Implementing a new statistical approach to project scheduling

Abstract

This dissertation develops improvements to a new project scheduling procedure being developed at the Institute of Statistics, Texas A&M University. The project scheduling algorithm is a five step iterative procedure capable of determining a minimum cost project schedule when the activities making up the project have durations which are random variables. The cost of an activity is assumed to be a convex piecewise linear function of the activity's mean duration. The problem is to determine the activity mean durations which both minimize the total project cost and insure that the mean (or some specified percentile) of the corresponding project completion time distribution is less than or equal to a specified project deadline. The entire distribution of the project's completion time under the minimum cost schedule is a valuable by-product. A critical step, Subnetwork Analysis, in the proposed procedure is improved and extended. Subnetwork Analysis determines an estimate of the duration distribution, F(t), for each subnetwork identified in the previous steps. This estimate is extended to include an extrapolation of upper and lower bounds on F(t). This dissertation also develops a new sampling procedure which results in improved estimators for the bounds on F(t). A computer system implementing the project scheduling procedure (including the improvements in Subnetwork Analysis) has also been prepared.