OPERATIONS MANAGEMENT INTEGRATING MANUFACTURING AND SERVICES FIFTH EDITION Mark M. Davis Janelle Heineke Copyright ©2005, The McGraw-Hill Companies, Inc. PowerPoint Presentation by Charlie Cook, The University of West Alabama
SUPPLEMENT PowerPoint Presentation by Charlie Cook The University of West Alabama Copyright © 2005 The McGraw-Hill Companies. All rights reserved. Waiting Line Theory 16
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–3 SUPPLEMENT OBJECTIVES Introduce the major characteristics of waiting lines and describe how they can affect a customer’s waiting time. Identify the constraints and/or conditions that waiting line theory and its associated equations require for the results to be valid. Present waiting line theory in the form of a set of equations that represent the types of waiting line configurations that can be encountered.
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–4 Waiting Line Characteristics Major Components –The source population –The way customers arrive at the service facility –The physical line itself –The way customers are selected from the line –The characteristics of the service facility itself –The condition of the customers when they exit the system
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–5 Framework for Viewing Waiting Line Situations Exhibit SU16.1
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–6 Population Source Finite Population –Limited size of the customer pool Each customer leaving or returning to the pool changes the probability of a customer requiring service. Infinite Population –A customer pool so large that subtractions or additions to the pool do not significantly affect system probabilities.
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–7 Arrival Characteristics Pattern of Arrivals –Controllable or uncontrollable Size of Arrival Units –One at a time or in batches Distribution Pattern –Constant or statistically distributed rates of arrivals Degree of Patience –Whether the arrival stays in line or leaves Balking or reneging
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–8 Arrival Characteristics in Queues Exhibit SU16.2
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–9 Physical Features of Lines Length –Infinite potential length –limited line capacity Number of Lines –Single or multiple lines
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–10 Customer Selection Queuing Discipline –A queuing discipline is a priority rule, or set of rules for determining the order of service to customers who are waiting in line. Priority rules –First come, first served (FCFS), also known as first in, first out (FIFO). –Reservations first, emergencies first, highest-profit customer first, largest orders first, best customers first, longest waiting time in line, and soonest promised date are other examples of priority rules.
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–11 Factors in a Queuing Discipline Exhibit SU16.3
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–12 A Service Facility’s Structure Exhibit SU16.4
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–13 Arrival Characteristics (cont’d) Service Rate –The capacity of a service station, usually expressed in terms of customers per hour. –The reciprocal of the service rate is the average time to serve a customer. Capacity Utilization –The percentage of time a service station is busy serving a customer. Exit –Customer returns to the waiting population. –Customer does not return to the population.
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–14 Waiting Line Equations Average total waiting time in the system is equal to the average waiting time in the system plus the average service time: Little’s Formula—the average total number of customers in the system is directly related to the total time in the system:
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–15 Properties of Some Specific Waiting Line Models Exhibit SU16.5
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–16 Equations for Solving Five Model Problems Exhibit SU16.6
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–17 Equations for Solving Five Model Problems Exhibit SU16.6 (cont’d)
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–18 Notations for Equations (Exhibit S16.6) Exhibit SU16.7
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–19 Calculating the Relationship between Capacity Utilization and Waiting Time Exhibit SU16.8
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–20 The Relationship between Capacity Utilization and Waiting Time Exhibit SU16.9
Copyright © 2005 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin SU16–21 The Trade-Off between Balking and Reneging Exhibit SU16.10