4 Presentations

• 
  03:30 PM - 03:55 PM

  A Branch-and-Cut Approach for the Distributionally Robust Chance-Constrained Assignment Problem

  • Shanshan Wang, presenter, Northwestern University and Beijing Institute of Technology
  • Jinlin Li, Beijing Institute of Technology
  • Mehrotra Sanjay, Northwestern University

  We study a class of assignment problems with chance constraints that provide a probabilistic guarantee for bin capacity constraints, in which a set of items with random weights are assigned to the bins while minimizing the assignment cost. We firstly formulate chance-constrained assignment problem (CAP) as a 0-1 integer program with discrete distribution of random weights. We then extend (CAP) into distributionally robust chance-constrained assignment problem (DR-CAP), and robustify chance constraints by introducing a general family of ambiguity sets (e.g. moment matching set and Wasserstein set) with finite support. Moreover, we derive the bilinear integer reformulations for (CAP) and (DR-CAP) and propose two classes of valid inequalities. A Branch-and-Cut solution framework is proposed to solve (CAP) and (DR-CAP) respectively. An extensive study of surgery assignment problem using real data from a hospital is conducted.
  Keywords: Chance constrained assignment problem, distributionally robust optimization, Branch-and-Cut, valid inequalities
• 
  03:55 PM - 04:20 PM

  Equal risk pricing under worst-case risk measure

  • Saeed Marzban, presenter, HEC Montreal
  • Erick Delage, GERAD, HEC Montréal
  • Jonathan Li, University of Ottawa

  We study the equal risk framework in which the fair price of an option is the price that exposes both sides of a contract to the same level of risk. This framework takes into consideration both the perspective of the option writer and that of the buyer, which results in separate hedging strategies for each of them. In particular, we study the use of recursive risk measures by the option writer and the buyer for pricing and hedging options.
• 
  04:20 PM - 04:45 PM

  Probabilistic envelope constrained multiperiod stochastic EMS location model and decomposition scheme

  • Chun Peng, presenter, HEC Montreal
  • Erick Delage, GERAD, HEC Montréal
  • Jinlin Li, Beijing Institute of Technology

  This paper considers a multiperiod Emergency Medical Services (EMS) location problem and introduces two two-stage stochastic programming formulations that account for emergency demand uncertainty. While the first model considers both a constraint on the probability of covering the realized emergency demand and minimizing the expected cost of doing so, the second one employs probabilistic envelope constraints which allows us to the degradation of coverage under the more severe scenarios. These models give rise to large MIPs, which can be tackled by Branch-and-Benders-Cut method directly or using conservative approximation scheme. Finally, a practical study is conducted using historical data.
• 
  04:45 PM - 05:10 PM

  Adjustable robust optimization reformulations of two-stage worst-case regret minimization problems

  • Mehran Poursoltani, presenter, GERAD, HEC Montréal
  • Shiva Zokaee, GERAD, CIRRELT, Polytechnique Montréal
  • Erick Delage, GERAD, HEC Montréal

  Within the context of optimization under uncertainty, a well-known alternative to minimizing expected value or the worst-case scenario, a.k.a. robust optimization, consists in minimizing regret. We demonstrate that two-stage worst-case regret minimization problems can be reformulated as two-stage robust optimization models. This empowers us to employ recent advanced approximate and exact solution schemes for these hard problems.

  Keywords: Robust optimization, worst-case regret minimization, sequential decision making