Pieter Smet

Carlo S. Sartori, Pieter Smet, Greet Vanden Berghe

Simple temporal problems represent a powerful class of models capable of describing the temporal relations between events that arise in many real-world applications such as logistics, robot planning and management systems. The classic simple temporal problem permits each event to have only a single release and due date. In this paper, we focus on the case where events may have an arbitrarily large number of release and due dates. This type of problem, however, has been referred to by various names. In order to simplify and standardize nomenclatures, we introduce the name Simple Disjunctive Temporal Problem. We provide three mathematical models to describe this problem using constraint programming and linear programming. To efficiently solve simple disjunctive temporal problems, we design two new algorithms inspired by previous research, both of which exploit the problem's structure to significantly reduce their space complexity. Additionally, we implement algorithms from the literature and provide the first in-depth empirical study comparing methods to solve simple disjunctive temporal problems across a wide range of experiments. Our analysis and conclusions offer guidance for future researchers and practitioners when tackling similar temporal constraint problems in new applications. All results, source code and instances are made publicly available to further assist future research.

Pieter Smet

Uncertainty in optimization is often represented as stochastic parameters in the optimization model. In Predict-Then-Optimize approaches, predictions of a machine learning model are used as values for such parameters, effectively transforming the stochastic optimization problem into a deterministic one. This two-stage framework is built on the assumption that more accurate predictions result in solutions that are closer to the actual optimal solution. However, providing evidence for this assumption in the context of complex, constrained optimization problems is challenging and often overlooked in the literature. Simulating predictions of machine learning models offers a way to (experimentally) analyze how prediction error impacts solution quality without the need to train real models. Complementing an algorithm from the literature for simulating binary classification, we introduce a new algorithm for simulating predictions of multiclass classifiers. We conduct a computational study to evaluate the performance of these algorithms, and show that classifier performance can be simulated with reasonable accuracy, although some variability is observed. Additionally, we apply these algorithms to assess the performance of a Predict-Then-Optimize algorithm for a machine scheduling problem. The experiments demonstrate that the relationship between prediction error and how close solutions are to the actual optimum is non-trivial, highlighting important considerations for the design and evaluation of decision-making systems based on machine learning predictions.

Pieter Smet, Martina Doneda, Ettore Lanzarone et al.

The availability of downstream resources plays is critical in planning the admission of elective surgery patients. The most crucial one is inpatient beds. To ensure bed availability, hospitals may use machine learning (ML) models to predict patients' length-of-stay (LOS) in the admission planning stage. However, the real value of the LOS for each patient may differ from the predicted one, potentially making the schedule infeasible. To address such infeasibilities, it is possible to implement rescheduling strategies that take advantage of operational flexibility. For example, planners may postpone admission dates, relocate patients to different wards, or even transfer patients who are already admitted among wards. A straightforward assumption is that better LOS predictions can help reduce the impact of rescheduling. However, the training process of ML models that can make such accurate predictions can be very costly. Building on previous work that proposed simulated ML for evaluating data-driven approaches, this paper explores the relationship between LOS prediction accuracy and rescheduling flexibility across various corrective policies. Specifically, we examine the most effective patient rescheduling strategies under LOS prediction errors to prevent bed overflows while optimizing resource utilization

Martina Doneda, Pieter Smet, Giuliana Carello et al.

Disruptions to personnel rosters caused by absenteeism often necessitate last-minute adjustments to the employees' working hours. A common strategy to mitigate the impact of such changes is to assign employees to reserve shifts: special on-call duties during which an employee can be called in to cover for an absent employee. To maximize roster robustness, we assume a predict-then-optimize approach that uses absence predictions from a machine learning model to schedule an adequate number of reserve shifts. In this paper we propose a methodology to evaluate the robustness of rosters generated by the predict-then-optimize approach, assuming the machine learning model will make predictions at a predetermined prediction performance level. Instead of training and testing machine learning models, our methodology simulates the predictions based on a characterization of model performance. We show how this methodology can be applied to identify the minimum performance level needed for the model to outperform simple non-data-driven robust rostering policies. In a computational study on a nurse rostering problem, we demonstrate how the predict-then-optimize approach outperforms non-data-driven policies under reasonable performance requirements, particularly when employees possess interchangeable skills.