On-line control model for network construction projects

An activity-on-arc network project of the PERT type with random activity durations is considered. For each activity, its accomplishment is measured in percentages of the total project. When operated, each activity utilizes resources of a pregiven capacity and no resource reallocation is undertaken in the course of the project’s realization. Each activity can be operated at several possible speeds that are subject to random disturbances and correspond to one and the same resource capacity; that is, these speeds depend only on the degree of intensity of the project’s realization. For example, in construction projects partial accomplishments are usually measured in percentages of the total project, while different speeds correspond to different hours a day per worker. The number of possible speeds is common to all activities. For each activity, speeds are sorted in ascending order of their average values---namely speeds are indexed. It is assumed that at any moment t>0 activities, in operation at that moment, have to apply speeds of one and the same index that actually determines the project’s speed. The progress of the project can be evaluated only via inspection at control points that have to be determined. The project’s due date and the chance constraint to meet the deadline are pregiven. An on-line control model is suggested that, at each control point, faces a stochastic optimization problem. Two conflicting objectives are imbedded in the model.