Teaching Notes on Variability and Queues

Teaching Notes on Variability and Queues - 311 O PERATION M...

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Unformatted text preview: 311 O PERATION M ANAGEMENT I NFORMATION AND O PERATIONS M ANAGEMENT M ARSHALL S CHOOL OF B USINESS T EACHING N OTE ON V ARIABILITY AND Q UEUES A. Uncertainty: 1. Sources of Uncertainty: Operations are subject to three major sources of uncertainty: (1) Uncertainty in Processing Times, (2) Uncertainty in Demand and (3) Uncertainty in Supply Uncertainty in Processing Times: Time required to complete a task (e.g. time for a bank teller to serve a customer) is likely to differ each time the task is performed. A number of factors contribute to this uncertainty -- human inconsistency, differences among customers, variation in raw materials, machine failures, quality problems, absenteeism, etc. In facilities that produce many different products or serve different types of customers, the uncertainty in processing times is also due to variety. Uncertainty in Demand: The rate at which customers show up at a service facility / purchase a product also exhibits uncertainty. While some of this uncertainty is natural, marketing actions can also contribute to demand variations. Coupons, price changes, advertising, etc are likely to result in greater demand in one period and possibly lower in the next. 2. Measures of Variability: Measures of Processing Time Uncertainty : The standard deviation of processing times is a measure of variability. Example 1: The times to clean cars at a car wash (in minutes): 8, 7, 8, 9, 10 and 12. Since all processing times are equally likely (probability of 1/6) we get that the mean is: P AGE 1 311 OPERATIONS MANAGEMENT 9 6 12 10 9 8 7 8 = + + + + + We calculate the Standard Deviation in the following way: S.D. = 6329 . 1 6 ) 9 12 ( ) 9 10 ( ) 9 9 ( ) 9 8 ( ) 9 7 ( ) 9 8 ( 2 2 2 2 2 2 =- +- +- +- +- +- Average = 9 minutes. Standard Deviation = 1.6329 minutes. Example 2: The time to process a loan application (in minutes): 138, 137, 138, 139, 140 and 142. Average = 139 minutes Standard Deviation = 1.6329 minutes. The above examples illustrate the limitation of standard deviation. Although the standard deviation in both examples is exactly the same, intuitively the variation at the car-wash example appears to be significantly higher than that at the loan-processing center. A better measure of variability is the ratio of the standard deviation to the average. This ratio is called the coefficient of variation....
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This note was uploaded on 05/08/2008 for the course BUAD 311 taught by Professor Vaitsos during the Spring '07 term at USC.

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Teaching Notes on Variability and Queues - 311 O PERATION M...

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