To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting.

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Figure C.1 Customer population Service system Waiting line Priority rule Service facilities

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Customer population Service system Served customers Waiting line Priority rule Service facilities Figure C.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Arrangements Figure C.2 Service facilities (a) Single line

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Arrangements Service facilities (a) Single line Figure C.2 Service facilities (b) Multiple lines

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Service Facility Arrangements Service facility (a) Single channel, single phase Figure C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Service Facility Arrangements (b) Single channel, multiple phase Service facility 1 Service facility 2 Figure C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Service Facility Arrangements (c) Multiple channel, single phase Service facility 1 Service facility 2 Figure C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Service Facility Arrangements (d) Multiple channel, multiple phase Service facility 3 Service facility 4 Service facility 1 Service facility 2 Figure C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Service Facility Arrangements Figure C.3 (e) Mixed Service facility 3 Service facility 4 Service facility 1 Service facility 2 Routing for : 1–2–4 Routing for : 2–4–3 Routing for : 3–2–1–4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Probability Distributions Arrival rate = 2/hour Customer Arrivals Probability that 4 customers will arrive P(n) = e - T ( T) n n! Example C.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Probability Distributions Arrival rate = 2/hour Customer Arrivals Probability that 4 customers will arrive P(4) = e -2(1) [2(1)] 4 4! Example C.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Probability Distributions Arrival rate = 2/hour Customer Arrivals Probability that 4 customers will arrive P(4) = e -2 = 0.090 1624 Example C.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Probability Distributions Arrival rate = 2/hour Service time = 3/hour Service Time Probability that 4 customers will arrive P(4) = e -2 = 0.090 1624 Example C.2 Probability that a customer requires less than 10 minutes P(t ≤T) = 1 – e -  T

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Probability Distributions Arrival rate = 2/hour Service time = 3/hour Service Time Probability that 4 customers will arrive P(4) = e -2 = 0.090 1624 Probability that a customer requires less than 10 minutes P(t ≤ 0.167 hr) = 1 – e -3(0.167) Example C.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Probability Distributions Arrival rate = 2/hour Service time = 3/hour Service Time Probability that 4 customers will arrive P(4) = e -2 = 0.090 1624 Probability that a customer requires less than 10 minutes P(t ≤ 0.167 hr) = 1 – 0.61 = 0.39 Example C.2

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Operating Characteristics  Line Length  Number of Customers in System  Waiting Time in Line  Total Time in System  Service Facility Utilization

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Single-Server Model  = Average utilization of the system =  L = Average number of customers in the service system =  –  L q = Average number of customers in the waiting line =  L W = Average time spent in the system, including service = 1  –  W q = Average waiting time in line =  W  n = Probability that n customers are in the system = (1 –  )  n

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Channel, Single-Phase System Arrival rate = 30/hour Service rate = 35/hour Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Utilization =  =  Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Utilization =  = = 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Utilization =  = = = 0.857, or 85.7% 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Average number in system = L =  Utilization =  = = = 0.857, or 85.7% 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Average number in system = L = = 6 customers 30 35 – 30 Utilization =  = = = 0.857, or 85.7% 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Average number in line = L q =  L Average number in system = L = = 6 customers 30 35 – 30 Utilization =  = = = 0.857, or 85.7% 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Average number in line = L q = 0.857(6) Average number in system = L = = 6 customers 30 35 – 30 Utilization =  = = = 0.857, or 85.7% 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Average number in line = L q = 0.857(6) = 5.14 customers Average number in system = L = = 6 customers 30 35 – 30 Utilization =  = = = 0.857, or 85.7% 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Average time in system = W = 1  Average number in line = L q = 0.857(6) = 5.14 customers Average number in system = L = = 6 customers 30 35 – 30 Utilization =  = = = 0.857, or 85.7% 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Average time in system = W = 1 35 – 30 Average number in line = L q = 0.857(6) = 5.14 customers Average number in system = L = = 6 customers 30 35 – 30 Utilization =  = = = 0.857, or 85.7% 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Average time in system = W = = 0.20 hour, or 12 minutes 1 35 – 30 Average number in line = L q = 0.857(6) = 5.14 customers Average number in system = L = = 6 customers 30 35 – 30 Utilization =  = = = 0.857, or 85.7% 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Average time in line = W q =  W Average time in system = W = = 0.20 hour, or 12 minutes 1 35 – 30 Average number in line = L q = 0.857(6) = 5.14 customers Average number in system = L = = 6 customers 30 35 – 30 Utilization =  = = = 0.857, or 85.7% 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Average time in line = W q = 0.857(0.20) Average time in system = W = = 0.20 hour, or 12 minutes 1 35 – 30 Average number in line = L q = 0.857(6) = 5.14 customers Average number in system = L = = 6 customers 30 35 – 30 Utilization =  = = = 0.857, or 85.7% 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Arrival rate = 30/hour Service rate = 35/hour Average time in line = W q = 0.857(0.20) = 0.17 hour, or 10.28 minutes Average time in system = W = = 0.20 hour, or 12 minutes 1 35 – 30 Average number in line = L q = 0.857(6) = 5.14 customers Average number in system = L = = 6 customers 30 35 – 30 Utilization =  = = = 0.857, or 85.7% 3035 Single-Channel, Single-Phase System Example C.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Channel, Single-Phase System Figure C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Average time in system = 8 minutes Arrival rate =  = 30/hour Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Average time in system = 8 minutes = W = 1  –  Arrival rate =  = 30/hour Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Average time in system = 8 minutes = W = 1  –  30 Arrival rate =  = 30/hour Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Average time in system = 8 minutes = W = 1  –  30 Arrival rate =  = 30/hour Service rate =  = 37.52/hour Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Probability of more than 4 customers =  = 1 – ∑  n Arrival rate =  = 30/hour Service rate =  = 37.52/hour Average time in system = 8 minutes = W = 1  –  30 4 n = 0 Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Probability of more than 4 customers =  = 1 – ∑ (1 –  )  n Arrival rate =  = 30/hour Service rate =  = 37.52/hour Average time in system = 8 minutes = W = 1  –  30 4 n = 0 Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Probability of more than 4 customers =  = 1 – ∑ (1 –  )  n Arrival rate =  = 30/hour Service rate =  = 37.52/hour Average time in system = 8 minutes = W = 1  –  30 4 n = 0  = = 0.80 3037.52 Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Probability of more than 4 customers =  = 1 – 0.2(1 + 0.8 + 0.8 2 Arrival rate =  = 30/hour Service rate =  = 37.52/hour Average time in system = 8 minutes = W = 1  –  30  = = 0.80 3037.52 + 0.8 3 + 0.8 4 ) Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Probability of more than 4 customers =  = 0.328 Arrival rate =  = 30/hour Service rate =  = 37.52/hour Average time in system = 8 minutes = W = 1  –  30 Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Probability of more than 4 customers =  = 0.328 Arrival rate =  = 30/hour Service rate =  = 37.52/hour Average time in system = 8 minutes = W = 1  –  30 Service rate for a 10% chance of exceeding 4 customers in the system = 1 – (1 –  )(1  2  3  4 ) Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Service rate for a 10% chance of exceeding 4 customers in the system = 1 – 1 –  –  2 –  3 –  4 +  +  2 +  3 +  4 +   Probability of more than 4 customers =  = 0.328 Arrival rate =  = 30/hour Service rate =  = 37.52/hour Average time in system = 8 minutes = W = 1  – 30 Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Service rate for a 10% chance of exceeding 4 customers in the system =   or  =  1/5 Probability of more than 4 customers =  = 0.328 Arrival rate =  = 30/hour Service rate =  = 37.52/hour Average time in system = 8 minutes = W = 1  –  30 Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Service rate for a 10% chance of exceeding 4 customers in the system =   or  =  1/5 Probability of more than 4 customers =  = 0.328 Arrival rate =  = 30/hour Service rate =  = 37.52/hour Average time in system = 8 minutes = W = 1  –  30 If  = 0.10 Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Service rate for a 10% chance of exceeding 4 customers in the system =   or  = (0.10) 1/5 Probability of more than 4 customers =  = 0.328 Arrival rate =  = 30/hour Service rate =  = 37.52/hour Average time in system = 8 minutes = W = 1  –  30 If  = 0.10 Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Service rate for a 10% chance of exceeding 4 customers in the system =   or  = 0.63 Probability of more than 4 customers =  = 0.328 Arrival rate =  = 30/hour Service rate =  = 37.52/hour Average time in system = 8 minutes = W = 1  –  30 If  = 0.10 Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Service rate for a 10% chance of exceeding 4 customers in the system =   or  = 0.63 = Probability of more than 4 customers =  = 0.328 Arrival rate =  = 30/hour Service rate =  = 37.52/hour Average time in system = 8 minutes = W = 1  –  30 30 Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Service rate for a 10% chance of exceeding 4 customers in the system =   or  = 0.63 = Probability of more than 4 customers =  = 0.328 Arrival rate =  = 30/hour Service rate =  = 47.62/hour Average time in system = 8 minutes = W = 1  –  30 30 Example C.4

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Single-Server Model Example C.4 Service rate for a 10% chance of exceeding 4 customers in the system =   or  = 0.63 = Probability of more than 4 customers =  = 0.328 Arrival rate =  = 30/hour Service rate =  = 47.62/hour Average time in system = 8 minutes = W = 1  –  30 30

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  =  s Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 31(4) Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75 Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = [∑ + ( )] -1 (3/1) n n! (3/1) 4 4! 1 1 – 0.75 4 – 1 n = 0 Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q =  0 ( ) s  s!(1 –  ) 2 Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 0.0377(3/1) 4 (0.75) 4!(1 – 0.75) 2 Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = L q Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = 1.533 Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = 0.51 hours Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = 0.51 hours Average time in system = W = W q + 1 Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = 0.51 hours Average time in system = W = 0.51 + 11 Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = 0.51 hours Average time in system = W = 1.51 hours Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = 0.51 hours Average time in system = W = 1.51 hours Average trucks in system = L = W Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = 0.51 hours Average time in system = W = 1.51 hours Average trucks in system = L = 3(1.51) Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = 0.51 hours Average time in system = W = 1.51 hours Average trucks in system = L = 4.53 trucks Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = 0.51 hours Average time in system = W = 1.51 hours Average trucks in system = L = 4.53 trucks Labor costs: Idle truck cost: Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = 0.51 hours Average time in system = W = 1.51 hours Average trucks in system = L = 4.53 trucks Labor costs:$30(s)=$30(4)=$120.00 Idle truck cost: Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = 0.51 hours Average time in system = W = 1.51 hours Average trucks in system = L = 4.53 trucks Labor costs:$30(s)=$30(4)=$120.00 Idle truck cost:$50(L)=$50(4.53)=$226.50 Example C.5

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Multiple-Server Model Example C.5 4 Unloading baysCrew costs $30/hour 2 Employees/crewIdle truck costs $50/hour Arrival rate = 3/hourService time = 1 hour Utilization =  = 0.75  0 = 0.0377 Average trucks in line = L q = 1.53 trucks Average time in line = W q = 0.51 hours Average time in system = W = 1.51 hours Average trucks in system = L = 4.53 trucks Labor costs:$30(s)=$30(4)=$120.00 Idle truck cost:$50(L)=$50(4.53)=226.50 Total hourly cost=$346.50

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = [∑ ( ) n ] –1 N! (N – n)! N n = 0 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = [∑ ( ) n ] –1 10! (10 – n)! 0.0050.10 10 n = 0 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 –  0 Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = N – (1 –  0 ) +  +  Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 10 – (1 – 0.538) 0.005 + 0.10 0.005 Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = N – (1 –  0 )  Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 10 – (1 – 0.538) 0.100.005 Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot W q = L q [(N – L) ] –1 Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot W q = 0.30[(10 – 0.76)0.005] –1 Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot W q = 6.49 hours Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot W q = 6.49 hours W = L[(N – L) ] –1 Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot W q = 6.49 hours W = 0.76[(10 – 0.76)0.005] –1 Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model Example C.6  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot W q = 6.49 hours W = 16.45 hours

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model Figure C.6  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 - 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot W q = 6.49 hours W = 16.45 hours

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot W q = 6.49 hours W = 16.45 hours Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot W q = 6.49 hours W = 16.45 hours Labor cost: Idle robot cost: Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot W q = 6.49 hours W = 16.45 hours Labor cost:($10/hr)(8 hrs/day)(0.462 utilization)=$ 36.96 Idle robot cost: Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot W q = 6.49 hours W = 16.45 hours Labor cost:($10/hr)(8 hrs/day)(0.462 utilization)=$ 36.96 Idle robot cost:(0.76 robot)($30/robot hr)(8 hrs/day)=182.40 Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting Line Models Finite-Source Model  0 = 0.538 Number of robots = 10 Time between failures = 200 hrs Loss/machine hour = $30 Service time = 10 hrs Maintenance cost = $10/hr  = 1 – 0.538 = 0.462 L q = 0.30 robots L = 0.76 robot W q = 6.49 hours W = 16.45 hours Labor cost:($10/hr)(8 hrs/day)(0.462 utilization)=$ 36.96 Idle robot cost:(0.76 robot)($30/robot hr)(8 hrs/day)=182.40 Total daily cost=$219.36 Example C.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Decision Areas  Arrival Rates  Number of Service Facilities  Number of Phases  Number of Servers Per Facility  Server Efficiency  Priority Rule  Line Arrangement

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting.

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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting.

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Presentation on theme: "To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Waiting."— Presentation transcript:

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