mixed-integer programming

A Distributionally Robust Optimization Approach for Stochastic Elective Surgery Scheduling with Limited Intensive Care Unit Capacity

  • Rema Padman
  • Karmel S. Shehadeh
    • Categories (Mixed) Integer Linear Programming, Scheduling, Stochastic Programming Tags , , , , ,

    In this paper, we study the decision process of assigning elective surgery patients to available surgical blocks in multiple operating rooms (OR) under random surgery durations, random postoperative length-of-stay in the intensive care unit (ICU), and limited capacity of ICU. The probability distributions of random parameters are assumed to be ambiguous, and only the mean … Read more

    Mathematical Optimization and Machine Learning for Efficient Urban Traffic

  • Johanna Bethge
  • Maximilian Merkert
  • Sebastian Sager
  • Anton Savchenko
  • Rolf Findeisen
  • Do Duc Le
  • Hannes Rewald
  • Stephan Sorgatz
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Transportation Tags , , , , , ,

    Traffic jams cause economical damage which has been estimated between 10 and 100 billion Euros per year in Germany, also due to inefficient urban traffic. It is currently open how the situation will change with upcoming technological advances in autonomous and electric mobility. On the one hand, autonomous cars may lead to an increased number … Read more

    A Model of Supply-Chain Decisions for Resource Sharing with an Application to Ventilator Allocation to Combat COVID-19

  • Sanjay Mehrotra
  • Hamed Rahimian
  • Masoud Barah
  • Fengqiao Luo
  • Karolina Schantz
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , , , , ,

    We present a stochastic optimization model for allocating and sharing a critical resource in the case of a pandemic. The demand for different entities peaks at different times, and an initial inventory for a central agency is to be allocated. The entities (states) may share the critical resource with a different state under a risk-averse … Read more

    The Nurse Rostering Problem in COVID-19 emergency scenario

  • Ruggiero Seccia
    • Categories Applications - OR and Management Sciences, Scheduling Tags , , , ,

    Healthcare facilities are struggling in fighting the spread of COVID-19. While machines needed for patients such as ventilators can be built or bought, healthcare personnel is a very scarce resource that cannot be increased by hospitals in a short period. Furthermore, healthcare personnel is getting sick while taking care of infected people, increasing this shortage … Read more

    Distributionally Robust Bottleneck Combinatorial Problems: Uncertainty Quantification and Robust Decision Making

  • Shabbir Ahmed
  • Weijun Xie
  • Jie Zhang
    • Categories Stochastic Programming Tags , , , ,

    In a bottleneck combinatorial problem, the objective is to minimize the highest cost of elements of a subset selected from the combinatorial solution space. This paper studies data-driven distributionally robust bottleneck combinatorial problems (DRBCP) with stochastic costs, where the probability distribution of the cost vector is contained in a ball of distributions centered at the … Read more

    Learning Optimal Classification Trees: Strong Max-Flow Formulations

  • Sina Aghaei
  • Andrés Gómez
  • Phebe Vayanos
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Statistics Tags , , ,

    We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixed-integer programming (MIP) technology. Yet, existing approaches from the literature do not leverage the power of MIP to its full extent. Indeed, … Read more

    Solving Binary-Constrained Mixed Complementarity Problems Using Continuous Reformulations

  • Steven A. Gabriel
  • Martin Schmidt
  • Marina Leal
    • Categories (Mixed) Integer Nonlinear Programming, Complementarity and Variational Inequalities, Transportation Tags , , ,

    Mixed complementarity problems are of great importance in practice since they appear in various fields of applications like energy markets, optimal stopping, or traffic equilibrium problems. However, they are also very challenging due to their inherent, nonconvex structure. In addition, recent applications require the incorporation of integrality constraints. Since complementarity problems often model some kind … Read more

    Evaluating on-demand warehousing via dynamic facility location models

  • Kaan Unnu
  • Jennifer Pazour
    • Categories (Mixed) Integer Linear Programming, Supply Chain Management, Transportation Tags , , , , , ,

    On-demand warehousing platforms match companies with underutilized warehouse and distribution capabilities with customers who need extra space or distribution services. These new business models have unique advantages, in terms of reduced capacity and commitment granularity, but also have different cost structures compared to traditional ways of obtaining distribution capabilities. This research is the first quantitative … Read more

    Mixed-Integer Optimal Control Problems with switching costs: A shortest path approach

  • Felix Bestehorn
  • Christoph Hansknecht
  • Christian Kirches
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms Tags , , , ,

    We investigate an extension of Mixed-Integer Optimal Control Problems (MIOCPs) by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the … Read more

    Autonomous traffic at intersections: an optimization-based analysis of possible time, energy, and CO2 savings

  • Do Duc Le
  • Maximilian Merkert
  • Stephan Sorgatz
  • Mirko Hahn
  • Sebastian Sager
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Network Optimization Tags , , , , , ,

    In the growing field of autonomous driving, traffic-light controlled intersections as the nodes of large traffic networks are of special interest. We want to analyze how much an optimized coordination of vehicles and infrastructure can contribute to a more efficient transit through these bottlenecks. In addition, we are interested in sensitivity of the results with … Read more