4 présentations

• 
  13h00 - 13h22

  Enhancing Fairness in University Teacher Assignments: An MILP Approach

  • Yifan Zhu, prés., School of Computing, Queen's University
  • Tasnim Ahmed,
  • Salimur Choudhury, Queen's University

  The teacher assignment problem is a variant of the university timetabling problem, where the objective is to assign teachers to courses while accounting for their preferences and potential university-specific requirements. Previous research typically addressed this well-known NP-hard problem using linear programming approaches that primarily focused on hard constraints and only incorporated a few trivial soft constraints. In this paper, we propose a mixed integer linear programming model to solve this problem by maximizing teachers' preferences, ensuring consistency in course teaching, and enhancing fairness in assignments. The model was evaluated using real data, and upon human verification, we observed that the generated solutions closely resemble human-generated solutions while exhibiting better performance in certain aspects, such as fairness, and require only a fraction of the time taken by manual methods. Additionally, we explored the trade-off between relaxing specific soft constraints and maintaining solution quality to reduce computational effort.

• 
  13h22 - 13h44

  Optimizing ED Closures in Ontario: Minimizing Travel Burdens with ILP

  • Spencer Keene, prés., Queen's University
  • David Savage, NOSM University
  • Salimur Choudhury, Queen's University

  Emergency department (ED) closures in rural regions like Northern Ontario, often driven by limited resources, increase travel burdens, strain neighbouring facilities, and lead to longer wait times or a loss of access to care, diminishing healthcare quality. Limited public transportation and seasonal access challenges further exacerbate these issues, making strategic planning essential to mitigate the impacts of closures. A decision-making system is proposed to determine which EDs should close while minimizing travel burdens and balancing patient loads across remaining facilities. Using Integer Linear Programming (ILP), the system would evaluate potential closures based on travel times, ED capacities, and population data, while reassigning dissemination area (DA)-to-ED connections to optimize patient distribution, prevent bottlenecks, and reduce overall access times. This data-driven approach provides a comprehensive method for identifying closure scenarios that maintain equitable and timely access, enhancing the resilience of Ontario’s emergency healthcare network while minimizing disruptions.

• 
  13h44 - 14h06

  Warm-starting for mixed-integer nonlinear optimization

  • Jan Kronqvist, prés., KTH Royal Institute of Technology
  • Tamm Erik, KTH Royal Institute of Technology

  For certain types of applications, we are not considering a single optimization problem, but a sequence of optimization problems. Such sequences of problems, e.g., arise in model predictive control, multi-objective optimization, and machine learning. The problems in the sequence are closely related, and the changes from one problem in the sequence to the next are known. We investigate how to take advantage of having solved an earlier problem in the sequence to perform a warm-start.

  We focus on warm-starting within an outer approximation (OA) framework for convex mixed-integer nonlinear programming (MINLP). We show that it is possible to greatly reduce the number of iterations needed by OA by warm-starting. We also show that the naive approach of simply using the optimal solution from one problem as a starting point for the next problem can even result in worse performance than a cold start. We present two different approaches for warm-starting and present some numerical results.

• 
  14h06 - 14h28

  Combining column generation and elimination

  • Andre A. Cire, University of Toronto Scarborough
  • Ricardo Fukasawa, prés., University of Waterloo
  • Anthony Karahalios, Carnegie Mellon University
  • Matheus Jun Ota, University of Waterloo
  • Willem-Jan van Hoeve, Carnegie Mellon University

  Column elimination and generation are two techniques that are very useful when variables in an integer program define solution patterns. These two techniques have been applied to similar problems like vehicle routing variants.

  Though the two techniques share similarities, the overall philosophies are not easily combined. In this work, we overcome that obstacle to show how one can combine the two techniques to obtain state-of-the-art results for some hard combinatorial optimization problems.