 1 2 3Fraction Defective 0.04 0.06 0.04 0 0.04 0.06 0.04 0.02 0.04 0.06

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Qs. 3 - Six consecutive lots received from a vendor were inspected by sampling process by the buyer. The sample size was varied as per variation in the lot size. The number of defectives of each sample were recorded as under:

Sample No. 1 2 3 4 5 6Lot Size 2850 1860 480 970 4385 2568Sample Size 125 125 50 80 200 125No. of Defects 1 3 - 2 4 1

Construct a control chart for fraction defectives and no. of defectives.---------------------------------------------------------------------------------------------------

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Qs. 4 - For testing the quality of equipment in a plant, the Inspector selected at random 10 samples of 200 equipment each. The number of defective equipment in each sample was as follows:

Sample No. 1 2 3 4 5 6 7 8 9 10 TotalNo. of Defectives 8 14 21 35 47 28 16 22 7 2 200

Draw a fraction defective quality chart showing the upper and lower control limits. Also show above sample data in this chart and draw your conclusions about the quality of equipment.---------------------------------------------------------------------------------------------------

Qs. 5 – A machine is manufacturing a brass item whose standard weight is 2 kg. Ten samples of 5 items each were taken after every 2 hours which revealed the following :

Sample No. 1 2 3 4 5 6 7 8 9 10Mean Wt., kg 2.00 2.10 2.15 2.09 2.04 2.05 2.00 1.90 2.17 1.95Range, kg 0.20 0.25 0.30 0.20 0.20 0.25 0.05 0.10 0.15 0.20

Draw a control chart for the mean & range. Examine the quality of the product is under control.

Qs. 6 BBA – IP : 12 / 2010

Qs. 7 BBA – IP : 12 / 2010

ANSWERS

Waiting line model

A : 1.1 – 75% ; 1.2 – 2.25 Customers ; 1.3- 3customer; 1.4 - 9min ; 1.5 - 12 min 1.6 - 69%

A : 2.1 – 17% ;2.2 - 5CUSTOMERS ; 2.3- 15 MIN ; 2.4-4.16customers ;2.5 - 12.5 min A : 3.1 - 0.8 ;3.2- 0.2 ; 3.3- 1.6hrs ; 3.4- 66 customer ;3.5 - 4 customer ; 3.6- 3.2 customers ; 3.7- 16 min ; 3.8- 20 minA : 4.1 – 1/6 in good weather; 4/3in bad weather 4.2- 1/40 in good weather ;1/10 in bad weather

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INVENTORY MANAGEMENT

B 1: Economic order quantity-89.4 Units ; Reorder point-13.7(14) ; Total annual cost- Rs 12612

B 2 : Economic order quantity-1385 Units

B 3 : Economic order quantity-775 Units ; Total annual cost- Rs. 1,21,549 /-

B 4 : Reorder level in normal demand – 1000 Units ; Increase demand 1400 Units

B 5 : Reorder point – 2420 Units ; Maximum / Minimum / Average inventory – 5300 / 500 / 2900 Units

B 6 Economic batch size – 540 Units ; Duration of machine run – 3600 Hours.

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