The Development of a Resource Allocation Model for Pert/Cpm Analysis.

113 Pages·2017·3.8 MB·English

by  Don Roger Robinson

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LSU Historical Dissertations and Theses Graduate School
1971
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Don Roger Robinson
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Robinson, Don Roger, "The Development of a Resource Allocation Model for Pert/Cpm Analysis." (1971).
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ROBINSON, Don Roger, 1942-
THE DEVELOPMENT OF A RESOURCE ALLOCATION
MODEL FOR PERT/CPM ANALYSIS.
The Louisiana State University and Agricultural
and Mechanical College, D.B.A., 1971
Statistics
University Microfilms, A XEROX Company, Ann Arbor, Michigan
THE DEVELOPMENT OF A RESOURCE ALLOCATION
MODEL FOR PERT/CPM ANALYSIS
A DISSERTATION
Submitted to the Graduate Faculty of the
Louisiana State University and
Agricultural and Mechanical College
in partial fulfillment of the
requirements for the degree of
Doctor of Business Administration
in
The College of Business Administration
by
Don Roger Robinson
B.B.A., The University of Texas, 1965
M.B.A., The University of Texas, 1966
January, 1971
ACKNOWLEDGEMENTS
The origin of interest in the topic of PERT/CPM occur­
red in 1964 during an undergraduate course in decision theory.
A film viewed by the class on the use of PERT gave scant
mention to the method of allocating resources. With the
development and use of more and more powerful optimization
techniques, the area of PERT/CPM seemed fruitful ground
for further research.
The completion of the dissertation was assisted by sev­
eral individuals. Dr. R. L. Burford, the supervisor of my
doctoral program, stressed the need for practical illustration
as well as theoretical precision. These efforts together
with suggestions for the presentation of the theoretical sec­
tions strengthened the contribution of the research. Dr. V. E.
Cangelosi and Dr. J. W. Duggar provided valuable criticisms
for the preliminary chapters of the dissertation. The assist­
ance of Dr. E. Gray, Dr. L. Richardson, and Dr. D. R. Scholz
occurred during the course-work stage of my program, and
influenced my ideas concerning research in the quantitative
areas. Special thanks are given to my brother, Max A.
(American Institute of Architects), who undertook the pen
and ink work for the illustrations. And to my wife, Sandra,
love and thanks for enduring the agony and frustration of
typing the final draft.
I
TABLE OF CONTENTS
Chapter Page
List of Tables.......................................... vi
List of Figures............................................ vii
Abstract..................................................viii
I. INTRODUCTION ...................................... 1
Statement of the Problem......................... 1
Objective of the Research......................... 3
Research Design.................................... 4
Assumptions and Limitations of the Model........ 5
Organizational Plan................................ 6
II. REVIEW OF THE LITERATURE......................... 7
Resource Allocation Techniques ................... 8
Significant Models............................. 9
Implications of the Models..................... 16
Contributions in Dynamic Programming ............. 16
Implications of Existing Research................. 18
III. PRELIMINARY CONCEPTS OF THE MODEL................. 20
The Time-Cost Relationship....................... 20
Precedence Diagramming ........................... 25
Importance of the Preliminary Concepts .......... 33
IV. THE RESOURCE ALLOCATION MODEL..................... 34
Basic Objective of the Model..................... 34
Formulation of the Model ............... 36
Application to Large Networks..................... 45
Decomposition Principle ....................... 45
Advantages of Each Approach................... 49
Implications of the Model......................... 55
iv
V
Chapter Page
V. APPLICATION OF THE MODEL......................... 56
Example Project.................................... 56
Solution of the Problem........................... 59
Solution of the First Subnetwork.............. 60
Solution of the Second Subnetwork ............ 66
Solution of the Third Subnetwork.............. 69
Solution of the Fourth Subnetwork ............ 75
Allocation Among the Subnetworks............... 77
Optimum Allocation................................ 81
Subnetwork 1.................................... 82
Subnetwork I I .................................. 83
Subnetwork III.................................. 84
Subnetwork I V .................................. 85
Conclusions of the Application ................... 88
VI. EVALUATION AND IMPLICATION OF THE MODEL........... 89
Contribution of the Research..................... 89
Evaluation of the Model............................ 90
Advantages...................................... 91
Disadvantages .................................. 94
Areas for Further Research....................... 95
Conclusion........................................ 96
Bibliography ............................................ 98
Vita....................................................... 100
LIST OF TABLES
Table Page
1. Hypothetical Project .............................. 26
2. Hypothetical Precedence Relations................. 31
3. Cost-Time Functions................................ 58
vi
LIST OF FIGURES
Figure Page
1. Traditional Network............................... 27
2. Precedence Network................................ 27
3. Redundant Path.................................... 32
4. Precedence Diagram................................ 32
5. Sample Network.................................... 37
6. Example Network.................................. 42
7. Simple Subnetwork ................................ 50
8. Complex Subnetwork................................ 53
9. Example Project.................................. 57
10. Activity Functions................................ 57
11. Subnetwork 1....................................... 60
12. Subnetwork II . . . . . . . . . . . . 67
13. Subnetwork III.................................... 70
14. Subnetwork I V .................................... 7 5
15. Condensed Network ................................ 77
16. Optimum Allocation................................ 87
vii
ABSTRACT
Resource allocation to the activities in a PERT network
is a significant problem in economic analysis. Several at­
tempts to solve this problem have resulted in models that
provide approximate solutions. The objective of the research
is the development of an efficient model that produces the
most accurate solution to this resource allocation problem.
Previous models are inadequate for several reasons.
Some approaches provide optimum solutions for linear approx­
imations to the cost-time functions of the activities. Other
models, which use realistic cost-time functions, cannot dis­
tinguish between local and global optima. Models that meet
these shortcomings are so complex that their use is restricted
to relatively small networks.
Assumptions of the model involve the cost-time relation­
ships of the activities and the network diagramming procedure.
All of the resource allocation models assume a relationship
between the time and the cost necessary to complete an activity.
This relationship is generally assumed to be inverse— a re­
duction in time is made possible with the allocation of addi­
tional resources. It is assumed that the amount allocated
to an activity is used as efficiently as possible. Even
viii