1. 19-1 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines

2. 19-2 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines WAITING LINES AND SIMULATION PART SEVEN Chapter Nineteen Waiting Lines Chapter 19 Supplement Simulation

3. 19-3 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines Chapter 19 Waiting Lines

4. 19-4 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 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

5. 19-5 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines 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

6. 19-6 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines Queuing Analysis Optimum Cost of service capacity Cost of customers waiting Total cost Cost Service capacity Total cost Customer waiting cost Capacity cost =+ Figure 19- 1

7. 19-7 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines 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)

8. 19-8 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines Elements of Queuing System ArrivalsServiceWaiting line Exit Processing order System

9. 19-9 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines Queuing Systems Multiple channel Multiple phase

10. 19-10 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines Poisson Distribution Figure 19-4

11. 19-11 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines System Performance Average number of customers waiting Average time customers wait System utilization Implied cost Probability that an arrival will have to wait Measured by:

12. 19-12 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines Waiting Time vs. Utilization System Utilization Average number on time waiting in line 0 100% Figure 19-6

13. 19-13 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines Single channel, exponential service time Single channel, constant service time Multiple channel, exponential service time Multiple priority service, exponential service time Queuing Models: Infinite-Source

14. 19-14 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines Queuing Models Single channel, exponential service time Single channel, constant service time Multiple channel, exponential service time Multiple priority service

15. 19-15 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines Priority Model ArrivalsServiceWaiting line Exit Processing order System 11231 Arrivals are assigned a priority as they arrive

16. 19-16 McGraw-Hill Ryerson Operations Management, 2 nd Canadian Edition, by Stevenson & Hojati Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Waiting Lines Finite-Source Queuing Not waiting or being served Waiting Being served JLH UWT