class 8 and 9

class 8 and 9 - COMM 399: Operations Class 1: Class 2:...

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1 COMM 399: Operations Class 1: Course Overview and Introduction to Processes Class 2: House building game and process design Class 3: Process Analysis Class 4 and 5: Process Analysis Class 6: Process Analysis » Shouldice Class 7: Project Management Class 8: Variability in processes
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2 Required Readings Variability, Buffers and Inventory (in course pack)
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3 Learning Objectives Variability and process analysis What is variability? What impact does variability have on processes? How can we quantify the impact of variability on processes? How can we manage variability in processes?
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4 What is variability? Security check Variability comes from Variable input Variable capacity
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5 Types of variability Predictable variability refers to “knowable” changes in input and/or capacity rates Demand for pumpkins will go up during Halloween Unpredictable variability refers to “unknowable” changes in input and/or capacity rates Supply of pumpkins may go down if the crop fails Both types of variability exist simultaneously Pumpkin sales will go up during Halloween, but we do not know the exact sales of pumpkins
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6 Predictable variability Predictable variability can be controlled by making changes to the system We could increase or decrease the demand for pumpkins by increasing or decreasing the price Restaurants will add staff during peak demand (lunch, dinner, etc.)
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7 Unpredictable variability Unpredictable variability is the result of a lack of knowledge or information Usually can be expressed with a probability distribution, e.g., we can express the probability that the pumpkin crop will fail using a probability distribution Unpredictable variability can be reduced by gaining more knowledge or collecting information By paying close attention to weather patterns, we could increase the accuracy of our prediction that the pumpkin crop will fail
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8 Short Review on Probability 1 Discrete random variable and probability Throw a dice, the number you get is a discrete random variable: 1, w.p. 1/6 2, w.p. 1/6 3, w.p. 1/6 4, w.p. 1/6 5, w.p. 1/6 6, w.p. 1/6 X = P{X = 2} = 1/6 x 1    2    3     4    5    6 Probability 1/6 P{X ≤  x } is a function of  x , called the  cumulative distribution function (CDF) 1    2    3     4    5    6 Cumulative  probability 1/6 1/3 1/2 2/3 5/6 1 P(X≤ x ) x P{X ≤ 2} = P{X=1 or X=2} = 1/3 P{X ≤ 2.1} = P{X=1 or X=2} = 1/3
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9 Short Review on Probability 2 Continuous random variable and probability The time between two customers’ arrival times is a continuous random variable Probability  density x f ( x ) 0 P(X ≤  x ) =      f  (s) ds x 1 x 0 Cumulative distribution  function (CDF) 0
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10 Basic questions What are the effects of variability on processes? In particular, how does variability affect
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class 8 and 9 - COMM 399: Operations Class 1: Class 2:...

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