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%\title{Research Statement}
%\author{Dan Iancu}
%\date{}
%\keywords{robust optimization, multi-stage minimax, optimal policies, convex costs, dynamic, programming}


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  {\Large Research Statement} \\[20pt]
%  {\Large Dan Iancu}
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%My research thus far has been focused on two major directions, namely (1) providing new methodology for understanding and computing decisions in complex operational settings, and (2) examining how such methodology can be used to guide decision-making in particular concrete applications. The unifying theme 

Broadly speaking, my research thus far has been focused on providing new ways for understanding and computing decisions in complex operational settings, with a special emphasis on problems involving risk and (severe) uncertainty. My work has followed two major streams, by developing new methodology, and understanding how this can be used to guide decision-making in particular concrete applications. I elaborate on each of these below.

On the methodological front, most of my research has followed the robust optimization paradigm, whereby a decision maker is faced with the problem of optimizing a system under (very) limited information about future outcomes. %\footnote{Standard assumptions stipulate that the support of all uncertain quantities is known, but only partial knowledge of the distributions is available.} 
Prior to my work, several papers had examined such problems in dynamic settings, and had advocated the use of \emph{adjustable decision rules}, as an alternative to the classical Dynamic Programming (DP) paradigm.\footnote{Such decision rules essentially stipulate that the policy governing actions at future times should depend directly on observed uncertainties, as opposed to being parameterized in the states of the system.} Of key interest was the class of \emph{linear / affine} rules, which was known to be computationally tractable, and to deliver excellent performance in a variety of applications. When limiting attention to such policies, however, a key question of concern was sub-optimality, i.e., whether these considerably underperform as compared with the optimal policy. In a sequence of papers ([1], [3]), we provide sufficient conditions under which such affine policies are, in fact, \emph{provably optimal}, and show that these conditions hold for several relevant operational settings, including inventory replenishment and capacity planning with convex production costs, as well as the design of flexible retailer-supplier pre-commitment contracts. From a practical viewpoint, these results are important since they provide simple and intuitive interpretations for the optimal policies, and concrete guidelines for finding them, by solving simple (e.g., linear) optimization problems, even in settings where the classical DP paradigm would be intractable or would prescribe very complex policies. From a theoretical perspective, the results are the first of their kind, combining techniques from a variety of areas, such as polyhedral geometry, super-modularity, and lattice programming. Critically, however, they are relevant since they underscore several substantial differences between decision making under severe uncertainty and decision making under exact distributional information.\footnote{Intuitively, the Bellman optimality principle may be an unnecessarily stringent criterion for the former class of models, while it is strictly required for the latter. As such, robust decision models may admit structurally ``simpler'' optimal policies, and new methodology can be developed to find such policies, going beyond the direct use of DP.}

The earlier results critically depended on a feature that is intrinsic in robust decision making -- namely, that such problems often admit multiple optimal policies. While useful for finding simple policies in dynamic settings, this degeneracy may also cause serious inefficiencies in the decision process. To this end, in follow up work [5], we formalize and adapt the notion of Pareto efficiency in a robust decision-making context, and show that the classical robust optimization framework need not produce solution with this property.\footnote{We also prove that whether such solutions are generated critically depends on the software (i.e., algorithms) used to solve the resulting optimization problems.} We also provide a simple procedure to test whether a given solution is Pareto-efficient, and (if not) to generate such Pareto-efficient solutions. The procedure generates decisions with considerably improved performance in several applications, and does not increase the computational complexity of the nominal robust framework, resulting -- essentially -- in a strict enhancement of the framework.

Other related research, on which I do not elaborate here, includes extensions to the framework of computing decisions in dynamic robust models (with applications in inventory replenishment in multi-tier supply chains [2]), as well as work on understanding how static risk preferences can be approximated by dynamic risk measures, which are axiomatically-justified and computationally tractable [6].%\footnote{In [2], we show that, when affine decision rules are sub-optimal, polynomial rules can be tractably computed, delivering performance that is near-optimal, even for low degrees.}

On the applications front, my research has examined a broad range of problems, in supply chain management, revenue management, as well as financial engineering and healthcare. The unifying theme has been the use of quantitative tools to guide decision-making under risk, as well as a focus on understanding how operational decisions influence (and are influenced by) other considerations within and outside of the firm. I discuss some of these below.

In [6], we deal with the problem faced by a portfolio manager in charge of multiple accounts. We argue that, due to market impact costs, this setting differs in several subtle ways from the classical (single account) case, with a key distinction arising from the performance of each individual account being coupled with the trading strategies of other accounts. We propose a novel approach for jointly determining the trades and splitting the associated market impact costs across all the accounts. Our framework is flexible, allowing the manager to balance conflicting objectives, such as maximizing (risk-adjusted) aggregate wealth and distributing the gains equitably; it is also tractable, requiring convex optimization problems to be solved; furthermore, in numerical studies, it significantly outperforms existing methods employed in the industry or discussed in the literature.

In [7], we discuss optimal sourcing decisions in a multi-tier supply chain, consisting of three levels: a manufacturer, Tier 1 suppliers, and Tier 2 suppliers prone to disruption risk (e.g., from natural disasters, like earthquakes or floods). The manufacturer may not directly dictate which Tier 2 suppliers are used, but may influence the sourcing strategy of Tier 1 suppliers, and the resulting supply chain configuration, via contractual offerings. We find that the manufacturer's optimal strategy critically depends on the degree of overlap in the supply chain, with move overlap inducing less reliance on direct mitigation (procuring excess inventory and multisourcing in Tier 1), and more on indirect mitigation (paying larger prices, and inducing Tier 1 suppliers to mitigate disruption risk). We also show that, while the manufacturer always prefers less overlap in the supply chain, Tier 1 suppliers may prefer a different configuration; this results in a severe moral hazard problem, which cannot be mitigated through side payments, but which can be alleviated through penalty contracts. We also show that sourcing according to a robust strategy can significantly reduce the profit loss for the manufacturer, particularly at low or intermediate unit-revenues.

In [8], we study the interplay between financial covenants and the operational decisions of a retailer that obtains financing through a secured (asset-based) lending contract. While it is widely held that covenants serve to alleviate risk and protect lenders, the ways in which a retailer adapts his operations in response have not been studied. We show that retailers under debt manage inventory through riskier policies, involving potentially surprising (non-threshold) behavior. We characterize the market conditions, involving demand distribution, growth potential, profit margin, and inventory depreciation rate, under which covenants are necessary, and argue that these are routinely met in practice. We show that covenants are not substitutable by other contractual terms, such as interest rates and loan limits, and provide operational insights for their optimal design. We discuss when covenants ensure that system-optimal decisions are taken in equilibrium, and show that additional operational flexibility can impact their effectiveness in a surprising, non-monotonic way.

In [9], we deal with the problem of developing optimal treatments for particular chronic illnesses, such as multiple sclerosis or Crohn's disease. Currently available medication for such diseases is often effective only for a subgroup of the population, and biomarkers accurately assessing the response of a new patient do not exist. As such, physicians learn about drug effectiveness of primarily through risky experimentation, i.e., by initiating treatment and monitoring the patient's response. Precise guidelines for discontinuing treatment are often lacking or left entirely at the physician's discretion. We introduce a quantitative framework for developing adaptive, personalized treatments for such chronic diseases. Our model acknowledges that drug effectiveness can be assessed by aggregating information from several channels, e.g., by continuously monitoring the (self-reported) state of the patient, but also by (not) observing the occurrence of infrequent health events, such as relapses or disease flare-ups. Recognizing that the timing and severity of such events carries critical information for treatment design is a key point of departure in our framework compared with typical models used in healthcare. We show that our model can be analyzed in closed form for several settings of interest, resulting in optimal policies that are intuitive and have practical appeal. We showcase the effectiveness of the methodology by developing a treatment policy for multiple sclerosis, which is able to identify non-responders earlier than standard guidelines, leading to improvements in quality-adjusted life expectancy, as well as significant cost savings.

The examples above highlight a selection of the problems on which I have focused thus far in my research. In the past two years, my interests have shifted closer to questions related to the design of long-term contractual agreements, and understanding the role and impact of operations on other decisions of the firm. As such, my latest projects have focused increasingly on questions at the interface of operations and finance/accounting, a direction that I intend to continue pursuing in the near future. Some of my existing active projects directly fall in this realm. To give some concrete examples, we are currently looking at the design of optimal monitoring policies, leveraging the use of information technology and enterprise resource planning systems to dynamically learn and evaluate the operational status and performance of a borrower. Relatedly, we are also looking at questions of how dynamic operational decisions (such as inventory replenishment, production processes, pricing) can be impacted by financial milestones or bonus incentives. In a different project, we are looking at how the long-term design and management of loyalty and reward programs is influenced by marketing, operational, but also financial and accounting considerations. Finally, in a separate project, we study the impact of climate risk on the design of long-term contracts, including financial subsidies and/or other incentives for the adoption of sustainable practices in coffee and wool supply chains. In addition to these problems, I also intend to pursue several methodological questions, relating primarily to the development of specialized, computationally tractable and data-driven tools for the design of robust long-term contractual agreements.\\[10pt]

\begin{center}
  {\Large Teaching Statement}
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  My primary teaching responsibilities have involved the MBA classes on ``Optimization and Simulation Modeling'' (OIT 245 and OIT 247), which I have taught jointly with my colleague, Kostas Bimpikis. In addition, I have also developed and taught a new PhD class on the theory of inventory management (OIT 624), offered in alternate years. I briefly discuss both of these below.

  OIT 245 and OIT 247 are part of the foundational requirement for our first-year MBA students. Both courses teach basic skills for developing structured, quantitative models suitable for business decision making. Topics include basic optimization (linear, discrete, non-linear), as well as Monte-Carlo simulation and sensitivity analysis, all taught in a spreadsheet environment (currently, Microsoft Excel). Traditionally, both courses were offered during the first half of the winter quarter, in a very compact format (9 class sessions, of 145 minutes each), and consisted primarily of lecturing, coupled with some in-class exercises conducted on students' laptops. 

  During the past three years of teaching the class, Kostas and I have considerably reshaped both the content, as well as the way in which these two classes are taught. As such, I developed six mini-cases that we currently use to illustrate applications of linear (discrete) optimization, and, in conjunction with Kostas, gradually proceeded to eliminate or substantially rewrite most of the other mini-cases, with the goal of showcasing more modern application areas of optimization and simulation.\footnote{In particular, I developed mini-cases on: online advertising (``Marine Weekly'', 2012, reviewed in 2014), restaurant operations (``Impromptu'', 2012), optimizing family financials (``Family Financial Plan'', 2014), determining optimal diets (``Optimal Diet Problem'', 2014), rebalancing portfolios under transaction costs (``Portfolio Management'', 2014), store expansion and dual-channel operations (``Whole Wallet'', 2014), and helped write a mini-case on optimal sourcing and pricing for a coffee roasting business (``Starbucks Minicase'', 2013-2014).} 

During 2013, we also started exploring the use of educational technology, primarily with the goal of gradually ``flipping'' the classroom model. Initially, we simply developed several videos that students could watch, either in preparation for class or to revisit concepts taught in class. Given the success of the videos, coupled with feedback from the students, I decided to explore an entirely different class format during winter 2014, moving away from a tiered classroom to a lab environment (i.e., the RAIL classroom, B312). Consequently, I also shifted the in-class focus away from lecturing, and more towards hands-on exercises, conducted in teams of two, under the supervision of the teaching staff. The class preparation was also reduced (students would be required to watch videos or read short hand-outs, and turn in weekly assignments), and the new format allowed me to ensure that weaker students are able to follow the material, while at the same time keeping more advanced students engaged.\footnote{All teams would be required to fill out a shared Google sheet, allowing me to track real-time performance and help teams that were falling behind, while also reserving 20-30 minutes at the end of class to discuss the solution and the ``general lessons''.} The new format seemed to work quite well, and we are currently implementing the same method across all sections of OIT 245-247.

In the near future, I intend to continue experimenting with new educational techniques and paradigms (e.g., peer evaluations, a more quantitative assignment of team composition, depending on students' backgrounds and progress, etc.), with the goal of making learning more fun and engaging, but also more effective. Furthermore, in terms of new material, I believe there is considerable scope for developing more classes on quantitative modeling. Over the past 2-3 iterations of OIT 245/247, I have been consistently faced with questions from students concerning follow-up options, only to point them to classes taught outside the GSB, and not entirely suited to their needs. Of key note is an advanced elective class, combining optimization and simulation modeling with ideas from the Data \& Decisions classes (OIT 265/267). This new class could cover some new methodological tools (e.g., simple optimization under uncertainty, which we currently cannot teach in OIT 245/247 given the timing of OIT 265/267), while devoting enough class time for projects that revolve around data-driven analytical tools to address real-world problems. Such a class would align our curriculum well with the growing focus (in industry, and academia) on business analytics, while also addressing a gap in the current offerings. Another potential offering in the MBA curriculum would be an advanced elective, focusing on the interplay between operational decisions and financial/accounting considerations. HBS currently offers such a class, and I believe this could be well tied with my own research agenda.

In terms of PhD teaching, two years ago I offered a new class on (the theory of) inventory management. I intend to offer the same class in the winter quarter of 2014, with a slightly changed format, devoting roughly half the class to lecturing on traditional models and theory, and the second half to new directions (both in methodology, but also in applications). I would also like to offer a new PhD class on optimization methods, which would be better suited to PhD students in a business school. Topics would include both fundamentals (linear and nonlinear optimization, duality concepts, KKT, combinatorial optimization), but also new topics (such as conic/semidefinite, polynomial or robust optimization), and would cover theoretical, as well as computational and implementation issues. 

{\color{blue} {\it Not to be included:}
\begin{enumerate}
\item ``Optimality of Affine Policies in Multi-stage Robust Optimization,'' D. Bertsimas, D. A. Iancu, and P. Parrilo. Mathematics of Operations Research, vol. 35, No. 2, pp. 363-394, 2010.
\item ``A Hierarchy of Near-Optimal Policies for Multi-stage Adaptive Optimization,'' D. Bertsimas, D. A. Iancu, and P. Parrilo. IEEE Transactions on Automatic Control, vol. 56, No. 12, pp. 2809-2824, 2011.
\item ``Supermodularity and Affine Policies in Dynamic Robust Optimization,'' D. A. Iancu, M. Sharma, and M. Sviridenko, Operations Research, vol. 61, No. 4, pp. 941-956, 2013.
\item ``Pareto Efficiency in Robust Optimization,'' D. A. Iancu and N. Trichakis, Management Science, vol. 60, No. 1, pp. 130-147, 2014.
\item ``Tight Approximations of Dynamic Risk Measures,'' D. A. Iancu, M. Petrik, and D. Subramanian, Forthcoming in Mathematics of Operations Research.
\item ``Fairness and Efficiency in Multiportfolio Optimization,'' D. A. Iancu and N. Trichakis, Forthcoming in Operations Research.
\item ``Disruption Risk and Optimal Sourcing in Multi-tier Supply Networks,'' E. Ang, D. A. Iancu, and R. Swinney. Revise and Resubmit, Management Science.
\item ``Operationalizing Financial Covenants,'' D. A. Iancu, N. Trichakis, and G. Tsoukalas. Submitted to Management Science.
\item ``Dynamic Learning of Patient Response Rates: An Application to Treating Chronic Diseases,'' K. Bimpikis, M. Brandeau, D. A. Iancu, and D. Negoescu. Submitted to Management Science.
\item ``Long-Term Management of Loyalty and Reward Programs,'' S-Y. Chun, D. A. Iancu, and N. Trichakis.
\end{enumerate}
}



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