Project management using GERT analysis
LAURENCE J. MOORE
Virginia Polytechnic Institute and State University
Application of network analysis to project planning and control has been extensive since the late 1950’s , PERT and CPM, the best known network modeling techniques, have been applied to a diverse number of projects for planning and control purposes. However, PERT and CPM do have limited capabilities which prohibit modeling of many complex project network forms. A more flexible generalized network tool which has received increased attention recently is GERT (Graphical Evaluation and Review Technique) , GERT includes features such as probabilistic branching (stochastic models), network looping (feedback loops), multiple sink nodes (multiple outcomes), and multiple node realization (repeat events) which are unavailable in PERT/CPM. These GERT features provide the user with the capability to model and analyze projects and systems of a very general form. Since many real-world system problems do involve probabilistic occurences, false-starts, activity repetition, and multiple outcomes, GERT is an ideal tool for the modeling and analysis.
The purpose of this paper is to describe the GERT network modeling technique and simulation package, and demonstrate its capabilities via an example of R&D project planning. Included in this overview of GERT will be a discussion of the use of GERT output for management planning and control including sensitivity analysis and implementation.
The conceptual framework for construction of PERT/CPM networks is straight forward and generally well-known. However, since GERT networks are similar in construction to PERT/CPM networks it will be useful to briefly review the PERT/CPM components.
PERT/CPM networks consist of two major components, activities and events. Network activities represent actual operations of the real-world project, while events represent milestones in the project that occur at a point in time. Events can represent the beginning or end of an activity or both; and, the beginning or end of both of more than one activity. Activities generally consume time and resources. In network configuration, events are represented by arrows. PERT and CPM differ in that in CPM activities are assumed to have only a single time for duration while in PERT the activity times are probabilistic, and typically described by a three estimate beta distribution. (For a more detailed explanation of PERT and CPM see ).
Figure 1. The GERT Characteristics
Figure 1 presents a brief schematic which highlights the differences between PERT/CPM and GERT, and demonstrates the various GERT characteristics and attributes    . The primary difference between PERT/CPM and GERT networks is that GERT has two types of nodes, deterministic and probabilistic , Node 3 in Figure 1 (the identification number is on the right-hand side of the cone shaped node) is a probabilistic node. Instead of one deterministic branch (arrow) as in PERT/CPM there are four possible outcomes each with a probability of occurrence. Thus, at a probabilistic node a choice situation exists where one of several alternatives may be selected based on the associated probabilities. However, the sum of the probabilities for all activities emanating from a probabilistic node must be 1.00 (i.e., there is a 1.0 probability that one of the activities will be realized).
If the activity emanating from node 3 and looping back to node 2 occurs, this would cause activity 2-3 to be repeated. If, on the other hand, the activity labeled “failure” was realized, the network might flow to a “sink” node which ends the network. Alternatively, if the activity labeled “success” is realized, the network might continue for several more activities before the network ended in another (different) “sink” node. The fourth activity at node 3 is activity 3-3 representing a self-loop back to the same node. These alternative activities reflect the feedback, multiple outcome and repeating activities characteristics of GERT.
Node 2 is a deterministic node as used in PERT/CPM. Because node 2 is deterministic, the probability of realization for activity 2-3 is 1.0. In both node 2 and node 3 the number is the upper left-hand quadrant represents the number of releases necessary for the first realization of the node (in both cases shown only one activity release is required). The number in the lower left quadrant of each node is the number of activity releases required for all subsequent realizations of the node.
GERT is relatively easy to use since it requires only that the project of interest be (1) diagrammed in network form, (2) converted to program input data describing the network, and (3) simulated using the prewritten GERTS-IIIZ simulation package 5 . By simulating the network, statistical data can be collected at different nodes for network duration and cost. The GERTS-IIIZ program is maintained by Pritsker and Associates, Inc. (P.O. Box 2413 West Lafayette, Indiana 47906) and copies can be purchased for several hundred dollars. The program is written in FORTRAN IV and can be operated using any FORTRAN complier. The program is accompanied by a user’s manual which makes use of the program quite simple for anyone with minimal computer skills (also, see [5l). This ease with which GERT can be implemented facilitates model experimentation, network modification and sensitivity analysis.
The GERT simulation package has the capability for nine different probability distributions for activity times: constant, normal, uniform, erlang, lognormal, poisson, beta, gamma and the beta fitted to three parameters. The GERT model also has the capability for assigning fixed and variable costs to network activities, (i.e., a fixed cost can be assigned so that each time an activity takes place the cost is accumulated; the variable cost is tabulated depending on the length of time the activity consumes.)
GERT has been effectively applied to a number of systems problems including product planning , research and development planning , market research , production planning [l3], quality control [l], manpower planning  and Ph.D. program development , among others.
Figure 2. GERT Network of an R & D Project
GERT Application for an R&D Project
In this section the GERT modeling process and the GERTS-IIIZ simulation will be demonstrated via an example of a generalized research and development project. The projects follows the normal R&D process consisting of 5 basic stages: (1) problem definition, (2) research activity, (3) solution proposal, (4) prototype development, and (5) solution implementation. (This is a modified version of a more complex R&D model presented by Moore and Taylor ). Figure 2 is the GERT network which reflects this sequential R&D process.
The project is initiated in activity 2-3 which is followed by the first stage of the R&D process, formal definition of the problem to be attacked by the R&D team. Problem definition is represented by activity 3-4. Following the completion of stage 1, problem definition, the next stage, research activity is normally initiated. However, the possibility that the problem was not sufficiently defined is reflected by activity 4-3 which causes stage 1 to be repeated. If the process proceeds to activity 4-5, research activity, the next step is represented by activity 5-6, solution proposal.
At the completion of activity 5-6, four alternative outcomes are possible. First, it may be concluded that the problem was incorrectly defined to begin with, thus prohibiting the development of a viable solution proposal. This possibility is shown by activity 6-3, a loop back to node 3 for redefinition of the problem. Second, the search for a solution proposal may have indicated insufficient research in which case the network loops back (i.e., by activity 6-4) to node 4 for reconducting the research activity. Third, the attempt to propose a solution may indicate that no solution exists. This occurrence ‘is reflected by activity 6-7, defined as project washout. Node 7 is a “sink” node indicating project termination, and the end of the network. Finally, if a solution proposal is successfully developed the network proceeds to activity 6-8, prototype development.
When activity 6-8 is completed, two outcomes are possible. If the prototype was not developed properly, redevelopment is necessary which is shown by activity 88, a self-loop around node 8. (Note that it was not possible to loop back to node 6 in order to repeat activity 6-8 since this would have resulted in the possible realization of any one of the four alternative activities emanating from node 6 rather than just activity 6-8.) If a satisfactory prototype is developed, the solution is implemented in activity 8-9. Node 9 is a second network “sink” node representing successful completion of the R&D project.
TABLE 1 Activity Descriptions With Time And Cost Estimates
Table 1 provides a summary of all relevant network information, including activity descriptions, activity time estimates and associated probability distributions, outcome probabilities, and fixed and variable cost estimates. For example, activity 4-5, research activity, has a 0.80 probability of being realized. The time of duration is defined by a beta distribution with 3 estimates; a minimum of 60 days, a most likely of 100 days and a maximum of 120 days. Each time this activity is realized a fixed (i.e., set-up) cost of $2,000 is incurred. For each day the activity is in progress a variable cost of $300 is incurred. The three parameter beta distribution was used in this network since activity estimates tend to be subjective for an R&D project of this type as is true in PERT networks.
The GERT R&D network was simulated 1000 times from which time and cost statistics were generated. The results of the simulation are summarized in Tables 2 and 3. Interpreting the results, there is a .745 probability that the project will be successfully completed, with an expected completion time of 419 days. The average cost of successful completion is $473,000. The maximum time the project will take, as indicated by the simulation, is 1,514 days, with a cost of $1,147,900. Alternatively, there is a .255 probability the project will washout in an average time of 182 days, with an associated mean cost of $195,000. The GERTS-IIIZ simulation package can also provide time and cost statistics at individual network nodes in the form of frequency distributions, which can then be converted to histograms. Figure 3 shows an example of a histogram for time statistics collected on node 9, time to successful completion of the project. Similar histograms can be developed for time statistics on node 7, and cost statistics on both sink nodes.
The Use of GERT Results
The GERT simulation results can be used in several ways by management to facilitate and enhance project planning. The primary difference in the GERT results and the results obtained from a PERT or CPM network (apart from the fact that the GERT results reflect a stochastic network) are the cost statistics. These cost statistics provide a significant input into determining whether or not a project should be undertaken and/or how it can be best controlled.
TABLE 2 Network Simulation Results Time Statistics for R&D Project Network
|Node||Event||Probability||E(t)||ot||Min t||Max t|
Figure 3. Time to Successful Completion of Project
For the R&D example network it may be determined that if the project cost (of success) exceeds $700,000 then it should not be undertaken. Employing the histogram output for node 9 would lead to the forecast that there is a .07 probability that the total cost of a successful project will equal or exceed the $700,000 limit. Depending upon the amount of risk the firm is willing to assume, a .07 probability may or may not be acceptable. Probabilistic information of this type can also be obtained for project duration. For example, in the R&D network there is a .20 probability that the time for a successful completion of the project will exceed 1.4 years (i.e., 500 days). If a critical time deadline is established at 500 days then a 20 percent chance of not finishing on time may be too risky.
Network Simulation Results
Cost Statistics for R&D Project Network
|Cost (thousand $'s)|
|Node||Event||Probability||E(c)||oc||Min c||Max c|
This same type of probabilistic analysis can be performed for a project failure. In this way management can ascertain information regarding its potential losses since a project failure typically represents a loss. For the R&D example there is a .96 probability that, if the project washes out, a cost (i.e. loss) of at least $350,000 will be incurred. This potential loss may make the firm ponder its undertaking more in-depth. Probabilistic data on project failure can further be used to determine the most likely time a washout will occur so that contingency plans can be developed (i.e., alternative projects arranged) in order to keep R&D project teams and work forces fully scheduled.
GERT output can also be used to determine labor, equipment and resource needs for the project under analysis. Typically, cost statistics are employed as budget data with these factors included. For example, if statistics for project time showed an excessive project duration then extra labor, equipment or capital could be added to reduce total project time. Such additions could also be made to reduce the possibility of project failure at late stages in the project where associated costs would be highest. The effect of these resource increases would subsequently be reflected in the project cost statistics (i.e., budget). (An alternative to resource determination is to use the fixed and variable cost feature of the simulation model for resource units as opposed to dollar values in order to determine resource consumption directly).
The network itself can be modified and adjusted to reflect alternative project strategies. GERT networks in general are usually sensitive to outcome probability changes. For example, in Figure 2 if the probability of realization for activity 4-3, a problem redefinition, is altered the overall network time and cost can be significantly effected. Management can take advantage of this capability by adding and subtracting resources to see how outcome probabilities are effected and hence how the overall network is affected. For example, management might determine that their time frame is much more flexible than the expected time indicated by the network simulation. By reducing resources (i.e., pulling off men, capital and equipment), activity 3-4, problem definition is not as effective, thus, the probability of activity 4-3, problem redefinition, is increased which increases overall network time. In this instance the firm saves resources (which might be critical) in lieu of time which may be readily available. Of course, this logic can work in the opposite direction, wherein the time frame is critical and resources are available in abundance, in which case the outcome probabilities for looping are reduced by adding resources. In general, the GERT model is ideal for testing trade-off situations between project time and cost.
In general, the GERT network is not as sensitive to activity time changes as node branching probability changes. Of course if the project activity times are extremely cost sensitive then a slight alteration in an activity time can affect network (project) cost even though the overall network time might not be affected significantly. However, one of the unique capabilities available with GERT is the ability to use any one of nine probability distributions for activity times. Since projects which are networked tend to be unique, the selection of activity probability distributions is subject to a great deal of uncertainty. In such cases it can be useful to experiment with alternative distributions to observe the overall affect on network statistics. Such experimentation can lead management to perform much more in-depth research into the nature of activity time distributions rather than simply accepting the subjective beta distribution as is so often done in PERT This can lead to further insight into the activities and project analysis in general.
An important network modification which can have a significant affect on the management planning process is the probability of project washout (or failure). This aspect of network analysis was briefly mentioned previously but it needs to be discussed in greater detail. The probability of project failure reflected by node 7 in the example network (Figure 2) represents the inherent risk in undertaking the project. At the very least, the probability of a washout offers a guideline to compare with some acceptable risk level for the project’s undertaking. This risk indicator can become more complex if there are several opportunities for project washout. For example, in our R&D network, if there were chances of washout from nodes, 4, 5, and 8 as well as node 6, then the problem of determining how to reduce the probability of project failure becomes more difficult. In such a case the opportunities to affect project failure, either positively or negatively, increases via the additional activities directly affecting a washout.
The type of information discussed in this section can have important ramifications for project contract negotiations. If the project is for internal firm use, it is beneficial in contracting for labor, materials, capital and equipment. However, in the important case of project planning for external use, GERT information can aid in setting contract prices so that the firm can be assured of a profit. For example, since the probability of exceeding $700,000 for the successful completion of the project is .07, a contract price of $900,000 would seem to provide a reasonable chance to make a profit and management could react accordingly. The same analysis could be used for establishing a project due date. The washout data can enable the firm to build minimum losses into a contract and perhaps distribute the potential losses between the firm and the customer in an equitable fashion.
GERT vs PERT/CPM
As this point in the presentation it will be useful to elaborate in more detail about some of the important differences between GERT and PERT/CPM. CPM, the most widely used project network tool, provides very little information for planning beyond an estimate of project duration and a knowledge of activity sequencing. In fact, it is this latter attribute of activity sequencing that tends to be the primary use of CPM. The availability of data for use in detailed financial planning is extremely limited. PERT expands on CPM in that the requirements for several estimates of time data leads to more information regarding the probabilistic nature of the project. However, the PERT computed results are known to be biased, whereas the GERT simulation leads to unbiased statistical estimates. GERT in its simplest form can be used to replicate PERT networks by employing only deterministic branching and either constant or probabilistic activity time estimates. Added to this is the ability to model complex stochastic projects, and the large amount and variety of statistical data that can be generated. The preferrability of GERT as a planning tool for many real world situations should be apparent. In addition, during the past few years advances have been made in GERT which have extended its capabilities. The most important advancement now readily available to practitioners is Q-GERT which, among other things, can model queues at nodes and route items through servers based on user established decision rules 
The purpose of this paper has been to introduce the basic concepts and fundamentals of GERT networking for project management, demonstrate its use via an example, and comment on some of the possible uses of GERT statistical results for planning. However, it should be remembered that GERT is capable of handling extremely complex projects as well as on-going systems. Thus, the material presented offers only a superficial view of what can actually be accomplished with the GERT technique. The interested reader is encouraged to pursue the capabilities of GERT further through the references given at the end of this paper (especially  and ). In addition, only the most obvious uses of GERT results were reviewed in the section on model results. It is the authors belief that in most cases the result of project network planning can be more wisely used in the planning process than is often the case not only in GERT but for PERT/CPM as well.
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