Stochastic Task Networks Trading Performance for Stability

• Published in: Integration of AI and OR Techniques in Constraint Programming pp. 302 - 311
• Main Authors: Mountakis, Kiriakos Simon, Klos, Tomas, Witteveen, Cees
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing 2017
• Series: Lecture Notes in Computer Science
• Subjects: Activity network; Solution robustness; Stochastic scheduling
• ISBN: 9783319597751; 3319597752
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-59776-8_25

This paper concerns networks of precedence constraints between tasks with random durations, known as stochastic task networks, often used to model uncertainty in real-world applications. In some applications, we must associate tasks with reliable start-times from which realized start-times will (most likely) not deviate too far. We examine a dispatching strategy according to which a task starts as early as precedence constraints allow, but not earlier than its corresponding planned release-time. As these release-times are spread farther apart on the time-axis, the randomness of realized start-times diminishes (i.e. stability increases). Effectively, task start-times becomes less sensitive to the outcome durations of their network predecessors. With increasing stability, however, performance deteriorates (e.g. expected makespan increases). Assuming a sample of the durations is given, we define an LP for finding release-times that minimize the performance penalty of reaching a desired level of stability. The resulting LP is costly to solve, so, targeting a specific part of the solution-space, we define an associated Simple Temporal Problem (STP) and show how optimal release-times can be constructed from its earliest-start-time solution. Exploiting the special structure of this STP, we present our main result, a dynamic programming algorithm that finds optimal release-times with considerable efficiency gains.