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"Can you invent some time estimates for the various steps?" I ask him.

"With pleasure." Being a financial manager he cannot stop himself from asking, "Do you also want estimates of investments?"

"No need."

I wait until he finishes and returns to his seat. "According to the numbers that Fred picked, it will take ninety days to build the building and thirty days to make it functional. A total of one hundred twenty days."

"Fred, where did you get such unrealistic numbers," Ted shouts.

"Out of thin air," Fred calmly answers.

I ignore them both and continue. "To pick the vendors takes fifteen days."

"Only in Fred's dreams."

I give Ted a look. He signals, "Sorry." I finish my sentence, "And the time it will take them to supply is another ninety days. The installation of machines takes an additional thirty days. What is the critical path?"

"The building." Ted is very vocal today.

"Why?"

"Because, according to Fred's ridiculous numbers, it takes one hundred twenty days to prepare the building while the machines are ready in one hundred five days."

"You are too hasty," I tell him. "Critical path is defined as the longest chain of dependent steps. Longest in time, of course."

"I know," he impatiently says. Then more slowly, "The critical path is the path through the steps of building the building, making it functional and installing the machines in it. A total of one hundred fifty days."

"The critical path," I remind the class, "determines the time it will take to finish the project. Any delay on the critical path will delay the completion of the project. That's why the project manager must focus on it."

Nobody has a problem with what I've said. No wonder, considering their experience in projects.

"If we call the time we start the critical path ‘time zero,' the project is planned to be finished at time one hundred and fifty. When should we start the other path? When should we start picking the vendors for the machines?"

"There is no rush there," Brian volunteers an answer. "We can start picking the vendors at time fifteen."

"What?" Ted exclaims.

I signal Ted to calm down and ask Brian to come to the board and draw the corresponding Gantt chart. He does it without any difficulty.

"Brian chose the late start for picking the vendors," I say. "But, as we all heard, Ted probably has another suggestion. But Ted, rather than giving us a whole speech, go to the board and draw your Gantt chart."

That throws him off balance for a second, but just for a second. When his chart is done he turns and starts attacking Brian, "I don't know what's gotten into you. You are going to tell me that in the projects you manage you really start at the latest possible time? No wonder your projects are late. You've got spare time, take it! That's my motto."

"Fine, Ted," I calm him down. "But will you please go back to your seat so we all can see what you drew?

"Gantt charts, unlike PERT diagrams, involve decisions," I highlight to the class, "the decision of the planner when to start each path. Brian chose the late start for picking the vendors while Ted has chosen the early start."

"Of course," Ted almost shouts. "What's the point in taking unnecessary risks!"

"The point is," Fred interjects, "to postpone the investments until they are really necessary. Don't you think that's just as important?"

"I'm not sure," is Ted's response, but it's clear that he is less sure about his position.

"It's an optimization problem," Brian is confident. "We have to weigh the savings from postponing an investment against the chance of damage resulting from finishing the project a little late."

One thing I passionately hate is optimization problems. There are so many articles about these cases, all with involved mathematical models, all so tough and time-consuming to read. And from my experience, all have little practical use. But what can I do; it is an optimization problem.

Ruth raises her hand. Here it comes. Now I'll be forced to show them the