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PROJECT SCHEDULING WITH UNCERTAIN ACTIVITY TIMES 381

MANAGEMENT SCIENCE IN ACTION

Hospital Revenue Bond at Seasongood & Mayer
easongood & Mayer is an investment securities when the hospital signed the construction contract
S firm located in Cincinnati, Ohio. The firm engages and then made the bond proceeds available. The
in municipal financing including the underwriting of immediate predecessor relationships for the activ-
new issues of municipal bonds, acting as a market ities and the activity times were developed by a
maker for previously issued bonds and performing project management team.
other investment banking services. PERT/CPM analysis of the project network identi-
Seasongood & Mayer provided the underwrit- fied the ten critical path activities. The analysis also
ing for a $31 million issue of hospital facilities provided the expected completion time of 29 weeks,
revenue bonds for Providence Hospital in Hamil- or approximately seven months. The activity sched-
ton County, Ohio. The project of underwriting this ule showed the start time and finish time for each
municipal bond issue began with activities such activity and provided the information necessary to
as drafting the legal documents, drafting a monitor the project and keep it on schedule. PERT/
description of the existing hospital facilities and CPM was instrumental in helping Seasongood &
completing a feasibility study. A total of 23 activ- Mayer obtain the financing for the project within the
ities defined the project that would be completed time specified in the construction bid.

Henry L. Gantt developed at the right-hand side of the bar, usually with a different shading. The chart makes it
the Gantt chart as
graphical aid to easy to understand the sequencing of the various activities, the critical path activities
scheduling jobs on (with zero slack) and allows a manager to monitor the project’s progress over time.
machines in 1918. This We see, for example, that Activity B is non-critical (it has slack time) and can start at
application was the first the beginning of the project, could finish as early as the end of Week 6 but could
of what has become
know as project take as long as the end of Week 12 without delaying the overall project.
scheduling techniques.

NOTES AND COMMENTS

uppose that, after analyzing a PERT/CPM net- immediate predecessor relationships can be modified
S work, the project manager finds that the project so that at least some of the critical path activities can be
completion time is unacceptable (i.e., the project is done simultaneously. Second, consider adding resour-
going to take too long). In this case, the manager must cestocriticalpathactivitiesinanattempt to shortenthe
take one or both of the following steps. First, review critical path; we discuss this alternative, referred to as
the original PERT/CPM network to see whether any crashing, in Section 9.3.

9.2 Project Scheduling With Uncertain Activity Times

Clearly, in the example we have just worked through, we have treated the activity
times as certain. That is, for example, we have assumed Activity A will take exactly
five weeks. In practice, project activities may not be known for certain. Sometimes it
may be possible to complete some activities earlier than usual or later than usual.
Sometimes, with new projects we may have only a best-estimate of the likely activity

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