ALSO-X#: Better Convex Approximations for Distributionally Robust Chance Constrained Programs

This paper studies distributionally robust chance constrained programs (DRCCPs), where the uncertain constraints must be satisfied with at least a probability of a prespecified threshold for all probability distributions from the Wasserstein ambiguity set. As DRCCPs are often nonconvex and challenging to solve optimally, researchers have been developing various convex inner approximations. Recently, ALSO-X has … Read more

Two-stage and Lagrangian Dual Decision Rules for Multistage Adaptive Robust Optimization

In this work, we design primal and dual bounding methods for multistage adaptive robust optimization (MSARO) problems by adapting two decision rules rooted in the stochastic programming literature. This approach approximates the primal and dual formulations of an MSARO problem with two-stage models. From the primal perspective, this is achieved by applying two-stage decision rules … Read more

Stochastic Dynamic Lot-sizing with Supplier-Driven Substitution and Service Level Constraints

We consider a multi-stage stochastic lot-sizing problem with service level constraints and supplier-driven product substitution. A firm has multiple products and it has the option to meet demand from substitutable products at a cost. Considering the uncertainty in future demands, the firm wishes to make ordering decisions in every period such that the probability that … Read more

Data-Driven Stochastic Dual Dynamic Programming: Performance Guarantees and Regularization Schemes

We propose a data-driven scheme for multistage stochastic linear programming with Markovian random parameters by extending the stochastic dual dynamic programming (SDDP) algorithm. In our data-driven setting, only a finite number of historical trajectories are available. The proposed SDDP scheme evaluates the cost-to-go functions only at the observed sample points, where the conditional expectations are … Read more

Distributionally robust chance-constrained Markov decision processes

Markov decision process (MDP) is a decision making framework where a decision maker is interested in maximizing the expected discounted value of a stream of rewards received at future stages at various states which are visited according to a controlled Markov chain. Many algorithms including linear programming methods are available in the literature to compute … Read more

A comparison of different approaches for the vehicle routing problem with stochastic demands

The vehicle routing problem with stochastic demands (VRPSD) is a well studied variant of the classic (deterministic) capacitated vehicle routing problem (CVRP) where the customer demands are given by random variables. Two prominent approaches for solving the VRPSD model it either as a chance-constraint program (CC-VRPSD) or as a two-stage stochastic program (2S-VRPSD). In this … Read more

On Generalization and Regularization via Wasserstein Distributionally Robust Optimization

Wasserstein distributionally robust optimization (DRO) has found success in operations research and machine learning applications as a powerful means to obtain solutions with favourable out-of-sample performances. Two compelling explanations for the success are the generalization bounds derived from Wasserstein DRO and the equivalency between Wasserstein DRO and the regularization scheme commonly applied in machine learning. … Read more

Scheduling of healthcare professionals using Bayesian Optimization

In this paper we present a Bayesian optimization framework that iteratively “learns” good schedules for healthcare professionals of outpatient healthcare in a hospital, that minimize the overall number of patients in queue — we understand that a patient in schedule is one in queue. The hospital has several medical specialties and each is modeled as … Read more

Stochastic Programming Models for a Fleet Sizing and Appointment Scheduling Problem with Random Service and Travel Times

We propose a new stochastic mixed-integer linear programming model for a home service fleet sizing and appointment scheduling problem (HFASP) with random service and travel times. Specifically, given a set of providers and a set of geographically distributed customers within a service region, our model solves the following decision problems simultaneously: (i) a fleet sizing … Read more

A Simple Algorithm for Online Decision Making

\(\) Motivated by recent progress on online linear programming (OLP), we study the online decision making problem (ODMP) as a natural generalization of OLP. In ODMP, there exists a single decision maker who makes a series of decisions spread out over a total of \(T\) time stages. At each time stage, the decision maker makes … Read more