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Class5&6

# Class5&6 - Operations Management Class 1 Class 2 Class...

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1 Operations Management Class 1: Introduction to OM and Process Analysis Class 2: Process Analysis Class 3 and 4: Process Analysis Continued Class 5 and 6: Variability in Processes

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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? 2
What is Variability? 3 Security check Variable input Variable Capacity Variability comes from:

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Types of Variability Both types of variability exist simultaneously Pumpkin sales will go up during Thanksgiving, but we do not know the exact sales of pumpkins 4 Predictable Variability refers to “knowable” changes in input and/or capacity rates Demand of pumpkins will go up during Thanksgiving Unpredictable Variability refers to “unknowable” changes in input and/or capacity rates Supply of pumpkins will go down if the crop fails Predictable Variability Unpredictable 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.) 5 Is the result of the lack of knowledge or information Usually can be expressed with a probability distribution E.g., Express the probability that the pumpkin crop will fail using a probability distribution Can be reduced by gaining more knowledge or collection information By paying close attention to weather patterns, we could increase the accuracy of our prediction that the pumpkin crop will fail Predictable Variability Unpredictable Variability

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Short Review on Probability (1) Discrete Random Variable and Probability Throw a dice; the number you get is a discrete random variable: 6 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 (Probability  mass) 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
Short Review on Probability (2) Continuous Random Variable and Probability The time between two customers’ arrival times is a continuous random variable 7 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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Basic Questions What are the effects of variability on processes In particular, how does variability affect 8 If the effects are negative, how can we deal with it?
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