OM (with OM Online, 1 term (6 months) Printed Access Card)
OM (with OM Online, 1 term (6 months) Printed Access Card)
6th Edition
ISBN: 9781305664791
Author: David Alan Collier, James R. Evans
Publisher: Cengage Learning
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Chapter 18, Problem 14PA

(a)

Summary Introduction

Interpretation: The probability that the project is completed within 33weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(a)

Expert Solution
Check Mark

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

    ActivityOptimistic timeMost Probable TimePessimistic Time
    A456
    B2.533.5
    C678
    D55.59
    E678
    F135
    G81012

Table (1)

The expression for the estimated time is given by,

  te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

  Variance=(tpt0)236

The variance and estimated time of each activity is tabulated below.

    ActivityOptimistic timeMost Probable TimePessimistic TimeEstimated TimeVariance
    A45650.111
    B2.533.530.028
    C67870.111
    D55.5960.444
    E67870.111
    F13530.444
    G81012100.444

Table (2)

Calculate z value to find the probability of meeting a 33weeks deadline.

  z=33321.69=11.3=0.769

Refer probability distribution table.

For z0.769 .

  P(z0.769)=0.77935 .

Hence, the probability that the project is completed within 33weeks is 0.77935 .

(b)

Summary Introduction

Interpretation: The probability that the project is completed within 30weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(b)

Expert Solution
Check Mark

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

    ActivityOptimistic timeMost Probable TimePessimistic Time
    A456
    B2.533.5
    C678
    D55.59
    E678
    F135
    G81012

Table (1)

The expression for the estimated time is given by,

  te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

  Variance=(tpt0)236

The variance and estimated time of each activity is tabulated below.

    ActivityOptimistic timeMost Probable TimePessimistic TimeEstimated TimeVariance
    A45650.111
    B2.533.530.028
    C67870.111
    D55.5960.444
    E67870.111
    F13530.444
    G81012100.444

Table (2)

Calculate z value to find the probability of meeting a 30weeks deadline.

  z=30321.69=21.3=1.539

Refer probability distribution table.

For z1.539 .

  P(z1.539)=0.06178 .

Hence, the probability that the project is completed within 30weeks is 0.06178 .

(c)

Summary Introduction

Interpretation: The probability that the project is completed within 35weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(c)

Expert Solution
Check Mark

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

    ActivityOptimistic timeMost Probable TimePessimistic Time
    A456
    B2.533.5
    C678
    D55.59
    E678
    F135
    G81012

Table (1)

The expression for the estimated time is given by,

  te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

  Variance=(tpt0)236

The variance and estimated time of each activity is tabulated below.

    ActivityOptimistic timeMost Probable TimePessimistic TimeEstimated TimeVariance
    A45650.111
    B2.533.530.028
    C67870.111
    D55.5960.444
    E67870.111
    F13530.444
    G81012100.444

Table (2)

Calculate z value to find the probability of meeting a 35weeks deadline.

  z=35321.69=31.3=2.308

Refer probability distribution table.

For z2.308 .

  P(z2.308)=0.99134 .

Hence, the probability that the project is completed within 35weeks is 0.99134 .

(d)

Summary Introduction

Interpretation: The probability that the project is completed within 32weeks is to be determined.

Concept Introduction:

Project Scheduling is used in Project planning and coordination by using Program Evaluation Review Technique (PERT) and Critical Path Method (CPM). PERT is a network based scheduling procedure. This technique is used to plan, schedule and control different project such as construction works, design installation of system, maintenance work and research and development process.

(d)

Expert Solution
Check Mark

Explanation of Solution

The activity with optimistic, most probable and pessimistic time is tabulated below.

    ActivityOptimistic timeMost Probable TimePessimistic Time
    A456
    B2.533.5
    C678
    D55.59
    E678
    F135
    G81012

Table (1)

The expression for the estimated time is given by,

  te=t0+4tm+tp6

Here, te is the estimated time of an activity, t0 is the optimistic time, tm is the most probable time and tp is the pessimistic time.

The expression for variance is given by,

  Variance=(tpt0)236

The variance and estimated time of each activity is tabulated below.

    ActivityOptimistic timeMost Probable TimePessimistic TimeEstimated TimeVariance
    A45650.111
    B2.533.530.028
    C67870.111
    D55.5960.444
    E67870.111
    F13530.444
    G81012100.444

Table (2)

Calculate z value to find the probability of meeting a 32weeks deadline.

  z=32321.69=01.3=0

Refer probability distribution table.

There is no value for z=0 .

Hence, the probability that the project is completed within 32weeks cannot be determined.

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