Decision-support tool for scheduling activities with stochastic durations in project networks

Abstract

A decision-support tool is designed and developed in the Visual Studio.Net environment. The tool allows managers to model project networks and schedule start times of stochastic activities. The project faces linearly increasing holding costs and delay penalties. Start times are generalized from the single-period newsvendor model in two ways: 1) non-final parallel activities are coordinated to balance the expected holding costs resulting from either finishing early and having to wait for other parallel activities, or from finishing late and making other parallel activities wait; 2) final actives are coordinated to balance the expected holding costs resulting from completing an activity before the output can be shipped, and the expected delay costs resulting from completing the project after the due date. The tool uses spreadsheet heuristics and simulation to coordinate non-final activities, estimate the probabilistic distribution of the maximum duration of parallel activities, estimate the probabilistic distribution of the duration of the sum of successive activities and coordinate final activities. The performance of the heuristics is compared to exact solutions obtained in Mathematica 5 using numerical integration. The divergence between the heuristic and the more exact solutions is found to be small and to follow distinct patterns.