Virtual Network Embedding (VNE) approaches typically assume static or slowly-changing network topologies, but emerging applications require deployment in mobile environments where traditional methods become insufficient. This work extends VNE to constrained mesh networks of mobile edge devices, addressing the unique challenges of rapid topology changes and limited resources. We develop models incorporating device capabilities, connectivity, mobility and energy constraints to evaluate optimal deployment strategies for mobile edge environments. Our approach handles the dynamic nature of mobile networks through three allocation strategies: an integer linear program for optimal allocation, a greedy heuristic for immediate deployment, and a multi-objective genetic algorithm for balanced optimization. Our initial evaluation analyzes application acceptance rates, resource utilization, and latency performance under resource limitations. Results demonstrate improvements over traditional approaches, providing a foundation for VNE deployment in highly mobile environments.

In this paper, we describe a branch-and-price algorithm for the personalized nurse scheduling problem. The variants that appear in the literature involve a large number of constraints that can be hard or soft, meaning that they can be violated at the price of a penalty. We capture the diversity of the constraints on individual schedules by seven generic constraints characterized by lower and upper bounds on a given quantity. The core of the column generation procedure is in the identification of individual schedules with minimum reduced cost. For this, we solve a shortest path problem with resource constraints (SPPRC) where several generic constraints are modeled as resource constraints. We then describe dominance rules adapted to the presence of both upper and lower bounds on the resources and leverage soft constraints to improve the dominance. We also describe several acceleration techniques for the solution of the SPPRC, and branching rules that fit the specificities of the problem. Our numerical experiments are based on the instances of three benchmarks of the literature including those of the two international nurse rostering competitions (INRC-I and INRC-II). Their objective is threefold: assess the dominance rules and the acceleration techniques, investigate the capacity of the algorithm to find provable optimal solutions of instances that are still open, and conduct a comparison with best published results. The most noticeable conclusion is that the improved solution of the SPPRC allows to solve optimally all the INRC-II instances where a four-week planning horizon is considered and 40% of the eight-week instances. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2023.0019 .

Patient scheduling is a difficult task involving stochastic factors, such as the unknown arrival times of patients. Similarly, the scheduling of radiotherapy for cancer treatments needs to handle patients with different urgency levels when allocating resources. High-priority patients may arrive at any time, and there must be resources available to accommodate them. A common solution is to reserve a flat percentage of treatment capacity for emergency patients. However, this solution can result in overdue treatments for urgent patients, a failure to fully exploit treatment capacity, and delayed treatments for low-priority patients. This problem is especially severe in large and crowded hospitals. In this paper, we propose a prediction-based approach for online dynamic radiotherapy scheduling that dynamically adapts the present scheduling decision based on each incoming patient and the current allocation of resources. Our approach is based on a regression model trained to recognize the links between patients’ arrival patterns and their ideal waiting time in optimal off-line solutions when all future arrivals are known in advance. When our prediction-based approach is compared with flat-reservation policies, it does a better job of preventing overdue treatments for emergency patients and also maintains comparable waiting times for the other patients. We also demonstrate how our proposed approach supports explainability and interpretability in scheduling decisions using Shapley additive explanation values. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: Mitacs Accélération IT26995 and Canada Research Chair in Analytics and Logistics in Healthcare (HANALOG). Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1289 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0342 ) at ( http://dx.doi.org/10.5281/zenodo.7579533 ).