This gave birth to learning-augmented algorithms, which use these predictions to go beyond the standard long-standing worst-case limitations. The design of such algorithms requires establishing good tradeoffs between consistency and robustness, i.e. having improved performance when the predictions are accurate, and not behaving poorly

Suppose a revenue-maximizing recommendation algorithm concludes from past data that more revenue is generated by showing the ad to Group A compared to Group B. In that case, the ad-serving algorithm will eventually end up showing that ad exclusively to Group A

Modeling scheduling problems with conditional time intervals and cumulative functions has become a common approach when using modern commercial constraint programming solvers. This paradigm enables the modeling of a wide range of scheduling problems, including those involving producers and consumers. However, it is unavailable in existing open-source solvers and practical implementation details remain undocumented. In this work, we present an implementation of this modeling approach using a single, generic global constraint called the Generalized Cumulative. We also introduce a novel time-table filtering algorithm specifically designed to handle tasks defined on conditional time-intervals. Experimental results demonstrate that this approach, combined with the new filtering algorithm, performs competitively with existing solvers enabling the modeling of producer and consumer scheduling problems and effectively scales to large-scale problems.

Abstract--This article presents a novel coordination and task-planning framework to enable the simultaneous conflict-free collaboration of multiple unmanned aerial vehicles (UA Vs) for aerial 3D printing. The proposed framework formulates an optimization problem that takes a construction mission divided into sub-tasks and a team of autonomous UA Vs, along with limited volume and battery. It generates an optimal mission plan comprising task assignments and scheduling, while accounting for task dependencies arising from the geometric and structural requirements of the 3D design, inter-UA V safety constraints, material usage and total flight time of each UA V. The potential conflicts occurring during the simultaneous operation of the UA Vs are addressed at a segment-level by dynamically selecting the starting time and location of each task to guarantee collision-free parallel execution. An importance prioritization is proposed to accelerate the computation by guiding the solution towards more important tasks. Additionally, a utility maximization formulation is proposed to dynamically determine the optimal number of UA Vs required for a given mission, balancing the trade-off between minimizing makespan and the deployment of excess agents. The proposed framework's effectiveness is evaluated through a Gazebo-based simulation setup, where agents are coordinated by a mission control module allocating the printing tasks based on the generated optimal scheduling plan while remaining within the material and battery constraints of each UA V. A video of the whole mission is available in the following link: https://youtu.be/b4jwhkNPT Note to Practitioners--This framework addresses the critical need for efficiency and safety in planning and scheduling multiple aerial robots for parallel aerial 3D printing. Existing approaches lack safety guarantees for UA Vs during parallel construction. This work tackles these challenges by ensuring safety during parallel operations and effectively managing task dependencies.

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.

Abstract--Effective agent shift scheduling is crucial for businesses, especially in the Contact Center as a Service (CCaaS) industry, to ensure seamless operations and fulfill employee needs. Most studies utilizing mathematical model-based solutions approach the problem as a single-step process, often resulting in inefficiencies and high computational demands. In contrast, we present a multiphase allocation method that addresses scalability and accuracy by dividing the problem into smaller sub-problems of day and shift allocation, which significantly reduces number of computational variables and allows for targeted objective functions, ultimately enhancing both efficiency and accuracy . Each subproblem is modeled as a Integer Programming Problem (IPP), with solutions sequentially feeding into the subsequent subproblem. We then apply the proposed method, using a multi-objective framework, to address the difficulties posed by peak demand scenarios such as holiday rushes, where maintaining service levels is essential despite having limited number of employees.