About

Andrew J. Schaefer is the Noah Harding Chair and Professor of Computational Applied Mathematics and Operations Research at Rice University. He joined the Rice faculty in 2015 after spending 15 years with the Department of Industrial Engineering at the University of Pittsburgh, where he held positions including the John A. Swanson Chair in Engineering and the William Kepler Whiteford Professor of Industrial Engineering. His research interests are in the broad area of operations research and industrial engineering, specifically focusing on mixed-integer programming, stochastic optimization, and large-scale optimization. He earned a Ph.D. in industrial and systems engineering from Georgia Tech in 2000, a master’s degree in computational and applied mathematics from Rice University in 1994, and a B.A. in the same discipline from Rice University in 1994. Throughout his career, Schaefer has received numerous awards, including the NSF CAREER Award in 2006, the Outstanding Young Industrial Engineering Education Award from the Institute of Industrial Engineers in 2007, and the Outstanding Young Engineer by the Rice Engineering Alumni Association in 2013. He has also received a Best Paper Award from IIE Transactions on Operations Engineering in 2016.

Research topics

• Computer Science
• Medicine
• Machine Learning
• Surgery
• Artificial Intelligence
• Internal medicine
• Nuclear medicine
• Mathematical optimization
• Radiology
• Medical physics
• Oncology
• Mathematics

Selected publications

• Lead distance under a pickoff limit in Major League Baseball: A sequential game model

  arXiv (Cornell University) · 2026-01-22

  preprintOpen accessSenior author

  Major League Baseball (MLB) recently limited pitchers to three pickoff attempts, creating a cat-and-mouse game between pitcher and runner. Each failed attempt adds pressure on the pitcher to avoid using another, and the runner can intensify this pressure by extending their leadoff toward the next base. We model this dynamic as a two-player zero-sum sequential game in which the runner first chooses a lead distance, and then the pitcher chooses whether to attempt a pickoff. We establish optimality characterizations for the game and present variants of value iteration and policy iteration to solve the game. Using lead distance data, we estimate generalized linear mixed-effects models for pickoff and stolen base outcome probabilities given lead distance, context, and player skill. We compute the game-theoretic equilibria under the two-player model, as well as the optimal runner policy under a simplified one-player Markov decision process (MDP) model. In the one-player setting, our results establish an actionable rule of thumb: the Two-Foot Rule, which recommends that a runner increase their lead by two feet after each pickoff attempt.

  PublisherDOI

• Lead distance under a pickoff limit in Major League Baseball: A sequential game model

  ArXiv.org · 2026-01-22

  articleOpen accessSenior author

  Major League Baseball (MLB) recently limited pitchers to three pickoff attempts, creating a cat-and-mouse game between pitcher and runner. Each failed attempt adds pressure on the pitcher to avoid using another, and the runner can intensify this pressure by extending their leadoff toward the next base. We model this dynamic as a two-player zero-sum sequential game in which the runner first chooses a lead distance, and then the pitcher chooses whether to attempt a pickoff. We establish optimality characterizations for the game and present variants of value iteration and policy iteration to solve the game. Using lead distance data, we estimate generalized linear mixed-effects models for pickoff and stolen base outcome probabilities given lead distance, context, and player skill. We compute the game-theoretic equilibria under the two-player model, as well as the optimal runner policy under a simplified one-player Markov decision process (MDP) model. In the one-player setting, our results establish an actionable rule of thumb: the Two-Foot Rule, which recommends that a runner increase their lead by two feet after each pickoff attempt.

  PublisherOA PDF

• Inverse of the Gomory corner relaxation of integer programs

  Discrete Optimization · 2026-03-09

  articleOpen accessSenior author

  We explore the inverse of integer programs (IPs) by studying the inverse of their Gomory corner relaxations (GCRs). We propose a linear programming (LP) formulation for solving any inverse GCR problem under the L 1 and L ∞ norms by reformulating the inverse GCR problem as the inverse of a shortest path problem. We show that the minimum objective of the inverse GCR across all feasible bases of the LP relaxation yields an upper bound on the optimal value of the inverse IP that is at least as tight as the optimal value of the inverse of the LP relaxation. We provide conditions under which this upper bound is exactly equal to the optimal value of the inverse IP.

  PublisherDOI

• Optimal timing of organs-at-risk-sparing adaptive radiation therapy for head-and-neck cancer under re-planning resource constraints

  Physics and Imaging in Radiation Oncology · 2025-01-01 · 1 citations

  articleOpen access

  Background and purpose: Prior work on adaptive organ-at-risk (OAR)-sparing radiation therapy has typically reported outcomes based on fixed-number or fixed-interval re-planning, which represent one-size-fits-all approaches and do not account for the variable progression of individual patients' toxicities. The purpose of this study was to determine the personalized optimal timing of re-planning in adaptive OAR-sparing radiation therapy, considering limited re-planning resources, for patients with head and neck cancer (HNC). Materials and methods: A novel Markov decision process (MDP) model was developed to determine optimal timing of re-planning based on the patient's expected toxicity, characterized by normal tissue complication probability (NTCP), for four toxicities. The MDP parameters were derived from a dataset comprising 52 HNC patients treated between 2007 and 2013. Kernel density estimation was used to smooth the sample distributions. Optimal re-planning strategies were obtained when the permissible number of re-plans throughout the treatment was limited to 1, 2, and 3, respectively. Results: The MDP (optimal) solution recommended re-planning when the difference between planned and actual NTCPs (ΔNTCP) was greater than or equal to 1%, 2%, 2%, and 4% at treatment fractions 10, 15, 20, and 25, respectively, exhibiting a temporally increasing pattern. The ΔNTCP thresholds remained constant across the number of re-planning allowances (1, 2, and 3). Conclusion: In limited-resource settings that impeded high-frequency adaptations, ΔNTCP thresholds obtained from an MDP model could derive optimal timing of re-planning to minimize the likelihood of treatment toxicities.

  PublisherOA PDFDOI

• Overview of the Head and Neck Tumor Segmentation for Magnetic Resonance Guided Applications (HNTS-MRG) 2024 Challenge

  Lecture notes in computer science · 2025-01-01 · 3 citations

  articleOpen access

  Magnetic resonance (MR)-guided radiation therapy (RT) is enhancing head and neck cancer (HNC) treatment through superior soft tissue contrast and longitudinal imaging capabilities. However, manual tumor segmentation remains a significant challenge, spurring interest in artificial intelligence (AI)-driven automation. To accelerate innovation in this field, we present the Head and Neck Tumor Segmentation for MR-Guided Applications (HNTS-MRG) 2024 Challenge, a satellite event of the 27th International Conference on Medical Image Computing and Computer Assisted Intervention. This challenge addresses the scarcity of large, publicly available AI-ready adaptive RT datasets in HNC and explores the potential of incorporating multi-timepoint data to enhance RT auto-segmentation performance. Participants tackled two HNC segmentation tasks: automatic delineation of primary gross tumor volume (GTVp) and gross metastatic regional lymph nodes (GTVn) on pre-RT (Task 1) and mid-RT (Task 2) T2-weighted scans. The challenge provided 150 HNC cases for training and 50 for testing, hosted on grand-challenge.org using a Docker submission framework. In total, 19 independent teams from across the world qualified by submitting both their algorithms and corresponding papers, resulting in 18 submissions for Task 1 and 15 submissions for Task 2. Evaluation using the mean aggregated Dice Similarity Coefficient showed top-performing AI methods achieved scores of 0.825 in Task 1 and 0.733 in Task 2. These results surpassed clinician interobserver variability benchmarks, marking significant strides in automated tumor segmentation for MR-guided RT applications in HNC.

  PublisherOA PDFDOI

• Changes in patient-sharing patterns after oncologist departures in rural and urban settings: a Medicare cohort study

  Applied Network Science · 2025-12-02

  articleOpen access

  Cancer care relies on effective coordination within a multidisciplinary care team. Changes to teams due to departures remain understudied despite rising oncologist turnover in the United States. In this study, we aimed to investigate the impact of oncologist departures on the remaining care team members. We used Medicare claims associated with beneficiaries aged 66-99 to identify physicians involved in care for common cancer types (i.e., breast, lung, and colorectal cancer). We restricted our analysis to medical oncologists, radiation oncologists, and surgeons specializing in oncology (collectively, "oncologists"). We identified oncologists who left a practice location in 2017-2019 using the Medicare Carrier file and linked them to retained oncologists based on shared patients. Multivariable hierarchical linear regression was used to investigate how retained oncologists' patient-sharing patterns changed after a colleague's departure. Our results support that retained rural-practicing oncologists experienced an expansion and restructuring of their patient-sharing ties following oncologist departures while retained urban-practicing oncologists experienced a consolidation. Network restructuring may demonstrate an adaptive response that ensures patient continuity of care, but it may also reflect unique challenges faced by oncologists practicing in rural versus urban settings. Supplementary Information: The online version contains supplementary material available at 10.1007/s41109-025-00762-3.

  PublisherDOI

• Maximizing the Score in "Ticket to Ride"

  ArXiv.org · 2025-11-11

  preprintOpen accessSenior author

  We give two graph-theoretic models and a mixed-integer program to calculate the maximum achievable score in the popular board game "Ticket to Ride." In Ticket to Ride, players compete to claim railway routes on a map, with points awarded based on the length of each route and the successful completion of destination tickets connecting specific city pairs. Each player has 45 train cars available, and each route can be chosen by only one player. Using the mixed-integer programming model, we examine the optimal solution with the 45 allocatable train cars, leading to an optimal score of 285 points. We also calculate the optimal solutions for up to 50 train cars. We determine the most frequently chosen tickets and routes over these 50 instances, giving insight into how optimization might be used to balance games. In particular, we identify several instances in which the point values can be adjusted to better balance the game.

  PublisherOA PDFDOI

• Development and validation of a histology-specific natural history model of ovarian cancer

  American Journal of Obstetrics and Gynecology · 2025-07-05 · 2 citations

  article
  PublisherDOI

• Externally validated digital decision support tool for time-to-osteoradionecrosis risk-stratification using right-censored multi-institutional observational cohorts

  Radiotherapy and Oncology · 2025-04-11 · 4 citations

  articleOpen access
  PublisherOA PDFDOI

• On the Structure of the Inverse-Feasible Region of a Multiobjective Integer Program

  SSRN Electronic Journal · 2025-01-01

  preprintOpen accessSenior author
  PublisherDOI

Recent grants

• Collaborative Research: Optimization of the Design and Operation of Surgery Delivery Systems

  NSF · $120k · 2006–2010

• Optimizing the Regional Distribution of Organ Procurement Organizations

  NSF · $318k · 2004–2008

• Collaborative Research: Physiologically Based Optimization of ICU Management

  NSF · $224k · 2016–2020

• Optimizing Flu Shot Design Under Uncertainity

  NSF · $327k · 2008–2012

• CAREER: Next-Generation Research and Education in Therapeutic Optimization

  NSF · $416k · 2006–2012

Frequent coauthors

• Mark S. Roberts

  59 shared

• Clifton D. Fuller

  The University of Texas MD Anderson Cancer Center

  25 shared

• Temitayo Ajayi

  23 shared

• Oleg A. Prokopyev

  20 shared

• Steven M. Shechter

  University of British Columbia

  18 shared

• R. Scott Braithwaite

  17 shared

• Lisa M. Maillart

  University of Pittsburgh

  16 shared

• Abdallah Mohamed

  16 shared

Labs

• Andrew J. Schaefer LabPI

Education

• PhD, Industrial and Systems Engineering

  Georgia Institute of Technology

  2000

Awards & honors

• Outstanding Young Engineer by the Rice Engineering Alumni as…
• Outstanding Young Industrial Engineering Education Award fro…
• NSF CAREER Award (2006)
• Best Paper Award, IIE Transactions on Operations Engineering…
• Outstanding Young Engineering Alumni Award, Rice University…