Markov Chain-based Policies for Multi-stage Stochastic Integer Linear Programming with an Application to Disaster Relief Logistics

We introduce a novel aggregation framework to address multi-stage stochastic programs with mixed-integer state variables and continuous local variables (MSILPs). Our aggregation framework imposes additional structure to the integer state variables by leveraging the information of the underlying stochastic process, which is modeled as a Markov chain (MC). We present a novel branch-and-cut algorithm integrated … Read more

Neur2SP: Neural Two-stage Stochastic Programming

Stochastic programming is a powerful modeling framework for decision-making under uncertainty. In this work, we tackle two-stage stochastic programs (2SPs), the most widely applied and studied class of stochastic programming models. Solving 2SPs exactly requires evaluation of an expected value function that is computationally intractable. Additionally, having a mixed-integer linear program (MIP) or a nonlinear … Read more

A Novel Model for Transfer Synchronization in Transit Networks and a Lagrangian-based Heuristic Solution Method

To realize the benefits of network connectivity in transfer-based transit networks, it is critical to minimize transfer disutility for passengers by synchronizing timetables of intersecting routes. We propose a mixed-integer linear programming timetable synchronization model that incorporates new features, such as dwell time determination and vehicle capacity limit consideration, which have been largely overlooked in … Read more

Approximate Dynamic Programming for Crowd-shipping with In-store Customers

Crowd-shipping has gained significant attention as a last-mile delivery option over the recent years. In this study, we propose a variant of dynamic crowd-shipping model with in-store customers as crowd-shippers to deliver online orders within few hours. We formulate the problem as a Markov decision process and develop an approximate dynamic programming (ADP) policy using … Read more

Multistage Stochastic Fractionated Intensity Modulated Radiation Therapy Planning

Intensity modulated radiation therapy (IMRT) is a widely used cancer treatment technique as it can deliver highly complex beam distributions, targeting malignant cells while avoiding or limiting exposure of healthy organs and tissues. To further increase the destructive effect on tumor cells and reduce side effects, radiotherapy is usually divided into several treatments called fractions … Read more

A Multiobjective Approach for Sector Duration Optimization in Stereotactic Radiosurgery Treatment Planning

Sector duration optimization (SDO) is a problem arising in treatment planning for stereotactic radiosurgery on Gamma Knife. Given a set of isocenter locations, SDO aims to select collimator size configurations and irradiation times thereof such that target tissues receive prescribed doses in a reasonable amount of treatment time, while healthy tissues nearby are spared. We … Read more

Copositive Duality for Discrete Markets and Games

Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer (2009) that mixed-binary quadratic programs can be written as completely positive programs, which are convex. Completely positive reformulations of discrete optimization problems therefore have … Read more

Stochastic RWA and Lightpath Rerouting in WDM Networks

In a telecommunication network, Routing and Wavelength Assignment (RWA) is the problem of finding lightpaths for incoming connection requests. When facing a dynamic traffic, greedy assignment of lightpaths to incoming requests based on predefined deterministic policies leads to a fragmented network that cannot make use of its full capacity due to stranded bandwidth. At this … Read more

A Branch-and-Price Algorithm Enhanced by Decision Diagrams for the Kidney Exchange Problem

Kidney paired donation programs allow patients registered with an incompatible donor to receive a suitable kidney from another donor, as long as the latter’s co-registered patient, if any, also receives a kidney from a different donor. The kidney exchange problem (KEP) aims to find an optimal collection of kidney exchanges taking the form of cycles … Read more

On the Impact of Deep Learning-based Time-series Forecasts on Multistage Stochastic Programming Policies

Multistage stochastic programming provides a modeling framework for sequential decision-making problems that involve uncertainty. One typically overlooked aspect of this methodology is how uncertainty is incorporated into modeling. Traditionally, statistical forecasting techniques with simple forms, e.g., (first-order) autoregressive time-series models, are used to extract scenarios to be added to optimization models to represent the uncertain … Read more