# Gert

Branching from a node is probabilistic. Various possible probability distributions for time estimates. Flexibility in node realization. Looping back to earlier events is acceptable. Difficult to use as a control tool. Arcs may represent time, cost, reliability, etc.

PERT/CPM

Branching from a node is deterministic. Only the beta distribution for time estimates. No flexibility in node realization. Looping back is not allowed.

### Easy to use for control. Arcs represent time only.

While there are computer programs that optimize PERT/CPM problems, GERT and its various enhancements are computer simulations. Most of the programs (and the enhancements) are the result of work conducted by Pritsker [■44). His modeling package called Q-GERT simulates queues, or waiting lines, in the network. (There are other extensions of PERT that have some features similar to GERT and Q-GERT—VERT, for example—but GERT seems to be the most widely used extension.)

The steps employed in using GERT are these:

1. Convert the qualitative description of the project action plan into a network, just as in the use of PERT/CPM.

2. Collect the necessary data to describe the arcs of the network, focusing not only on the specific activity being modeled, but also on such characteristics of the activity as the likelihood it will be realized, the chance it might fail, any alternative activities that exist, and the like.

3. Determine the equivalent function of the network.

4. Convert the equivalent function of the network into the following two performance measures:

The probability that specific nodes are realized. The "moment generating function" of the arc times.

5. Analyze the results and make inferences about the system.

It is not appropriate to deal here with the complex solution techniques employed for GERT networks. They make use of topology equations, equivalent functions, moment generating functions, and extensive calculation. The interested reader is urged to consult the papers of Pritsker and others 11, 44, 50] for formal descriptions of the methods involved in formulating and solving GERT networks. Instead, we will describe how to construct a GERT network of a simple situation. The list of common GERT symbols, together with a few examples, is given in ■ Figure 8-25. This figure describes the left, or input side of the nodes first, and then the right-hand output side next. All combinations of input and output symbols are feasible, as shown in the examples.

Now let us describe a manufacturing project situation developed by Pritsker and portray it through the GERT approach. This situation concerns the initiation of a new production process developed by manufacturing engineering for an electronic component. The resulting GERT model could just as well describe an R & D project, a government project, or a Girl Scout project.