PERT-CPM-PDM & SPIDER - Aspects of Modern Project Management


    Part I gives an overview of Project Management and is divided into five sections. These discuss  (1) its origins, (2) advantages, (3) the basic concept, (4) the calculation and conclude with (5) a note on float.  Part II gives a brief introduction to Project Management software.


I. Project Management, an Overview

1) Introductory Comments1 and the Origins of Project Management

    Project management is a sophisticated subject with an extensive literature,2 including many textbooks. The short introduction here is, per force, limited. A good source for further information is the Project Management Institute (PMI). Lest anyone with a quantitative background who finds the mathematics straightforward underestimate the fine points, see the brief note at (5) about Float.

    Eight fundamental laws of project management have been stated by the American Production and Inventory Control Society, APICS, (Slack et al.) in 1998. To quote the three most important, and their consequences:

    1) Projects progress quickly until they are 90% complete, and then remain there forever.

    2) If project change is freely allowed, the rate of change will exceed the rate of progress.

    3) When things are going well, something will go wrong. When things just cannot get any worse, they will. When things appear to be going better, you have overlooked something.

    The consequences are two. First, if a minor project finishes on time and within budget, that means the content has been severely compromised. Second, no major project is ever installed on time, within budget, or with the same staff that started it. Yours will not be the first. 

    There was little written evidence of project management methods until the 20th century. In 1917 Henry L. Gantt, an American engineer, developed the bar chart that bears his name as a production control tool. It led in turn to milestone charts. These had become common by the 1950s, which also saw the creation of CPM and PERT. 

    Basically, CPM (Critical Path Method) and PERT (Program Evaluation Review Technique) are project management techniques. CPM  is best suited for projects where the tasks have fairly certain completion times with little variation. In quantitative terms, CPM is a  deterministic model. PERT is better suited for projects that entail uncertain completion times. PERT, a probabilistic model, allows different estimates of time (e.g. optimistic, expected, pessimistic) for each activity.

    In 1956 E.I. du Pont de Numours (Du Pont) had acquired an UNIVAC computer, but was not quite sure what to use it for. Scheduling large, complex projects seemed like a good possibility. Morgan R. Walker received the assignment. 

    CPM began in 1956. From late 1956 to April 1957 Walker worked on the project with J.E. Kelly, a mathematician of Remington Rand Univac,  and John Mauchly.  In 1957 a joint project was formed, with Dupont contributing $167,700 and Remington Rand Univac $58,700 for a total of $226,4000. The team was lead by Walker and Kelley, who developed a CPM schedule in July 1957. The first test was made in 1958, when CPM was used to plan the construction of a chemical plant. However in 1959 Dupont and Univac dropped the CPM project. Undaunted, Mauchly  and Kelly started a company to commercialize it.  They charged as much as the cost of a new car for solving scheduling problems!

    PERT was devised in 1957/58 for the Polaris missled program by Gordon Perhson at the Program Evaluation Branch, Bureau of Ordinance, Special Projects Office, of the U.S. Navy. Support was provided by Bill Pocock of Booz-Allen & Hamilton, a management consulting firm, and by the Lockheed Missle Systems Division. The PERT team introduced the term "critical path. The calculations were done on the IBM Naval Ordinance Research Computer (NORC) at Dahlgren, Virginia.

    As computers became more powerful, project management software became more sophisticated. From the mid-1950s to the beginning of the 1970s limited computer capabilities led to "faux rules." For example, an activity used one resource, which led to "ladder feed" diagrams for sequential projects. Typical examples are transportation projects such as building highways or canals. To avoid "waterfall" and "wagon wheel" dependency errors, one use dummy variables. The limitations imposed by "dummy" dependencies were overcome by John Fohndahl'S (1924-2008) Precedence Diagram Method, PDDM. After serving in the Marine Corps, he completed his engineering studies at Dartmouth University and then moved to California. 

    He became a professor at Stanford. Upon arriving, he co-founded Stanford´s graduate Construction Engineering and Management (CEM) program in 1955. Later, in 1969, he also co-founded the very well regarded Project Management Institute (PMI), which today has over 70,000 members.

    The U.S. Navy´s Bureau of Yards and Docks and its Special Projects Office funded John Fondahl´s research at Stanford University. In 1961/62 he published an article at Stanford introducing PDM: "A Non-computer Approach to Critical Path Methods for the Construction Industry." PDM was presented as a manual alternative to the expensive computer-based CPM. Ironically, PDM is now used by computers. It eventually displaced PERT and CPM.  Refinements to PDM were made leading to its becoming popularized in the 1970s, among others via Western Construction. Essentially what Fondahl did was to reverse the traditional diagramming of Activity-on-Arrow with Activity-on-Node, using only Finish-to-Start relationships.

    The U.S. Navy's Bureau of Yards and Docks and its Special Projects Office funded John Fondahl's research at Stanford University. He published an article at Stanford in 1961/62 introducing PDM: "A Non-computer Approach to Critical Path Methods for the Construction Industry." PDM was presented as a manual alternative to the expensive computer-based CPM. Ironically, PDM is now used by computers.

    It eventually displaced PERT and CPM. Refinements to PDM led to its becoming popular in the 1970s, partly in thanks to its support by Western Construction. Essentially John Fondahl reversed the traditional diagramming of Activity-on-Arrow with Activity-on-Node, using only Finish-to-Start relationships.

    PDM features were steadily added as computers became more and more powerful. PDM programs became able to account for multiple resources (per activity), relationships, and lead and lag times for dependicies. They became correspondingly more difficult to use. In fact, their very complexity often creates an illusion of control, that matters are well in hand, when they are note. The bête noire is the attention to detail that is needed to prepare properly Work Breakdown Structures. These need to account for contract and sub-contract deliverables, resource determination and allocation as well as cost and earnings loading.

2) Planning, Scheduling and Control Advantages
    Besides the direct project management benefits, PERT/CPM/PDM provide ancillary ones. The methods are an important communications bridge between the driving strategy and the tactics critical to realizing it, i.e. getting the project done on-time, on-budget. Meeting the PDM/PERT/CPM plan also has come to be used as a benchmark for evaluating individuals and teams.

    The methods address the following main concerns:

    - ETA (estimated time of arrival, i.e. completion) of the project

    - Potential project bottlenecks

    - Progress control - the meeting of milestones

    - Risks of exceeding the budget

    - Risks of missing the deadline


3) The Basic Network Concept of PERT and CPM

    PERT and CPM have six steps in common:

    1. Set the start and end dates for the project as a whole.

    2. Break up the project into a series of individual tasks, i.e. activities.

    3. Develop the sequence for these activities and their relationship to one another. For example, A must be finished before B, C, or D can start; B must be finished before D can start (but not before C), etc.

    4. Estimate the time needed for each activity.

    5. Estimate the cost for each activity.

    6. Compute the longest path through the network, which is known as the critical path. 

    The activities that make up the longest path control the project. Therefore focus should be upon them, with adequate resources (the best people, other top quality input) allocated to them. Implicit to PERT/CPM is continuous feedback and the ability to adjust to changes in activity times/budgets to optimize project completion.


4) The Calculation
    Usually Wikipedia is a good point of departure, but in this case there is a far better article from Interventions (India) Pvt. Ltd. The article explains very well the underlying mathematics with a worked example and excellent diagrams from:

    Jerome D. Wiest, Ferdinand K. Levy A Management Guide to PERT/CPM, New Delhi: Prentice-Hall of India Private Limited, 1974

    Barry Render, Ralph M. Stair Jr. Quantitative Analysis for Management, Allyn & Bacon, 1982, pp. 525-563

John E. Freund Modern Elementary Statistics, New Delhi: Prentice-Hall of India Private Limited, 1979


5) A Note on Float

    Float or slack gives the leeway, the margin of error. The two main categories are Free Float and Total Float. The former is the buffer, the extra available time, when all the preceding activities finish at the earliest possilbe times, AND all the suceeding activities happen at the earliest possible times.

    The latter, Total Float, is the available time when all the preceding activities finish at the earliest possible times AND all the succeeding activities happen at the latest possible times. Restated as a simple formula:

Total Float = Latest Start - Earliest Start.

When an activity has zero Total Float, Free Float will also be zero. Activities with zero Total Float are on the Critical Path. If the above is all intuitively obvious to you, then you are ready to progress to the variations of float: Independent, Early Free, Early Interfering, Late Free and Late Interfering. Note that float can be negative. Float is treated in the literature at length.


II. Project Management (PM) Software

    A good point of departure is the Wikipedia article on comparison of PM software, with about about 120 products listed. This list is by no means complete.  One can make a graph similar to the one at Wikipedia listing the features important for one's own project. (Making this kind of Excel spreadsheet is a good task for the computer-savy student intern.)

    Microsoft Project is the benchmark against which other such software is measured. Its first version, for DOS, was released in 1984. Microsoft Project '98 was reasonably priced and had straightforward features. Both the features and the price have steadily escalated. In 2010 Version 14.0 had a price tag of about $1500.

    The most conspicuous absence from the Wikipedia list is SPIDER, arguably the most sophisticated project management currently available. In any case, it is considerably more powerful than Microsoft Project, although not nearly as widespread. SPIDER has been used in 28 countries; the ubiquitous Microsoft competitor has probably been used in a 100.

    SPIDER is used for virtually all major projects in Russia, including the planning of the 2014 Olympics. The English version of the website is well-done, cf.




1 In addition to Wikipedia (2010) articles and my own project management experience, another source was "A Brief History of Scheduling - Back to the Future," a presentation by Patrick Weaver, Director, Mosaic Project Services, April 2006 ( and (2011) (formerly at



2 Just one arbitrary example, selected more or less at random, is the work by Eric L. Demeulemeester and Willy Heroelen, Project Scheduling, a Research Handbook, Kluwer´s International Series, 2002, 307 pp., $249. The review of it at states (slightly edited):

". . . The builders of the pyramids in Egypt and the Great Wall of China are often cited as the world´s first project managers. (Both are cited on the preceding subpage "Megaprojects, worldwide.") Without the help of computers or planning software, they managed exceptionally complex projects, using the simplest of tools. . . Our objectives are threefold: (1) Provide a unified scheme for classifying the numerous scheduling problems occurring in practice. . . (2) Provide a unified and up-to-date treatment of the state-of-the-art procedures developed for their solution; (3) Alert the reader to various important problems that are still in need of considerable research effort." 


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