My research focuses on the development of novel optimization methods and the application of those methods to solve complex decision-making problems primarily in healthcare and sports.

### Inverse optimization

The goal of inverse optimization is to “reverse engineer” parameters of an optimization model that make a given, observed decision optimal. If it is not possible to make the decision exactly optimal, e.g., the data is noisy or the model is an approximation, then a measure of suboptimality is typically minimized. Viewed through the lens of model fitting, my main interest is to develop new approaches for inverse optimization that optimize and measure data-model fit. Given the increasing amounts of data that are generated as the result of a decision process, I am also interested in finding innovative applications for inverse optimization. Relevant publications:

- A. Babier, R. Mahmood, A. L. McNiven, A. Diamant, T. C. Y. Chan, “Knowledge-based automated planning with three-dimensional generative adversarial networks,”
, accepted 2019.**Medical Physics** - T. C. Y. Chan, N. Kaw, “Inverse optimization for the recovery of constraint parameters,”
, accepted 2019.**European Journal of Operational Research** - A. Goli, J. J. Boutilier, M. B. Sharpe, T. Craig, T. C. Y. Chan, “A small number of objective function weight vectors is sufficient for automated treatment planning in prostate cancer,”
, Vol. 63, 195004, 2018.**Physics in Medicine and Biology** - A. Babier, J. J. Boutilier, M. B. Sharpe, A. L. McNiven, T. C. Y. Chan, “Inverse optimization of objective function weights for treatment planning using clinical dose-volume histograms,”
, Vol. 63, 105004, 2018.**Physics in Medicine and Biology** - A. Babier, J. J. Boutilier, A. L. McNiven, T. C. Y. Chan, “Knowledge-based automated planning for oropharyngeal cancer,”
, Vol. 45, pp. 2875-2883, 2018.**Medical Physics** - T. C. Y. Chan, T. Lee, “Trade-off preservation in inverse multi-objective convex optimization,”
, Vol. 270, pp. 25-39, 2018.*European Journal of Operational Research* - T. C. Y. Chan, T. Lee, D. Terekhov, “Inverse optimization: Closed-form solutions, geometry, and goodness of fit,”
, Vol. 65, pp. 1115-1135, 2019.*Management Science* - J. J. Boutilier, T. Craig, M. B. Sharpe, T. C. Y. Chan, “Sample size requirements for knowledge-based treatment planning,”
, Vol. 43, 1212, 2016.*Medical Physics* - J. J. Boutilier, T. Lee, T. Craig, M. B. Sharpe, T. C. Y. Chan, “Models for predicting objective function weights in prostate cancer IMRT,”
, Vol. 42, 1586, 2015.*Medical Physics* - T. C. Y. Chan, T. Craig, T. Lee, M. B. Sharpe, “Generalized inverse multi-objective optimization with application to cancer therapy,”
, Vol. 62, pp. 680-695, 2014.*Operations Research* - T. Lee, M. Hummad, T. C. Y. Chan, T. Craig, M. B. Sharpe, “Predicting objective function weights from patient anatomy in prostate IMRT treatment planning,”
, Vol. 40, 121706, 2013.*Medical Physics* - S. D. O. Turner, T. C. Y. Chan, “Examining the LEED rating system using inverse optimization,”
, Vol. 135, 040901, 2013.*Journal of Solar Energy Engineering*

### Robust optimization

Robust optimization is used to optimize in the face of uncertainty. I am interested in theory, modeling, solution methods, and applications of robust optimization. The majority of my work to date has been in robust optimization, especially applied to radiation therapy treatment planning. Relevant publications:

- J. J. Boutilier, T. C. Y. Chan, “Ambulance Emergency Response Optimization in developing countries,”
, accepted 2019.*Operations Research* - J. Unkelbach, M. Alber, M. Bangert, R. Bokrantz, T. C. Y. Chan, J. Deasy, A. Fredriksson, B. L. Gorissen, M. van Herk, W. Liu, H. Mahmoudzadeh, O. Nohadani, J. V. Siebers, M. Witte, H. Xu, “Robust radiotherapy planning,”
, Vol. 63, 22TR02, 2018.*Physics in Medicine and Biology* - T. C. Y. Chan, D. Fearing, “Process flexibility in baseball: The value of positional flexibility,”
, 2017.*accepted to Management Science* - T. C. Y. Chan, Z.-J. M. Shen, A. Siddiq, “Robust deﬁbrillator deployment under cardiac arrest location uncertainty via row-and-column generation,”
, Vol. 66, pp. 358-379, 2018.*Operations Research* - T. C. Y. Chan, P. A. Mar, “Stability and continuity in robust optimization,”
, Vol. 27, pp. 817-841, 2017. Online supplement*SIAM Journal on Optimization* - H. Mahmoudzadeh, T. G. Purdie, T. C. Y. Chan, “Constraint generation methods for robust optimization in radiation therapy,”
, Vol. 8, pp. 85-90, 2016.*Operations Research for Health Care* - H. Li, J. P. Bissonnette, T. Purdie, T. C. Y. Chan, “Robust PET-guided intensity-modulated radiation therapy,”
, Vol. 42, 4863, 2015.*Medical Physics* - V. V. Misic, T. C. Y. Chan, “The perils of adapting to dose errors in radiation therapy,”
, Vol. 10, e0125335, 2015.*PLOS ONE* - P. A. Mar, T. C. Y. Chan, “Adaptive and robust radiation therapy in the presence of drift,”
, Vol. 60, pp. 3599-3615, 2015.*Physics in Medicine and Biology* - H. Mahmoudzadeh, J. Lee, T. C. Y. Chan, T. G. Purdie, “Robust optimization methods for cardiac sparing in tangential breast IMRT,”
, Vol. 42, 2212, 2015.*Medical Physics* - T. C. Y. Chan, H. Mahmoudzadeh, T. G. Purdie, “A robust-CVaR optimization approach with application to breast cancer therapy,”
, Vol. 238, pp. 876-885, 2014.*European Journal of Operational Research* - T. C. Y. Chan, V. V. Misic, “Adaptive and robust radiation therapy optimization for lung cancer,”
, Vol. 231, pp. 745-756, 2013.**European Journal of Operational Research** - T. Bortfeld, T. C. Y. Chan, A. Trofimov, J. N. Tsitsiklis, “Robust management of motion uncertainty in intensity modulated radiation therapy,”
Vol. 56, pp. 1461-1473, 2008.**Operations Research**, - J. Unkelbach, T. C. Y. Chan, T. Bortfeld, “Accounting for range uncertainties in the optimization of intensity modulated proton therapy,”
, Vol. 52, pp. 2755-2773, 2007.*Physics in Medicine and Biology* - T. C. Y. Chan, T. Bortfeld, J. N. Tsitsiklis, “A robust approach to IMRT optimization,”
, Vol. 51, pp. 2567-2583, 2006.*Physics in Medicine and Biology*

### Radiation therapy

Radiation therapy is one of the primary techniques used to treat cancer. Beams of radiation are delivered from different angles around a patient, targeting a tumor at their intersection while aiming to spare nearby critical organs. I deploy a combination of robust optimization, inverse optimization, and machine learning to improve the quality of treatments and the efficiency of the treatment planning process. Relevant publications:

- A. Babier, R. Mahmood, A. L. McNiven, A. Diamant, T. C. Y. Chan, “Knowledge-based automated planning with three-dimensional generative adversarial networks,”
, accepted 2019.**Medical Physics** - J. Unkelbach, M. Alber, M. Bangert, R. Bokrantz, T. C. Y. Chan, J. Deasy, A. Fredriksson, B. L. Gorissen, M. van Herk, W. Liu, H. Mahmoudzadeh, O. Nohadani, J. V. Siebers, M. Witte, H. Xu, “Robust radiotherapy planning,”
, Vol. 63, 22TR02, 2018.*Physics in Medicine and Biology* - A. Goli, J. J. Boutilier, M. B. Sharpe, T. Craig, T. C. Y. Chan, “A small number of objective function weight vectors is sufficient for automated treatment planning in prostate cancer,”
, Vol. 63, 195004, 2018.**Physics in Medicine and Biology** - A. Babier, J. J. Boutilier, M. B. Sharpe, A. L. McNiven, T. C. Y. Chan, “Inverse optimization of objective function weights for treatment planning using clinical dose-volume histograms,”
, Vol. 63, 105004, 2018.**Physics in Medicine and Biology** - A. Babier, J. J. Boutilier, A. L. McNiven, T. C. Y. Chan, “Knowledge-based automated planning for oropharyngeal cancer,”
, Vol. 45, pp. 2875-2883, 2018.**Medical Physics** - I. Dayarian, T. C. Y. Chan, D. Jaffray, T. Stanescu, “A mixed-integer optimization approach for homogeneous magnet design,”
, Vol. 6, pp. 49-58, 2018.**Technology** - T. C. Y. Chan, T. Lee, “Trade-off preservation in inverse multi-objective convex optimization,”
, Vol. 270, pp. 25-39, 2018.*European Journal of Operational Research* - T. C. Y. Chan, T. Lee, D. Terekhov, “Inverse optimization: Closed-form solutions, geometry, and goodness of fit,”
, Vol. 65, pp. 1115-1135, 2019.*Management Science* - J. J. Boutilier, T. Craig, M. B. Sharpe, T. C. Y. Chan, “Sample size requirements for knowledge-based treatment planning,”
, Vol. 43, 1212, 2016.*Medical Physics* - H. Mahmoudzadeh, T. G. Purdie, T. C. Y. Chan, “Constraint generation methods for robust optimization in radiation therapy,”
, Vol. 8, pp. 85-90, 2016.*Operations Research for Health Care* - H. Li, N. Becker, S. Raman, T. C. Y. Chan, J.-P. Bissonnette, “The value of nodal information in predicting lung cancer relapse using 4DPET/4DCT,”
, Vol. 42, 4727, 2015.*Medical Physics* - H. Li, J. P. Bissonnette, T. Purdie, T. C. Y. Chan, “Robust PET-guided intensity-modulated radiation therapy,”
, Vol. 42, 4863, 2015.*Medical Physics* - V. V. Misic, T. C. Y. Chan, “The perils of adapting to dose errors in radiation therapy,”
, Vol. 10, e0125335, 2015.*PLOS ONE* - P. A. Mar, T. C. Y. Chan, “Adaptive and robust radiation therapy in the presence of drift,”
, Vol. 60, pp. 3599-3615, 2015.*Physics in Medicine and Biology* - H. Mahmoudzadeh, J. Lee, T. C. Y. Chan, T. G. Purdie, “Robust optimization methods for cardiac sparing in tangential breast IMRT,”
, Vol. 42, 2212, 2015.*Medical Physics* - J. J. Boutilier, T. Lee, T. Craig, M. B. Sharpe, T. C. Y. Chan, “Models for predicting objective function weights in prostate cancer IMRT,”
, Vol. 42, 1586, 2015.*Medical Physics* - T. C. Y. Chan, H. Mahmoudzadeh, T. G. Purdie, “A robust-CVaR optimization approach with application to breast cancer therapy,”
, Vol. 238, pp. 876-885, 2014.*European Journal of Operational Research* - T. C. Y. Chan, T. Craig, T. Lee, M. B. Sharpe, “Generalized inverse multi-objective optimization with application to cancer therapy,”
, Vol. 62, pp. 680-695, 2014.*Operations Research* - Y. Liu, T. C. Y. Chan, C.-G. Lee, Y. B. Cho, M. K. Islam, “A stochastic model for tumor geometry evolution during radiation therapy in cervical cancer,”
, Vol. 41, 021705, 2014.*Medical Physics* - T. Lee, M. Hummad, T. C. Y. Chan, T. Craig, M. B. Sharpe, “Predicting objective function weights from patient anatomy in prostate IMRT treatment planning,”
, Vol. 40, 121706, 2013.*Medical Physics* - T. C. Y. Chan, V. V. Misic, “Adaptive and robust radiation therapy optimization for lung cancer,”
, Vol. 231, pp. 745-756, 2013.*European Journal of Operational Research* - T. C. Y. Chan, “Motion-compensating intensity maps in intensity-modulated radiation therapy,”
, Vol. 3, pp. 1-22, 2013.*IIE Transactions on Healthcare Systems Engineering* - T. C. Y. Chan, J. N. Tsitsiklis, T. Bortfeld, “Optimal margin and edge-enhanced intensity maps in the presence of motion and uncertainty,”
Vol. 55, pp. 515-533, 2010.**Physics in Medicine and Biology**, - C. Vrancic, A. Trofimov, T. C. Y. Chan, G. C. Sharp, T. Bortfeld, “Experimental evaluation of a robust optimization method for IMRT of moving targets,”
, Vol. 54, pp. 2901-2914, 2009.*Physics in Medicine and Biology* - T. Bortfeld, T. C. Y. Chan, A. Trofimov, J. N. Tsitsiklis, “Robust management of motion uncertainty in intensity modulated radiation therapy,”
Vol. 56, pp. 1461-1473, 2008.**Operations Research**, - A. Trofimov, C. Vrancic, T. C. Y. Chan, G. C. Sharp, T. Bortfeld, “Tumor trailing strategy for intensity-modulated radiation therapy of moving targets,”
, Vol. 35, pp. 1718-1733, 2008.*Medical Physics* - J. Unkelbach, T. C. Y. Chan, T. Bortfeld, “Accounting for range uncertainties in the optimization of intensity modulated proton therapy,”
, Vol. 52, pp. 2755-2773, 2007.*Physics in Medicine and Biology* - T. C. Y. Chan, T. Bortfeld, J. N. Tsitsiklis, “A robust approach to IMRT optimization,”
, Vol. 51, pp. 2567-2583, 2006.*Physics in Medicine and Biology*

### Cardiac arrest and public access defibrillator location

The likelihood of survival from cardiac arrest is very time sensitive. One method to reset the heart’s normal rhythm is to deliver an electric shock using an automated external defibrillator (AED), which can be used by lay responders with little to no training. My research focuses on developing optimization methods for AED deployment, ranging from static deployment in public locations to delivery via drone. Accordingly, I am interested in approaches to estimate cardiac arrest risk and quantify accessibility. Relevant publications:

- C. L. F. Sun, L. Karlsson, C. Torp-Pedersen, L. J. Morrison, S. C. Brooks. F. Folke, T. C. Y. Chan, “In silico trial of optimized versus real public defibrillator locations,”
, accepted 2019.*Journal of the American College of Cardiology* - M. Shuvy, M. Koh, F. Qiu, S. C. Brooks, T. C. Y. Chan, S. Cheskes, P. Dorian, G. Geri, S. Lin, D. C. Scales, D. T. Ko, “Health care utilization prior to out-of-hospital cardiac arrest: a population-based study,”
, accepted 2019.**Resuscitation** - C. L. F. Sun, L. Karlsson, C. Torp-Pedersen, L. J. Morrison, F. Folke, T. C. Y. Chan, “Spatiotemporal AED optimization is generalizable,”
, Vol. 131, pp. 101-107, 2018.**Resuscitation** - M. Lee, D. Demirtas, J. E. Buick, M. J. Feldman, S. Cheskes, L. J. Morrison, T. C. Y. Chan, “Increased cardiac arrest survival and bystander intervention in enclosed pedestrian walkway systems,”
, Vol. 118, pp. 1-7, 2017.*Resuscitation* - T. C. Y. Chan, Z.-J. M. Shen, A. Siddiq, “Robust deﬁbrillator deployment under cardiac arrest location uncertainty via row-and-column generation,”
, Vol. 66, pp. 358-379, 2018.*Operations Research* - J. J. Boutilier, S. C. Brooks, A. Janmohamed, A. Byers, J. E. Buick, C. Zhan, A. P. Schoellig, S. Cheskes, L. J. Morrison, T. C. Y. Chan, “Optimizing a drone network to deliver automated external defibrillators,”
, Vol. 135, pp. 2454-2465, 2017.*Circulation* - C. L. F. Sun, S. C. Brooks, L. J. Morrison, T. C. Y. Chan, “Ranking businesses and municipal locations by spatiotemporal cardiac arrest risk to guide public defibrillator placement,”
, Vol. 135, pp. 1104-1119, 2017.*Circulation* - T. C. Y. Chan, “Rise and shock: Optimal defibrillator placement in a high-rise building,”
, Vol. 21, pp. 309-314, 2017.*Prehospital Emergency Care* - C. L. F. Sun, D. Demirtas, S. C. Brooks, L. J. Morrison, T. C. Y. Chan, “Overcoming spatial and temporal barriers to public access defibrillators via optimization,”
, Vol. 68, pp. 836-845, 2016.**Journal of the American College of Cardiology** - T. C. Y. Chan, D. Demirtas, R. H. Kwon, “Optimizing the deployment of public access defibrillators,”
, Vol. 62, pp. 3617-3635, 2016.*Management Science* - A. A. Siddiq, S. C. Brooks, T. C. Y. Chan, “Modeling the impact of public access defibrillator range on public location cardiac arrest coverage,”
, Vol. 84, pp. 904-909, 2013.*Resuscitation* - T. C. Y. Chan, H. Li, G. Lebovic, S. K. Tang, J. Y. T. Chan, H. C. K. Cheng, L. J. Morrison, S. C. Brooks, “Identifying locations for public access defibrillators using mathematical optimization,”
, Vol. 127, pp. 1801-1809, 2013.*Circulation* - S. C. Brooks, J. H. Hsu, S. K. Tang, R. Jeyakumar, T. C. Y. Chan, “Determining risk for out-of-hospital cardiac arrest by location type in a Canadian urban setting to guide future public access defibrillator placement,”
, Vol. 61, pp. 530-538, 2013.*Annals of Emergency Medicine*

### Global health

I am interested in bringing operations research methods to bear on important problems in global health. My main research project in this domain focuses on developing optimization models to guide ambulance deployment and routing in developing country settings, which are subject to major uncertainties in demand and travel time. Click here for a two-minute introduction to the project. Relevant publications:

- F. J. Mateen, K. H. B. Leung, A. C. Vogel, A. Fode Cisse, T. C. Y. Chan, “A drone delivery network for antiepileptic drugs: a framework and modeling case study in a lowest-income country,”
, accepted 2019.**Transactions of the Royal Society of Tropical Medicine and Hygiene** - J. J. Boutilier, T. C. Y. Chan, “Ambulance Emergency Response Optimization in developing countries,”
, accepted 2019.*Operations Research* - B. D. Bradley, T. Jung, A. Tandon-Verma, B. Khoury, T. C. Y. Chan, Y.-L. Cheng, “Operations Research in Global Health: A scoping review with a focus on the themes of health equity and impact,”
, Vol. 15, 32, 2017.**Health Research Policy and****Systems** - B. D. Bradley, S. R. C. Howie, T. C. Y. Chan, Y.-L. Cheng, “Estimating oxygen needs for childhood pneumonia in developing country health systems: a new model for expecting the unexpected,”
, Vol. 9, e89872, 2014.*PLOS ONE*

### Sports analytics

I am a passionate sports fan and enjoy analyzing interesting (decision) problems in sports. I have worked on topics in hockey, baseball, tennis, golf, football, and curling. Click here for a video of a talk I gave on sports analytics. Here is my TEDxUofT talk on baseball flexibility. A team of students and I developed an interactive NHL Expansion Draft optimization tool, which allows users to optimize protection and selection decisions in real time. Relevant publications:

- C. Fernandes, R. Yakubov, Y. Li, A. Prasad, T. C. Y. Chan, “Predicting plays in the National Football League,”
, accepted 2019.**Journal of Sports Analytics** - K. E. C. Booth, T. C. Y. Chan, Y. Shalaby, “A mathematical optimization framework for expansion draft decision making and analysis,”
, Vol. 15, pp. 27-40, 2019.**Journal of Quantitative Analysis in Sports** - T. C. Y. Chan, R. Singal, “A Bayesian regression approach to handicapping tennis players based on a rating system,”
, vol. 14, pp. 131-141, 2018.**Journal of Quantitative Analysis in Sports** - T. C. Y. Chan, D. Madras, M. L. Puterman, “Improving fairness in match play golf through enhanced handicap allocation,”
, Vol. 4, pp. 251-262, 2018.*Journal of Sports Analytics* - T. C. Y. Chan, D. Fearing, “Process flexibility in baseball: The value of positional flexibility,”
, 2017.*accepted to Management Science* - T. C. Y. Chan, R. Singal, “A Markov Decision Process-based handicap system for tennis,”
, Vol. 12, pp. 179-189, 2016.**Journal of Quantitative Analysis in Sports** - T. C. Y. Chan, J. A. Cho, D. C. Novati, “Quantifying the contribution of NHL player types to team performance,”
, Vol. 42, pp.131-145, 2012.*Interfaces*

### Healthcare operations

I am interested in a variety of healthcare operations problems including scheduling and process flexibility. Relevant publications:

- B. K. Eagen, T. C. Y. Chan, M. W. Carter, “Women’s College Hospital uses Operations Research to create an ambulatory clinic schedule,”
, Vol. 10, pp. 230-240, 2018.**Service Science**

### Sustainability

Although I am not currently active in this area, I have previous experience applying optimization methods to problems in green building design and wind farm layout. Relevant publications:

- S. D. O. Turner, D. A. Romero, P. Y. Zhang, C. H. Amon, T. C. Y. Chan, “A new mathematical programming approach to optimize wind farm layouts,”
, Vol. 63, pp. 674-680, 2014.*Renewable Energy* - S. D. O. Turner, T. C. Y. Chan, “Examining the LEED rating system using inverse optimization,”
, Vol. 135, 040901, 2013.*Journal of Solar Energy Engineering*

### Education

I enjoy developing innovative teaching methods using games and other interactive activities. Relevant publications:

- T. C. Y. Chan, “Deal or No Deal: A spreadsheet game to introduce decision making under uncertainty,”
, Vol. 14, pp. 53-60, 2013.*INFORMS Transactions on Education*