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311_Session12_Chen

311_Session12_Chen - Session12:WaitingLines PreviousClass...

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Operations Management Session 12:  Waiting Lines
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Session 12 Operations Management 2 Previous Class Understanding the phenomenon of waiting  Impact of variability/uncertainty & utilization rate
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Session 12 Operations Management 3 Objectives Formula/macro for waiting-line calculation Practices waiting time using formulas Risk pooling effect in waiting line
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Session 12 Operations Management 4 M/M/1 Performance Evaluation The arrival rate to the main branch of Key bank is  10 customers per hour. The service rate is 15 customers per hour. Management promise to each consumer that enter  the bank and sees more than 3 customers in front  of him $10. What is the probability that a customer will get $10? 
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Session 12 Operations Management 5 M/M/1 Performance Evaluation Probability that a customer gets $10 =     1 – Probability that the customer does not              get $10 Probability that the customer does not get $10 =     Probability of 0 customers + Probability of 1 +  Probability of 2  + probability of 3
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Session 12 Operations Management 6 M/M/1 Performance Evaluation = - + - + - + - = 3 2 ) 15 10 )( 15 10 1 ( ) 15 10 )( 15 10 1 ( 15 10 ) 15 10 1 ( ) 15 10 1 ( } 3 Pr{ X 78 . 0 09 . 0 14 . 0 22 . 0 33 . 0 = + + + = The probability of a consumer getting $10 is 1-0.78 =0.22 On average how much money will the bank pay every hour? 0.22*average number of customers*$10 =$22
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Session 12 Operations Management 7 M/M/c Performance Evaluation What if we have  c  servers? There is no simple equation.  But, The book page 304 provides the values for the number of  customers in the queue (L q ). How do we calculate the number of customers in the  system and the waiting time in the queue and in the  system?
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Session 12 Operations Management 8 What if … What if the waiting line is not M/M/1 or M/M/c? Use the general formula b/c it applies to everything What kind of information do we need?
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Session 12 Operations Management 9 What are the Key Information?
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