The Bike-sharing allocation and rebalancing problem is the problem of determining the initial daily allocation of bikes to stations in a bike-sharing system composed of one depot and multiple capacitated stations, in which bikes can be rebalanced at a point in time during the day. Due to the uncertain demand in each station, we propose … Read more
Home care provides personalized medical care and social support to patients within their own home. Our work proposes a dynamic scheduling framework to assist in the assignment of patients to health practitioners (HPs) at a single home care agency. We model the decision of which patients to assign to HPs as a discrete-time Markov decision … Read more
We study distributionally robust chance-constrained programming (DRCCP) optimization problems with data-driven Wasserstein ambiguity sets. The proposed algorithmic and reformulation framework applies to distributionally robust optimization problems subjected to individual as well as joint chance constraints, with random right-hand side and technology vector, and under two types of uncertainties, called uncertain probabilities and continuum of realizations. … Read more
We introduce a generalized value function of a mixed-integer program, which is simultaneously parameterized by its objective and right-hand side. We describe its fundamental properties, which we exploit through three algorithms to calculate it. We then show how this generalized value function can be used to reformulate two classes of mixed-integer optimization problems: two-stage stochastic … Read more
We provide an exact deterministic reformulation for data-driven chance constrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the $1$-norm or the $\infty$-norm, the cone is the nonnegative … Read more
The increase in the energy consumption puts pressure on natural resources and environment and results in a rise in the price of energy. This motivates residents to schedule their energy consumption through demand response mechanism. We propose a multi-stage stochastic programming model to schedule different kinds of electrical appliances under uncertain weather conditions and availability … Read more
We propose a method to compute derivatives of multi-stage linear stochastic optimization problems with respect to parameters that influence the problem’s data. Our results are based on classical envelope theorems, and can be used in problems directly solved via their deterministic equivalents as well as in stochastic dual dynamic programming for which the derivatives of … Read more
This paper studies a distributionally robust chance constrained program (DRCCP) with Wasserstein ambiguity set, where the uncertain constraints should be satisfied with a probability at least a given threshold for all the probability distributions of the uncertain parameters within a chosen Wasserstein distance from an empirical distribution. In this work, we investigate equivalent reformulations and … Read more
We study the strategic decision-making problem of assigning time windows to customers in the context of vehicle routing applications that are affected by operational uncertainty. This problem, known as the Time Window Assignment Vehicle Routing Problem, can be viewed as a two-stage stochastic optimization problem, where time window assignments constitute first-stage decisions, vehicle routes adhering … Read more
We introduce an inexact variant of Stochastic Mirror Descent (SMD), called Inexact Stochastic Mirror Descent (ISMD), to solve nonlinear two-stage stochastic programs where the second stage problem has linear and nonlinear coupling constraints and a nonlinear objective function which depends on both first and second stage decisions. Given a candidate first stage solution and a … Read more