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Proactive and Reactive Constraint Programming for Stochastic Project Scheduling with Maximal Time-Lags

Kim van den Houten, Léon Planken, Esteban Freydell, David M. J. Tax, Mathijs de Weerdt

TL;DR

The paper addresses scheduling under stochastic durations and maximal time lags in the $SRCPSP/Max$ problem, comparing proactive CP-based SAA, fully reactive CP-based rescheduling, and STNU-based POS approaches. It introduces three new methods and subjects them to a rigorous statistical benchmarking framework using PSPlib-derived instances with varying noise levels, reporting feasibility, solution quality, and offline/online computation times. Across comprehensive experiments, the STNU-based method achieves the best solution quality and robust feasibility, while reactive scheduling often outperforms proactive variants, and offline/online time trade-offs emerge depending on problem size and uncertainty. The findings provide practical guidance for selecting scheduling strategies under uncertainty and point to promising directions for extending STNU-based methods and incorporating probabilistic or learning-based enhancements.

Abstract

This study investigates scheduling strategies for the stochastic resource-constrained project scheduling problem with maximal time lags (SRCPSP/max)). Recent advances in Constraint Programming (CP) and Temporal Networks have reinvoked interest in evaluating the advantages and drawbacks of various proactive and reactive scheduling methods. First, we present a new, CP-based fully proactive method. Second, we show how a reactive approach can be constructed using an online rescheduling procedure. A third contribution is based on partial order schedules and uses Simple Temporal Networks with Uncertainty (STNUs). Our statistical analysis shows that the STNU-based algorithm performs best in terms of solution quality, while also showing good relative offline and online computation time.

Proactive and Reactive Constraint Programming for Stochastic Project Scheduling with Maximal Time-Lags

TL;DR

The paper addresses scheduling under stochastic durations and maximal time lags in the problem, comparing proactive CP-based SAA, fully reactive CP-based rescheduling, and STNU-based POS approaches. It introduces three new methods and subjects them to a rigorous statistical benchmarking framework using PSPlib-derived instances with varying noise levels, reporting feasibility, solution quality, and offline/online computation times. Across comprehensive experiments, the STNU-based method achieves the best solution quality and robust feasibility, while reactive scheduling often outperforms proactive variants, and offline/online time trade-offs emerge depending on problem size and uncertainty. The findings provide practical guidance for selecting scheduling strategies under uncertainty and point to promising directions for extending STNU-based methods and incorporating probabilistic or learning-based enhancements.

Abstract

This study investigates scheduling strategies for the stochastic resource-constrained project scheduling problem with maximal time lags (SRCPSP/max)). Recent advances in Constraint Programming (CP) and Temporal Networks have reinvoked interest in evaluating the advantages and drawbacks of various proactive and reactive scheduling methods. First, we present a new, CP-based fully proactive method. Second, we show how a reactive approach can be constructed using an online rescheduling procedure. A third contribution is based on partial order schedules and uses Simple Temporal Networks with Uncertainty (STNUs). Our statistical analysis shows that the STNU-based algorithm performs best in terms of solution quality, while also showing good relative offline and online computation time.
Paper Structure (57 sections, 1 theorem, 6 equations, 16 figures, 25 tables)

This paper contains 57 sections, 1 theorem, 6 equations, 16 figures, 25 tables.

Table of Contents

  1. Introduction
  2. The Scheduling Problem
  3. Background and Related Work
  4. Proactive Scheduling
  5. Sample Average Approximation
  6. SORU and SORU-H
  7. Partial Order Scheduling
  8. Constructing Ordering Constraints
  9. Temporal Networks
  10. Execution Strategies
  11. Benchmarking Approaches
  12. Scheduling Methods
  13. Constraint Programming for RCPSP/max
  14. New Methods for SRCPSP/max
  15. Proactive Method
  16. ...and 42 more sections

Key Result

Proposition 1

Suppose we are given a problem instance $1$ with durations $d^1$, resource requirements $r^1$, and capacity $c^1$, and let $s^1$ be a feasible schedule for this instance. Suppose now that we transform instance $1$ into instance $2$, where all parameters stay equal except that one or more of the acti

Figures (16)

  • Figure 1: Example project graph schutt2013solving.
  • Figure 2: Example Gantt chart (figure adjusted from fu2012robustls). The X-axis is time, and Y-axis shows resource demand. The arrows indicate an example of generating a POS with chaining, starting from a fixed solution schedule.
  • Figure 3: Summarizing illustration of the partial ordering of the different methods for solution quality.
  • Figure 4: Summarizing illustration of the partial ordering of the different methods for time offline.
  • Figure 5: Summarizing illustration of the partial ordering of the different methods for time online.
  • ...and 11 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof