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 12PA
Summary Introduction

Interpretation: The total project completion time is to be calculated along with the lowest cost solution if the project is to be completed 3 weeks early.

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.

Expert Solution & Answer
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Explanation of Solution

The activity with their immediate predecessor and estimated time, crash time, crash cost and normal cost is tabulated below.

    ActivityImmediate PredecessorEstimated Normal TimeCrash TimeNormal CostCrash Cost
    A-54400750
    BA8618002200
    CA768001100
    D-656001000
    EB, D, C8617002200
    FD328001000
    GD32500650
    HE43400600
    IF, G, H659001300

Table (1)

The network diagram for the activity shown in table (1) is shown below.

  OM (with OM Online, 1 term (6 months) Printed Access Card), Chapter 18, Problem 12PA , additional homework tip  1

Figure (1)

Therefore, the network diagram of the given project is shown in Figure (1).

The expression for the cost slope is given by,

  Cost Slope=Crash CostNormal CostNormal TimeNormal Cost

The cost slope for each activity is tabulated below.

    ActivityImmediate PredecessorEstimated Normal TimeCrash TimeNormal CostCrash CostCost Slope
    A-54400750350
    BA8618002200200
    CA768001100300
    D-656001000400
    EB, D, C8617002200250
    FD328001000200
    GD32500650150
    HE43400600200
    IF, G, H659001300400

Table (2)

Consider figure (1), the different paths and their completion times is tabulated below.

    PathCompletion time (weeks)
    A-B-E-H-I5+8+8+4+6=31
    A-C-E-H-I5+7+8+4+6=30
    D-E-H-I6+8+4+6=24
    D-G-I6+3+6=15
    D-F-I6+3+6=15

Table (3)

From Table (3), the maximum completion time is taken by path A-B-E-H-I . So, this is the critical path.

Therefore, the critical path is A-B-E-H-I and its duration is 31weeks .

Now the project is to be completed 3 weeks earlier.

Consider the critical path activities.

The lowest crash cost per week is of activity B and activity H.

Crash Activity B by 2 weeks and activity H by 1week .

  Crash B=2×200=400

And,

  Crash H=1×200=200

Thus, the additional cost of crashing the activity by 3weeks is,

  Additional cost=200+400=600

The new network diagram is shown in figure below.

  OM (with OM Online, 1 term (6 months) Printed Access Card), Chapter 18, Problem 12PA , additional homework tip  2

Figure (2)

Consider figure (2), the different paths and their completion times is tabulated below.

    PathCompletion time (weeks)
    A-B-E-H-I5+7+7+3+6=28
    A-C-E-H-I5+7+8+3+6=29
    D-E-H-I6+8+3+6=23
    D-G-I6+3+6=15
    D-F-I6+3+6=15

Table (4)

From Table (4), the maximum completion time is taken by path A-C-E-H-I . So, this is the critical path.

Therefore, the critical path is A-C-E-H-I and its duration is 29weeks .

But the desired project duration is 28 weeks .

Try different option.

Crash Activity B by 1 week, activity E by 1week and activity H by 1week .

  Crash B=1×200=200

And,

  Crash H=1×200=200

And,

  Crash E=1×250=250

Thus, the additional cost of crashing the activity by 3weeks is,

  Additional cost=200+200+250=650

The new network diagram is shown in figure below.

  OM (with OM Online, 1 term (6 months) Printed Access Card), Chapter 18, Problem 12PA , additional homework tip  3

Figure (3)

Consider figure (3), the different paths and their completion times is tabulated below.

    PathCompletion time (weeks)
    A-B-E-H-I5+7+7+3+6=28
    A-C-E-H-I5+7+7+3+6=28
    D-E-H-I6+7+3+6=22
    D-G-I6+3+6=15
    D-F-I6+3+6=15

Table (4)

From Table (4), the maximum completion time is taken by path A-C-E-H-I and A-B-E-H-I So, this are the critical path.

Therefore, the critical path are A-C-E-H-I and A-B-E-H-I and its duration is 28weeks .

Therefore, the crashing cost of the project is $650 .

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