In this paper, we present a new stochastic mixed-integer linear programming model for the Stochastic Outpatient Procedure Scheduling Problem (SOPSP). In this problem, we schedule a day’s worth of procedures for a single provider, where each procedure has a known type and associated probability distribution of random duration. Our objective is to minimize the expectation … Read more
We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash equilibrium. Despite the non-convex nature of the ambiguity set, we prove that the estimation problem is equivalent to a tractable convex … Read more
We introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our ambiguity sets we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover’s distances that includes both the total variation distance and the Wasserstein metrics. We discuss the main … Read more
We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and backward passes of the method are solved with bounded errors (inexactly). This inexact variant of SDDP is described both for … Read more
In this paper, we discuss input modeling and solution techniques for several classes of chance constrained programs (CCPs). We propose to use Gaussian mixture models (GMM), a semi-parametric approach, to fit the data available and to model the randomness. We demonstrate the merits of using GMM. We consider several scenarios that arise from practical applications … Read more
Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic optimization. The problem is stated in generality first. The paper discusses time consistent decision-making by addressing risk measures which are recursive, nested, dynamically … Read more
This paper presents stochastic decomposition (SD) algorithms for two classes of stochastic programming problems: 1) two-stage stochastic quadratic-linear programming (SQLP) in which a quadratic program defines the objective function in the first stage and a linear program defines the value function in the second stage; 2) two-stage stochastic quadratic-quadratic programming (SQQP) which has quadratic programming … Read more
We introduce two-stage distributionally robust disjunctive programs (TSDR-DPs) with disjunctive constraints in both stages and a general ambiguity set for the probability distributions. The TSDR-DPs subsume various classes of two-stage distributionally robust programs where the second stage problems are non-convex programs (such as mixed binary programs, semi-continuous program, nonconvex quadratic programs, separable non-linear programs, etc.). … Read more
We study a variant of the capacitated vehicle routing problem (CVRP), which asks for the cost-optimal delivery of a single product to geographically dispersed customers through a fleet of capacity-constrained vehicles. Contrary to the classical CVRP, which assumes that the customer demands are deterministic, we model the demands as a random vector whose distribution is … Read more
Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable technologies have motivated study of various classes of stochastic unit commitment models. In two-stage models, the generation schedule for the entire day is fixed while the … Read more