McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. 18 Management of Management of Waiting Lines.

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McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. 18 Management of Management of Waiting Lines

18-2 Learning Objectives  Explain why waiting lines form in systems that are underloaded.  Identify the goal of queuing (waiting-line) management.  List the measures of system performance that are used in queuing.  Discuss the assumptions of the basic queuing models presented.  Solve typical problems.

18-3 Disney World  Waiting in lines does not add enjoyment  Waiting in lines does not generate revenue Waiting lines are non-value added occurrences

18-4 Waiting Lines  Queuing theory: Mathematical approach to the analysis of waiting lines.  Goal of queuing analysis is to minimize the sum of two costs  Customer waiting costs  Service capacity costs  Waiting lines are non-value added occurrences

18-5  Cost to provide waiting space  Loss of business  Customers leaving  Customers refusing to wait  Loss of goodwill  Reduction in customer satisfaction  Congestion may disrupt other business operations Implications of Waiting Lines

18-6 Queuing Analysis Optimum Cost of service capacity Cost of customers waiting Total cost Cost Service capacity Total cost Customer waiting cost Capacity cost =+ Figure 18. 1

18-7 System Characteristics  Population Source  Infinite source: customer arrivals are unrestricted  Finite source: number of potential customers is limited  Number of observers (channels)  Arrival and service patterns  Queue discipline (order of service)

18-8 Elements of Queuing System ArrivalsServiceWaiting line Exit Processing order System Figure 18.2

18-9 Queuing Systems Multiple channel Multiple phase Figure 18.3 Channel: A server in a service system

18-10 Poisson Distribution Figure 18.4

18-11 Waiting line Models  Patient  Customers enter the waiting line and remain until served  Reneging  Waiting customers grow impatient and leave the line  Jockeying  Customers may switch to another line  Balking  Upon arriving, decide the line is too long and decide not to enter the line

18-12 Waiting Time vs. Utilization System Utilization Average number on time waiting in line 0 100% Figure 18.7

18-13 System Performance 1.Average number of customers waiting 2.Average time customers wait 3.System utilization 4.Implied cost 5.Probability that an arrival will have to wait Measured by:

Single channel, exponential service time 2.Single channel, constant service time 3.Multiple channel, exponential service time 4.Multiple priority service, exponential service time Queuing Models: Infinite-Source

18-15 Priority Model ArrivalsServiceWaiting line Exit Processing order System Arrivals are assigned a priority as they arrive

18-16 Finite-Source Formulas Average number being served Service factor Average number waiting Average waiting time Average number running Number in population Table 18.6

18-17 Finite-Source Queuing Not waiting or being served Waiting Being served JLH UWT

18-18 Other Approaches  Reduce perceived waiting time  Magazines in waiting rooms  Radio/television  In-flight movies  Filling out forms  Derive benefits from waiting  Place impulse items near checkout  Advertise other goods/services