Ph.D Thesis

Ph.D StudentBendavid Illana
SubjectSetting Release Gates for Activities in Projects with
Stochastic Activity Durations
DepartmentDepartment of Industrial Engineering and Management
Supervisor PROF. Boaz Golany


This work addresses the problem of controlling the scheduling of activities in projects with stochastic activity durations.

A first approach is to set a gate for each activity i.e., a time before which the activity cannot begin. Since the resources required for each activity are scheduled to arrive according to its gate, we may incur a “holding” cost when an activity is ready to be processed, but the resources required for it were scheduled to arrive at a later time; or we may incur a “shortage” cost when the required resources have arrived on time but the activity cannot start because its predecessors are not yet finished. Our objective is to set the gates so as to minimize the sum of the expected holding and shortage costs.

A second approach is, instead of setting one gate, to require that each activity will start within an interval of time and in this way introduce more flexibility in the contracts with the subcontractors. The subcontractors would now be expected to start their respective activities within certain time intervals rather than starting no earlier than a certain gate. Our objective is to set the intervals so as to minimize the sum of the expected holding, shortage and interval costs.

In the first approach, all the gates are determined in a “static” way, at “time zero”, before the project starts and before any uncertain parameters (the durations) are realized. In this way, all the risk induced by the uncertainty is assumed only by the project manager (PM). Introducing flexibility into contracts with the subcontractors can help reducing the uncertainty and sharing the risk between the PM and the subcontractors. Thus, the third approach takes advantage of the dynamics in our settings. We first solve the problem at “time zero” in a static way to obtain a basic guideline for the contract. Then, each time more information is obtained, the PM can incorporate it to solve the problem for the remaining activities and to adjust his future decisions in a dynamic way, allowing him to reduce uncertainty, thus to reduce his costs.

We employ the Cross-Entropy method to solve these problems. We describe the implementation of the method, compare its results to other heuristic methods and provide some insights towards actual applications.