Lecture Fundamentals of operations management (4/e): Chapter 16 - Davis, Aquilano, Chase

Chapter supplement 11 Waiting line theory. This chapter introduce the major characteristics that exist in waiting lines and describe how they can impact a customer’s waiting time, identify the various 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 various types of waiting line configurations that can be encountered.

DAVIS F   O   U   R   T   H       E   D   I   T   I   O   N AQUILANO CHASE supplement 11 Waiting Line Theory PowerPoint Presentation by Charlie Cook © The McGraw-Hill Companies, Inc., 2003 Supplement Objectives Supplement Objectives • Introduce the major characteristics that exist in waiting lines and describe how they can impact a customer’s waiting time • Identify the various 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 various types of waiting line configurations that can be encountered Fundamentals of Operations  Management 4e  © The McGraw­Hill  Companies, Inc., 2003 S11–2 Waiting Line Characteristics 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 Fundamentals of Operations  Management 4e  © The McGraw­Hill  Companies, Inc., 2003 S11–3 Framework for Viewing Waiting Line Structures Framework for Viewing Waiting Line Structures Fundamentals of Operations  Management 4e  © The McGraw­Hill  Companies, Inc., 2003 Exhibit S11.1 S11–4 Population Source 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 not significantly affect system probabilities FundamentalsofOperations Management4e âTheMcGrawưHill Companies,Inc.,2003 S115 ArrivalCharacteristics ArrivalCharacteristics ã 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 âTheMcGrawưHill ã Balking or reneging Fundamentals of Operations  Companies, Inc., 2003 Management 4e  S11–6 Arrival Characteristics in Queues Arrival Characteristics in Queues Fundamentals of Operations  Management4e âTheMcGrawưHill Companies,Inc.,2003 Exhibit S11.2 S117 PhysicalFeaturesofLines PhysicalFeaturesofLines ã Length –Infinite potential length –limited line capacity • Number of Lines –Single or multiple lines Fundamentals of Operations  Management 4e  © The McGraw­Hill  Companies, Inc., 2003 S11–8 Customer Selection CustomerSelection ã Factors in a Queuing Discipline FundamentalsofOperations Management4e âTheMcGrawưHill Companies, Inc., 2003 Exhibit S11.3 S11–9 Service  Service  Facility  Facility  Structure Structure FundamentalsofOperations Exhibit S11.4 Management4e âTheMcGrawưHill Companies,Inc.,2003 S1110 ArrivalCharacteristics(contd) ArrivalCharacteristics(contd) ã 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 © The McGraw­Hill  –Customer does not return to the population Fundamentals of Operations  Companies, Inc., 2003 Management 4e  S11–11 Waiting Line Equations 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: ts tl Little’s Formula—the average total number of  customers in the system is directly related to the total  time in the system: ns Fundamentals of Operations  Management 4e  t© The McGraw­Hill  s Companies, Inc., 2003 S11–12 Properties of Specific Waiting Line Models Properties of Specific Waiting Line Models Fundamentals of Operations  Management 4e  © The McGraw­Hill  Companies, Inc., 2003 Exhibit S11 S11–13 Equations for  Equations for  Solving Six  Solving Six  Model  Model  Problems Problems Fundamentals of Operations  Management 4e  © The McGraw­Hill  Companies, Inc., 2003 Exhibit S11.6a S11–14 Equations for  Equations for  Solving Six  Solving Six  Model  Model  Problems Problems (cont’d) (cont’d) Fundamentals of Operations  Management 4e  © The McGraw­Hill  Companies, Inc., 2003 Exhibit S11.6b S11–15 Notations  Notations  for  for  Equations  Equations  (Exhibit  (Exhibit  S11.6) S11.6) Fundamentals of Operations  Exhibit S11.7 Management 4e  © The McGraw­Hill  Companies, Inc., 2003 S11–16 Calculating the Relationship between  Calculating the Relationship between  Capacity Utilization and Waiting Time Capacity Utilization and Waiting Time Fundamentals of Operations  Management 4e  © The McGraw­Hill  Companies, Inc., 2003 Exhibit S11.8 S11–17 The Relationship between Capacity Utilization  The Relationship between Capacity Utilization  and Waiting Time and Waiting Time Fundamentals of Operations  Management 4e  © The McGraw­Hill  Companies, Inc., 2003 Exhibit S11.9 S11–18 The Trade­off between Balking and Reneging The Trade­off between Balking and Reneging Fundamentals of Operations  Management 4e  © The McGraw­Hill  Companies, Inc., 2003 Exhibit S11.10 S11–19 ... waiting line theory in the form of a set of equations that represent various types of waiting line configurations that can be encountered Fundamentals? ?of? ?Operations? ? Management4 e âTheMcGrawưHill... Discipline Fundamentals? ?of? ?Operations? ? Management? ?4e  © The McGraw­Hill  Companies, Inc., 2003 Exhibit S11.3 S11–9 Service  Service  Facility  Facility  Structure Structure Fundamentals? ?of? ?Operations? ?... distributed rates of arrivals • Degree of Patience –Whether the arrival stays in line or leaves © The McGraw­Hill  • Balking or reneging Fundamentals? ?of? ?Operations? ? Companies, Inc., 2003 Management? ?4e