4 présentations

• 
  13h00 - 13h22

  On the ReLU Lagrangian Cuts for Stochastic Mixed Integer Programming

  • Weijun Xie, prés., Georgia Institute of Technology
  • Haoyun Deng, Georgia Tech

  We study stochastic mixed integer programs with both first-stage and recourse decisions involving mixed integer variables. A new family of Lagrangian cuts, termed “ReLU Lagrangian cuts,” is introduced by reformulating the nonanticipativity constraints using ReLU functions. These cuts can be integrated into scenario decomposition methods. We show that including ReLU Lagrangian cuts is sufficient to achieve optimality in the original stochastic mixed integer programs. Without solving the Lagrangian dual problems, we derive closed-form expressions for these cuts. Furthermore, to speed up the cut-generating procedures, we introduce linear programming-based methods to enhance the cut coefficients. Numerical studies demonstrate the effectiveness of the proposed cuts compared to existing cut families.

• 
  13h22 - 13h44

  Interpretable Vaccine Administration and Inventory Replenishment Policies via Smooth-in-Expectation Decision Rules

  • Zoha Sherkat-Masoumi, University of Toronto
  • Merve Bodur, prés., University of Edinburgh
  • Jim Luedtke, University of Wisconsin at Madison

  The effective management of vaccine vials and inventory is imperative for ensuring widespread immunization coverage. We aim to address the challenges associated with this problem, including the need for interpretable policies. We propose a Markov decision process model, which offers flexibility to accommodate various operational aspects such as patient queues, clinic early closure considerations, and the requirement to serve every patient until exhausting vaccine inventory. For developing interpretable policies, we employ smooth-in-expectation decision rules, a recently proposed approach for multistage stochastic programs with mixed-integer recourse decisions and very many stages (e.g., hundreds). Leveraging these decision rules, we formulate and optimize the vaccine administration policies via a problem-specific flowchart design, alongside vial ordering decisions, facilitating interpretability and adaptability in real-world healthcare settings. We implement a batch stochastic gradient descent algorithm to solve the optimization problem, where for the initialization step we use the solution of a two-stage stochastic programming model we propose as an approximation to the multistage problem. Through extensive numerical experiments, we demonstrate the efficiency of the proposed approach and highlight the efficacy of various policies, including those considering patient queues.

• 
  13h44 - 14h06

  Infinite-horizon multi-stage stochastic programs on Markov chains

  • David Morton, prés., Northwestern University
  • Shuotao Diao, Northwestern University
  • Oscar Dowson, Dowson Farms
  • Bernardo Pagnoncelli, SKEMA Business School,

  We consider an infinite-horizon multi-stage stochastic linear program. Our model is defined on a discrete-time, finite-state, transient Markov chain. That is, we consider a policy graph. We argue that such a formulation is natural from a modeling perspective, and it provides computational advantages for SDDP (stochastic dual dynamic programming) style algorithms. Our approach hinges on a Bellman recursion that reformulates the infinite-horizon model. We provide conditions under which monotonicity and contraction properties hold, which ensure validity of the Bellman-recursion reformulation.

• 
  14h06 - 14h28

  Risk-Averse Contextual Predictive Maintenance and Operations Scheduling with Flexible Generation under Wind Energy Uncertainty

  • Beste Basciftci, prés., University of Iowa
  • Natalie Randall, University of Iowa

  We study a two-stage risk-averse contextual predictive generator maintenance and operations scheduling problem with traditional and flexible generation resources under wind energy uncertainty. We present a Gaussian Process Regression approach for predicting wind power and integrating contextual information into the resulting stochastic mixed-integer program. We propose a multi-step progressive hedging algorithm (PHA) for its solution leveraging the Frank-Wolfe decomposition and Lagrangian dual bounding, extending them to risk-averse setting, and presenting various computational enhancements, providing significant speedups against the classical PHA and off-the-shelf solvers. Our results further demonstrate the impact of adopting a risk-averse approach compared to risk-neutral and deterministic alternatives with a better worst-case performance, and highlight the value of integrating flexible generation and contextual information with resilient maintenance and operations schedules leading to cost-effective plans.