ebook img

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

113 Pages·2017·3.8 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

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

LLoouuiissiiaannaa SSttaattee UUnniivveerrssiittyy LLSSUU DDiiggiittaall CCoommmmoonnss LSU Historical Dissertations and Theses Graduate School 1971 TThhee DDeevveellooppmmeenntt ooff aa RReessoouurrccee AAllllooccaattiioonn MMooddeell ffoorr PPeerrtt//CCppmm AAnnaallyyssiiss.. Don Roger Robinson Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses RReeccoommmmeennddeedd CCiittaattiioonn Robinson, Don Roger, "The Development of a Resource Allocation Model for Pert/Cpm Analysis." (1971). LSU Historical Dissertations and Theses. 1945. https://digitalcommons.lsu.edu/gradschool_disstheses/1945 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. 71-20,617 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

Description:
most accurate solution to this resource allocation problem. Previous models are . The problem of resource allocation in PERT/CPM models is not new "^J. J. Moder and C. R. Phillips, Project Management with. CPM and PERT, (.
See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.