1. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter 14 Chapter 14 Waiting Lines and Queuing Theory Models

2. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-2 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Learning Objectives Students will be able to Describe the trade-off curves for cost-of-waiting time and cost-of- service. Understand the three parts of a queuing system: the calling population, the queue itself, and the service facility. Describe the basic queuing system configurations. Understand the assumptions of the common models dealt with in this chapter Analyze a variety of operating characteristics of waiting lines.

3. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-3 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter Outline 14.1 Introduction 14.2 Waiting Line Costs 14.3 Characteristics of a Queuing System 14.4 Single-Channel Queuing Model with Poisson Arrivals and Exponential Service Times 14.5 Multiple-Channel Queuing Model with Poisson Arrivals and Exponential service Times 14.6 Constant Service Time Model 14.7 Finite Population Model

4. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-4 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter Outline – cont. 14.8 Some General Operating Characteristics Relationships 14.9 More Complex Queuing Models and the Use of Simulation

5. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-5 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Queuing Costs and Service Levels Cost of Operating Service Facility Service Level Total Expected Cost Cost of Providing Service Cost of Waiting Time O ptimal Service Level

6. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-6 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Waiting Line Cost Analysis Three Rivers Shipping Number of Stevedore Teams 1234 5555 7432 35201510 $1,000 35,00029,000$15,000$10,000 $6,000$12,00018,000 $24,000 $41,000$32,000$33,000$34,000 Average waiting time per ship Total ship hours lost Est. cost per hour of idle ship time Value of ships' lost time Stevedore teams salary Total Expected Cost Avg. number of ships arriving per shift

7. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-7 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Characteristics of a Waiting Line System Calling Population Unlimited Limited

8. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-8 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Characteristics of a Waiting Line System - cont. Arrival Characteristics Arrival rate distribution Poisson other Pattern of arrivals random scheduled Behavior of arrivals join the queue, and wait till served balk; refuse to join the line renege; leave the line

9. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-9 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Characteristics of a Waiting Line System- cont. Waiting Line Characteristics Length of the queue limited unlimited Service priority/Queue discipline FIFO other

10. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-10 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Characteristics of a Waiting Line System - cont. Service Facility Characteristics Number of channels single multiple Number of phases in service system single multiple Service time distribution negative exponential other

11. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-11 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Poisson Distribution for Arrival Times.00.05.10.15.20.25.30.35 0123456789101 X P(X) P(X), = 2.00.05.10.15.20.25.30 0123456789101 X P(X) P(X), = 4

12. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-12 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Basic Queuing System Configurations Single Channel, Single Phase Queue Service facility Facility 1 Facility 2 Single Channel, Multi-Phase Queue Service Facility

13. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-13 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Basic Queuing System Configurations Service facility 1 Service facility 2 Service facility 3 Multi-Channel, Single Phase Queue Multi-Channel, Multiphase Phase Queue Type 1 Service Facility Type 2 Service Facility

14. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-14 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Exponential Distribution for Service Times Probability (for Intervals of 1 Minute) 30 60 90 120 150 180 Average Service Time of 1 Hour Average Service Time of 20 Minutes X

15. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-15 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Assumptions: M/M/1 Model 1. Queue discipline: FIFO 2. No balking or reneging 3. Independent arrivals; constant rate over time 4. Arrivals: Poisson distributed 5. Service times: negative exponential 6. Average service rate > average arrival rate

16. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-16 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Performance Measures of Queuing Systems Average time each customer spends in the queue Average length of the queue Average time each customer spends in the system Average number of customers in the system Probability that the service facility will be idle Utilization factor for the system Probability of a specific number of customers in the system

17. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-17 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Equations: M/M/1

18. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-18 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Equations: M/M/m

19. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-19 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Equations: M/D/1

20. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-20 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Equations Finite Population Model

21. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-21 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 General Operating Characteristics