Production and Operations Analysis, Seventh Edition
Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 10.5, Problem 20P

A.

Summary Introduction

Interpretation: All the paths in the network diagram are to be identified.

Concept Introduction: Program Evaluation and review technique is a planning and control tool, wherein the work flow of various activities of a project are graphically represented and analyzed. This technique is distinct in the way that it deals with uncertainty in the activity completion times.

B.

Summary Introduction

Interpretation: The critical path is to be identified by computing the expected completion times.

Concept Introduction: Program Evaluation and review technique is a planning and control tool, wherein the work flow of various activities of a project are graphically represented and analyzed. This technique is distinct in the way that it deals with uncertainty in the activity completion times.

C.

Summary Introduction

Interpretation: The probability that the project will be completed by 20 weeks, with the critical path based on expected completion times is to be computed.

Concept Introduction: Program Evaluation and review technique is a planning and control tool, wherein the work flow of various activities of a project are graphically represented and analyzed. This technique is distinct in the way that it deals with uncertainty in the activity completion times.

D.

Summary Introduction

Interpretation: The probability that the project will be completed by 20 weeks is to be computed, using the independence of paths A − C − E and B − F - G.

Concept Introduction: Program Evaluation and review technique is a planning and control tool, wherein the work flow of various activities of a project are graphically represented and analyzed. This technique is distinct in the way that it deals with uncertainty in the activity completion times. Path independence method is used to compute critical paths other than the one with the longest completion time.

E.

Summary Introduction

Interpretation: The probability that the project will be completed by 20 weeks is to be computed, using independence of paths.

Concept Introduction: Program Evaluation and review technique is a planning and control tool, wherein the work flow of various activities of a project are graphically represented and analyzed. This technique is distinct in the way that it deals with uncertainty in the activity completion times.

F.

Summary Introduction

Interpretation: The accuracy of the probability of completing the project within 20 weeks with the critical path and path independence method is to be commented

Concept Introduction: Program Evaluation and review technique is a planning and control tool, wherein the work flow of various activities of a project are graphically represented and analyzed. This technique is distinct in the way that it deals with uncertainty in the activity completion times.

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The network diagram of a project with four activities is presented below. Start A B C D The estimated optimistic, most likely, and pessimistic times of each task are given in the table below. The expected time and variance of acitivities A are also given in the table. The expected time and variance of activity C and D are irrelevant in this problem. So they can be ignored. optimistic 14 4 5 5 most likely B 18 10 7 10 End pessimistic 23 18 13 12 Expected time 18.167 XX mm variance 81/36 [Three decimal places for all answers) (1) What is the expected task time of activity B? (2) What is the variance of the task time for activity B (3) What is the expected length of path A-B? (2) What is the standard deviation of the length of path A-B? yy 22
Consider a project that has been modeled as in Table 1 Draw the PERT/CPM network for this project and determine the project’s expected completion time µP and its critical path.  Suppose the standard deviations of the activity durations are σA = 2, σB = 1, σC = 0, σD = 2, σE = 3, and σF = 0. Then please estimate the standard deviation of the overall project’s standard deviation σP .  Suppose for the standard Normal random variable Z, we know P[−1 ≤ Z ≤ +1] ' 68%, P[−2 ≤ Z ≤ +2] ' 95%, and P[−3 ≤ Z ≤ +3] ' 99.7%. Then, approximately what time T is one for which there is only a less than 2.5% chance for the completion time to beat (be shorter than)?
The project duration in a network model can be determined by the largest value of which variable associated with the critical path?
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