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Abstract
This paper formulates a model for the scheduling and control of a multiphase project that consists of a given sequence of jobs to be completed by a specified due date. The duration of each job is the sum of a known fixed time and a random delay; and, while the former may be shortened within given limits, there is no control over the latter. The decision variables are the level of activity in each job and the starting time of the first in the sequence. An optimal decision policy for this model is obtained assuming a simple cost structure. It is shown that, if this policy is followed, a minimum a priori probability of meeting the due date is guaranteed.
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