Data-driven optimization and analytics for operations management applications by Joline Ann Villaranda Uichanco Submitted to the Sloan School of Management in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Operations Research at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2013 ⃝c Massachusetts Institute of Technology 2013. All rights reserved. Author............................................................................ Sloan School of Management August 1, 2013 Certified by........................................................................ Georgia Perakis William F. Pounds Professor of Management Professor of Operations Research and Operations Management Thesis Supervisor Certified by........................................................................ Retsef Levi J. Spencer Standish (1945) Professor of Management Associate Professor of Operations Managementat Thesis Supervisor Accepted by....................................................................... Dimitris Bertsimas Boeing Professor of Operations Research Co-director, Operations Research Center 2 Data-driven optimization and analytics for operations management applications by Joline Ann Villaranda Uichanco Submitted to the Sloan School of Management on August 1, 2013, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Operations Research Abstract In this thesis, we study data-driven decision making in operation management contexts, with a focus on both theoretical and practical aspects. The first part of the thesis analyzes the well-known newsvendor model but under the assumption that, even though demand is stochastic, its probability distribution is not part of the input. Instead, the only information available is a set of independent samples drawn from the demand distribution. We analyze the well-known sample average approximation (SAA) approach, and obtain new tight analytical bounds on the accuracy of the SAA solution. Unlike previous work, these bounds match the empirical performance of SAA observed in extensive computational experiments. Our analysis reveals that a distribution's weighted mean spread (WMS) impacts SAA accuracy. Furthermore, we are able to derive distribution parametric free bound on SAA accuracy for log-concave distributions through an innovative optimization-based analysis which minimizes WMS over the distribution family. In the second part of the thesis, we use spread information to introduce new families of demand distributions under the minimax regret framework. We propose order policies that require only a distribution's mean and spread information. These policies have several attractive properties. First, they take the form of simple closed-form expressions. Second, we can quantify an upper bound on the resulting regret. Third, under an environment of high profit margins, they are provably near-optimal under mild technical assumptions on the failure rate of the demand distribution. And finally, the information that they require is easy to estimate with data. We show in extensive numerical simulations that when profit margins are high, even if the information in our policy is estimated from (sometimes few) samples, they often manage to capture at least 99% of the optimal expected profit. The third part of the thesis describes both applied and analytical work in collaboration with a large multi-state gas utility. We address a major operational resource allocation problem in which some of the jobs are scheduled and known in advance, and some are unpredictable and have to be addressed as they appear. We employ a novel decomposition approach that solves the problem in two phases. The first is a job scheduling phase, where regular jobs are scheduled over a time horizon. The second is a crew assignment phase, which assigns jobs to maintenance crews under a stochastic number of future emergencies. We propose heuristics for both phases using linear programming relaxation and list scheduling. Using our models, we develop a decision support tool for the utility which is currently being piloted in one of the company's sites. Based on the utility's data, we project that the tool will result in 55% reduction in overtime hours. Thesis Supervisor: Georgia Perakis Title: William F. Pounds Professor of Management 3 Professor of Operations Research and Operations Management Thesis Supervisor: Retsef Levi Title: J. Spencer Standish (1945) Professor of Management Associate Professor of Operations Managementat 4 Acknowledgments There are many people I would like to thank who have helped and supported me in my Ph.D. journey, which culminates with this thesis. I dedicate this thesis to my mother, Jocelyn, who has sacrificed so much throughout the years and who has raised two children despite personal difficulties. Without her, I would not be where I am. Through her example, she has taught me tenacity, resilience, and strong values. I also thank my brother, Joseph, who I know I can count on in times of trouble. I send my heartfelt thanks to my two fantastic research advisors, Retsef and Georgia, who I have known since my Masters program at MIT. I could not have had better advisors. My Ph.D. journey has had many emotional highs and lows which I could not have weathered without them. They have given me mentorship, moral support and encouragement. I also thank my Masters advisors, Karthik Natarajan and Melvyn Sim, who still remain my mentors. I would like to send special thanks to Steve Graves and Melvyn Sim for participating in my thesis committee. Thanks to employees at National Grid, whose help was valuable in writing my thesis. Thanks to Mallik Angalakudati, Sid Balwani, Jorge Calzada, Bikram Chatterjee, and Nick Raad. I thank all the friends that I made throughout the past five years. I am grateful for the friendship I have found in Ilke Kalcioglu, who has been my roommate for two years and who remains like a sister to me. I thank Ruben Lobel for also being supportive and being such a good friend. Special thanks also goes to Sun Wei, who is also like a sister and who never fails to give advice when I need it. I thank my good friends, Chaitanya Bandi, Ozan Candogan, Mihalis Markakis, and Yehua Wei, who were in the academic job search with me. I'm glad we went through this process together. I wish them all the best for the future. I'm grateful for my friends from the ORC. I'm grateful to Ta Chiraphadhanakul, Cristian Figueroa, and Matthieu Monsch for the times we spent studying for Quals, having dinner at Pad Thai Cafe, and watching movies during our first few years. Thanks to the rest of my classmates, Dimitrios Bisias, Michael Frankovich, Zach Leung, Xin Lu, Anna Teytelman, Eric Zarybnisky, and Yuan Zhong. Thanks to Jason Acimovic, Kostas Bimpikis, Shi Cong, Doug Fearing, Dan Iancu, Ilan Lobel, Nikos Trichiakis and Gerry Tsoukalas, who graduated before me but who all have still supported me. I also thank the friends I made at the ORC, Ross Anderson, Fernanda Bravo, Andre Calmon, Maxime Cohen, Adam Elmachtoub, Matthew Fontana, Paul Grigas, Vishal Gupta, Shubham Gupta, Swati Gupta, Kris Johnson, Nathan Kallus, Phil Keller, John Kessler, Jonathan Kluberg, Angie King, Maokai Lin, Will Ma, Allison O'Hair, Eric Robinson, Joel Tay, Leon Valdes, and Nataly Youssef. I'm glad for all the memories we've made throughout 5 the years of INFORMS, ISMP and MSOM trips, of barbecues, parties and concerts, of camping trips, of C-Functions, of Thirsty Ear karaoke nights, and of many others. Thanks to my friends outside of the ORC, who have shared experiences with me and who have also been good emotional support. Thanks to Burak Alver, Doug Clendenin, Laura Kligler, Roza Mahmoodian, Karen Nadua, Ferron Ocampo, Nestor Precioso, Nikolas Pyrgiotis, Val San Antonio, Yannis Simiakis, and Melis Tanner, and Derek Yao. Finally, I am grateful for the ORC Co-directors, Dimitris Bertsimas and Patrik Jaillet, who have truly been committed to the welfare of the students and the Center. Also, thanks to the amazing ORC administrative staff, Andrew Carvalho, Paulette Mosley, and Laura Rose. 6 Contents 1 Introduction 15 2 The data-driven newsvendor 17 2.1 Introduction .................................... 17 2.1.1 Contributions and Insights ....................... 18 2.1.2 Literature Review ............................ 19 2.1.3 Outline .................................. 22 2.2 The Data-driven Newsvendor Problem ..................... 22 2.3 Distribution-Free Uniform Probability Bounds ................. 24 2.4 New Approximation to the Sϵ Interval ..................... 27 2.4.1 Tightness of distribution-dependent bound .............. 30 2.5 Optimization-Driven Bound on WMS ..................... 31 2.5.1 Probability bound for log-concave distributions ............ 32 2.6 Balancing the cost and benefit of sampling ................... 35 2.7 Computational Experiments ........................... 37 2.8 Conclusions .................................... 39 3 Regret optimization with spread information 41 3.1 Introduction .................................... 41 3.1.1 Contributions ............................... 42 3.1.2 Literature Review ............................ 43 3.1.3 Outline .................................. 44 3.2 Regret optimization under spread information ................. 45 3.3 Optimality properties of policies using spread information .......... 48 3.4 Interval Information on AMS .......................... 54 3.5 Data-driven estimation of AMS ......................... 54 3.6 Computational Experiments ..........................