Network resource allocation models under risk

This paper discusses the problem of controlling selected parameters of a project represented by an activity-on-arc network with random activity times. The expected project completion time, the main characteristic dealt with, is controlled by incurring additional cost (so called crashing cost) to carry out an activity. This cost changes its expected duration, thus altering the expected project completion time. The problems in question are reduced to finding suboptimal allocation of resources among activities of the project allowing for optimization of selected criteria functions. A family of linear and convex optimization problems is constructed to obtain approximate, yet satisfactory, solutions. The problem of how ‘good’ the solutions are, is discussed as well. The so called reliability level of carrying out an activity is also considered as an additional constraint in the formulated problems.