Vessel Deployment with Limited Information: Distributionally Robust Chance Constrained Models

This paper studies the fundamental vessel deployment problem in the liner shipping industry, which decides the numbers of mixed-type ships and their sailing frequencies on fixed routes to provide sufficient vessel capacity for fulfilling stochastic shipping demands with high probability. In reality, it is usually difficult (if not impossible) to acquire a precise joint distribution … Read more

Energy and Reserve Dispatch with Distributionally Robust Joint Chance Constraints

We develop a two-stage stochastic program for energy and reserve dispatch, which ensures the safe operation of a power system with a high penetration of renewables and a strong interdependence with the natural gas system. Distributionally robust joint chance constraints with Wasserstein ambiguity sets ensure that there is no need for load shedding and renewable … Read more

Bounds for Probabilistic Programming with Application to a Blend Planning Problem

In this paper, we derive deterministic inner approximations for single and joint probabilistic constraints based on classical inequalities from probability theory such as the one-sided Chebyshev inequality, Bernstein inequality, Chernoff inequality and Hoeffding inequality (see Pinter 1989). New assumptions under which the bounds based approximations are convex allowing to solve the problem efficiently are derived. … Read more

Constrained Bundle Methods for Upper Inexact Oracles with Application to Joint Chance Constrained Energy Problems

Joint chance constrained problems give rise to many algorithmic challenges. Even in the convex case, i.e., when an appropriate transformation of the probabilistic constraint is a convex function, its cutting-plane linearization is just an approximation, produced by an oracle providing subgradient and function values that can only be evaluated inexactly. As a result, the cutting-plane … Read more

Asymptotic Analysis of Sample Average Approximation for Stochastic Optimization Problems with Joint Chance Constraints via CVaR/DC Approximations

Conditional Value at Risk (CVaR) has been recently used to approximate a chance constraint. In this paper, we study the convergence of stationary points when sample average approximation (SAA) method is applied to a CVaR approximated joint chance constrained stochastic minimization problem. Specifically, we prove, under some moderate conditions, that optimal solutions and stationary points … Read more