Practice Problems Problem 1 The following represent activities

Practice Problems Problem 1: The following represent activities in a major construction project. Draw the network to represent this project. Activity Immediate Predecessor A — B — C A D B E B F C, E G D H F, G Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 1 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Practice Problems Problem 1: The following represent activities in a major construction project. Draw the network to represent this project. Activity Immediate Predecessor A — B — C A D B E B F C, E G D H F, G Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 2 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Practice Problems Problem 2: Given the following Time Chart and Network Diagram, find the Critical Path. Activity A B C D E a 2 1 4 1 1 m 3 2 5 3 2 b 4 3 12 5 3 t Variance 3 1/9 2 1/9 6 16/9 3 4/9 2 1/9 Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 3 Activity C t=6 Activity E t=2 Activity A t=3 Activity D t=3 Activity B t=2 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Practice Problems Problem 2: Given the following Time Chart and Network Diagram, find the Critical Path. Activity A B C D E a 2 1 4 1 1 m 3 2 5 3 2 b 4 3 12 5 3 t Variance 3 1/9 2 1/9 6 16/9 3 4/9 2 1/9 Activity C t=6 Activity E t=2 Activity A t=3 Activity D t=3 Activity B t=2 Critical Path Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 4 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Practice Problems Problem 3: What is the variance in completion time for the critical path found in Problem 2? Activity a m b t Variance A 2 3 4 3 1/9 B 1 2 3 2 1/9 C 4 5 12 6 16/9 D 1 3 5 3 4/9 E 1 2 3 2 1/9 Activity C t=6 Activity E t=2 Activity A t=3 Activity D t=3 Activity B t=2 Critical Path Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 5 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Practice Problems Total variance = variances of activities on critical path Problem. Total 3: variance = 1/9 + 16/9 + 4/9 + 1/9 = 23/9 = 2. 56 4. 796 23 completion What is the. And variance = in =23 = = 1. 6 and time for the critical path 3 9 found 3 in Problem 2? Activity C Activity a m b t Variance t=6 A 2 3 4 3 1/9 Activity A B 1 2 3 2 1/9 t=3 C 4 5 12 6 16/9 Activity D D 1 3 5 3 4/9 t=3 E 1 2 3 2 1/9 Activity B 2. 56 = 1 Activity E t=2 Critical Path Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 6 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Practice Problems Problem 4: A project has an expected completion time of 40 weeks and a standard deviation of 5 weeks. It is assumed that the project completion time is normally distributed. a. What is the probability of finishing the project in 50 weeks or less? b. What is the probability of finishing the project in 38 weeks or less? c. The due date for the project is set so that there is a 90% chance that the project will be finished by this date. What is the date? Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 7 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Practice X - Problems 50 – 40 a. Z = = =2 Problem 4: 5 Therefore: P(X 50) = P(Z 2) = 0. 97725 A project has an expected completion time of 40 weeks and a standard deviation of 5 weeks. It is assumed that the project completion time is normally distributed. a. What is the probability of finishing the project in 50 weeks or less? b. What is the probability of finishing the project in 38 weeks or less? c. The due date for the project is set so that there is a 90% chance that the project will be finished by this date. What is the date? Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 8 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Practice X - Problems 50 – 40 a. Z = = =2 Problem 4: 5 Therefore: P(X 50) = P(Z 2) = 0. 97725 A project has an expected. Xcompletion - – 2 time of 40 weeks and a = – 0. 4 standard deviation b. of 5 Zweeks. It is=assumed=that the project 5 completion time is normally distributed. Therefore: P(X 38) = P(Z – 0. 4) = 0. 34458 a. What is the probability of finishing the project in 50 weeks or less? b. What is the probability of finishing the project in 38 weeks or less? c. The due date for the project is set so that there is a 90% chance that the project will be finished by this date. What is the date? Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 9 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Practice X - Problems 50 – 40 a. Z = = =2 Problem 4: 5 Therefore: P(X 50) = P(Z 2) = 0. 97725 A project has an expected. Xcompletion - – 2 time of 40 weeks and a = – 0. 4 standard deviation b. of 5 Zweeks. It is=assumed=that the project 5 completion time is normally distributed. Therefore: P(X 38) = P(Z – 0. 4) = 0. 34458 a. What is the probability of finishing the project in 50 weeks or less? b. What is the probability of finishing the project in 38 weeks or less? c. The due date for the project is set so that there is a 90% chance that will be c. the 90%project Z = 1. 28 = finished (X – ) / by =this X – 40 / 5 date. What is the date? Therefore: X = 1. 28 * 5 + 40 = 46. 4 weeks Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 10 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Practice Problems Problem 5: Development of a new deluxe version of a particular software product is being considered. The activities necessary for the completion of this project are listed in the table below along with their costs and completion times in weeks. a. What is the project expected completion date? b. What is the total cost required for completing this project on normal time? c. If you wish to reduce the time required to complete this project by 1 week, which activity should be crashed, and how much will this increase the total cost? Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 11 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Practice Problems Problem 5: Normal Crash Immediate Activity Time Cost Predecessor A 4 3 2, 000 2, 600 — B 2 1 2, 200 2, 800 A C 3 3 500 A D 8 4 2, 300 2, 600 A E 6 3 900 1, 200 B, D F 3 2 3, 000 4, 200 C, E G 4 2 1, 400 2, 000 F Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 12 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Dt=8 Practice Problems Et=6 Problem 5: Bt=2 At=4 Gt=4 Ft=3 Normal Crash Normal Ct=3 Crash Immediate Critical Path Activity Time Cost Predecessor A 4 3 2, 000 2, 600 — B 2 1 2, 200 2, 800 A C 3 3 500 A D 8 4 2, 300 2, 600 A E 6 3 900 1, 200 B, D F 3 2 3, 000 4, 200 C, E G 4 2 1, 400 2, 000 F a. Project completion time = t. A + t. D + t. E + t. F + t. G = 4 + 8 + 6 + 3 + 4 Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 13 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Dt=8 Practice Problems Et=6 Problem 5: Bt=2 At=4 Gt=4 Ft=3 Normal Crash Normal Ct=3 Crash Immediate Critical Path Activity Time Cost Predecessor c. Crash D 1 week$2, 600 at A 4 3 – $2, 300 2, 000 $300 2, 600 — an additional cost = = B 2 18 – 4 2, 200 2, 800 A 4 = $75 C 3 3 500 A D 8 4 2, 300 2, 600 A E 6 3 900 1, 200 B, D F 3 2 3, 000 4, 200 C, E G 4 2 1, 400 2, 000 F a. Project completion time = t. A + t. D + t. E + t. F + t. G = 4 + 8 + 6 + 3 + 4 b. Total cost = $2, 000 + $2, 300 + $900 + $3, 000 + $1, 400 = $9, 60 Power. Point presentation to accompany Heizer/Render – Principles of Operations Management, 5 e, and Operations Management, 7 e 14 © 2004 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458