The research presented in this thesis is part of the Rolling Stock Life Cycle Logistics applied research and development program, conducted by NedTrain. As a company, NedTrain belongs to Nederlandse Spoorwegen (NS; the principal railway company in the Netherlands) and provides maintenance services for the NS train-fleet. The aim of this program is to enhance NedTrain’s competitiveness as a rolling-stock maintenance services provider. Our work focuses on the operational aspects of this R&D program, motivated by the challenge of scheduling tasks (or operations) in a NedTrain maintenance workshop, such that trains are delivered on-time for circulation in the rail network. Most tasks in the workshop have uncertain durations (or processing times), which complicates the scheduling process.@en

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.

@en

We discuss two flexibility metrics for Simple Temporal Networks (STNs): the so-called naive flexibility metric based on the difference between earliest and latest starting times of temporal variables, and a recently proposed concurrent flexibility metric. We establish an interesting connection between the computation of these flexibility metrics and properties of the minimal distance matrix DS of an STN S: the concurrent flexibility metric can be computed by finding a minimum weight matching of a weighted bipartite graph completely specified by DS, while the naive flexibility metric corresponds to computing a maximum weight matching in the same graph. From a practical point of view this correspondence offers an advantage: instead of using an O(n5) LP-based approach, reducing the problem to a matching problem we derive an O(n3) algorithm for computing the concurrent flexibility metric.@en