Research Statement

Nowadays, companies in a variety of industries routinely make use of analytical tools geared towards simplifying day-to-day operations, by automating as many of the decisions as possible, from inventory planning and routing, to pricing, markdowns, ad spending, portfolio rebalancing, etc. In parallel, the information technology (IT) sector has been responding to the “analytics” trend with numerous acquisitions and consolidations, betting on the fact that the vast amounts of data and increased computational power can generate advanced solutions for key business problems.

While useful in simplifying routine processes, such solutions are nonetheless often limited in their scope, flexibility, and robustness. For instance, they often make unrealistic assumptions concerning the decision environment, using simplistic models of uncertainty, treating decisions in segregation, ignoring the existence of agency issues or alternative incentives, etc. Such simplifications are often a byproduct of pragmatism, sacrificing modeling realism for the sake of computational tractability.

The main focus of my research thus far has been on providing new ways for understanding and computing optimal decisions and strategies in complex operational settings, in ways that not only support decision-making, but also make models more pertinent for realistic, business problems.

Some of my early work has followed the paradigm of Robust Optimization (RO), a methodology developed mainly during the last 15 years to analyze and optimize the performance of complex systems.^{1} My work in this area has several components. In [4] and [7], I investigate several classical inventory management models under a robust objective, and show that a new class of ordering policies, which depend affinely on past-observed demands, is actually optimal. These policies are very intuitive, specifying a decomposition of orders into safety stocks and satisfaction of backlogged demand. The results are very relevant on a practical level, since they allow finding optimal policies by solving very simple (i.e., linear) optimization problems. This is the case even when traditional approaches for solving the corresponding dynamic problems, such as Dynamic Programming (DP), are intractable or prescribe overly complex policies. The same approach can be extended to more complex capacity planning problems, as well as the design of flexible retailer-supplier pre-commitment contracts. From a theoretical perspective, the results are the first of their kind, and the proof techniques are entirely novel, combining continuous and discrete optimization to construct the optimal strategy. In follow-up work in [6], I also examine more complex, multi-tier supply chains, where I show how a flexible hierarchy of asymptotically optimal replenishment policies can be computed by solving tractable optimization problems. The latter approach performs very well in simulation studies, and is attractive since the decision-maker can directly control, through a single parameter, the trade-off between performance and the amount of computation.

At the heart of the earlier results lies a key observation concerning the differences between decision making under severe uncertainty (i.e., RO) and decision making under exact distributional information. Namely, that the former setting generally admits multiple optimal policies, with simpler structure than the latter. While useful for dynamic policies, this degeneracy may also cause serious inefficiencies in the decision process. To this end, in [2], I introduce and formalize the concept of Pareto efficiency in RO. I show that decisions generated using RO need not have this property, and that particular algorithms/software used in RO problems are guaranteed to produce inefficient outcomes. I also provide a simple procedure to test whether a given solution is Pareto-efficient, and (if not) to generate such Pareto-efficient outcomes. The methodology is, in essence, a strict improvement of the RO framework, incurring no extra computational cost, and significantly reducing conservativeness.

1The framework has a long history in various disciplines (including economics, engineering, and statistics), and is built around the premise that an exact probability distribution is often unavailable in a decision process, due to, e.g., the lack of ample historical data or inherent non-stationarities. The standard approach is to assume that all unknown parameters belong to particular (suitable) uncertainty sets, and to seek decisions optimizing the worst-case performance among all possible outcomes.

Through recent developments in convex optimization, RO has emerged as an eminently tractable methodology for addressing real-world problems, with recent years witnessing an explosion of applications in management science.

Portfolio Management. Since the seminal work of Markowitz, multiple facets and extensions of this problem have been studied in the literature, and several software solutions now exist to guide trading decisions. An issue typically overlooked in most prior (implemented) models is the fact that a manager is usually in charge of several client accounts. In [1], I show 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 account being coupled with the trading strategies of other accounts. I propose a novel approach for jointly determining the trades and splitting the associated market impact costs across all the accounts. The 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.^{2}

In more recent work, I have also started examining several new issues that I believe are critical when developing operationally implementable solutions. The first is the role of agency issues, which I have explored in two classical operational contexts (sourcing in multi-tier supply chains [10], and inventory replenishment and liquidation under debt [8]). The second is the interplay between traditional operational decisions and financial, accounting or marketing considerations, which I have looked at in the context of financial covenants in inventory-based lending [8], as well as in ongoing research on dynamic pricing under debt [12] and the management of loyalty programs [11]. I briefly elaborate on some of these below.

Disruption Risks in Supply Chains. Despite extensive research in supply chain management, most models examining the contractual agreements in a complex supply chain typically ignore either the agency issues or the multi-tier structure of the chain (e.g., assuming a unique tier, of direct suppliers to a manufacturer). In [10], I discuss optimal sourcing decisions in a multi-tier chain, where the manufacturer is unable to directly dictate the sourcing decisions of its immediate Tier 1 suppliers (from a set of risky Tier 2 suppliers), but can influence their strategy through the contracts offered. I 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 or multisourcing in Tier 1), and more on indirect mitigation (paying larger prices, and inducing Tier 1 suppliers to mitigate risk). While the manufacturer always prefers less overlap, Tier 1 suppliers may prefer a different configuration; this results in a severe moral hazard problem, which cannot be mitigated through side payments, but can be alleviated through penalty contracts. I also show that, when the supply chain structure is unknown, sourcing according to a robust strategy can significantly reduce the manufacturer’s profit loss, particularly at low margins.

Financial Covenants in Inventory-based Lending. Classical papers focusing on operational decisions such as inventory replenishment or liquidation typically ignore the financing terms through which the inventory was purchased. In [8], I study the interplay between financial covenants and the operational decisions of a retailer who obtains financing through a secured (inventory-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. I show that retailers under debt manage inventory through riskier policies, involving surprising (non-threshold) behavior, and characterize the market conditions (involving demand distribution, growth potential, profit margin, inventory depreciation rate) under which covenants emerge as strictly necessary terms in lending agreements. I show that these conditions are routinely met in practice, and provide operational insights for the optimal design of covenants, arguing that additional operational flexibility can impact their effectiveness in a surprising, non-monotonic way.

In my active research, I am following up on several of these problems, with the dual goal of (a) developing a better understanding of the incentive mechanisms at play in complex operational settings, and (b) developing tractable and implementable decision support tools. To give some concrete examples, in [12], [15] and [16], I am currently looking at the design of optimal monitoring policies, leveraging the use of IT systems to dynamically learn the operational status and performance of a borrower. In [11] and [17], I am looking at how the long-term design and management of loyalty and reward programs and of contracts for ad display is influenced by marketing, operational, but also financial and accounting considerations. Finally, in [13], I study the impact of climate risk on the design of long-term contracts, including financial subsidies and other incentives for the adoption of sustainable practices in coffee and wool supply chains, and in [14] I look at policies for disaster relief in the Philippines, in the face of severe uncertainty (e.g., typhoon paths), and issues of equity in the availability of supplies. In addition to these problems, I also intend to pursue several methodological questions, related primarily to the development of specialized, computationally tractable, and data-driven tools for the design of robust long-term contractual agreements.

2Other related research, on which I do not elaborate for space reasons, includes [9], which develops optimal personalized treatments for chronic illnesses such as multiple sclerosis (through a quantitative model that explicitly uses all the channels available for acquiring information), as well as [3], which seeks to approximate a manager’s static risk preferences (that may be simpler to formulate) by dynamic risk measures (that are axiomatically justified and computationally tractable.

Teaching Statement

My primary teaching responsibilities have involved the MBA classes on “Optimization and Simulation Modeling” (OIT 245/247), taught jointly with my colleague, Kostas Bimpikis. In addition, I have also developed a new PhD class on inventory management (OIT 624), offered in alternate years.

During the past three years, Kostas and I have considerably reshaped the content, as well as the way in which OIT 245/247 are taught. As part of this effort, 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. During 2013, we also started exploring the use of educational technology, primarily with the goal of gradually “flipping” the classroom model. Initially, we developed videos that students could watch, either as preparation 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 watch videos or read short handouts, and turn in weekly assignments), and the new format allowed me to ensure that weaker students are able to follow the material, while keeping more advanced students engaged. The new format seemed to work quite well, and we are currently implementing it across all sections of OIT 245/247.

In the near future, I intend to continue experimenting with educational technology and new paradigms (e.g., peer evaluations, a quantitative assignment of team composition, depending on students’ backgrounds/progress, etc.), with the goal of making learning more fun and engaging, but also more effective. 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 245/7, I have been consistently faced with questions concerning follow-up options, only to point students to courses outside the GSB, and not entirely suited to their needs. Of key note is an advanced elective, combining optimization and simulation 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 around the use of data-driven analytical tools for 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.

In terms of PhD teaching, I intend to keep offering the class on inventory management, but in a slightly changed format, devoting half the class to traditional models and theory, and half to new directions for research. I would also like to offer a new PhD class on optimization methods, better suited to PhD students in a business school. Topics would include fundamentals (linear and nonlinear optimization, duality concepts, KKT, combinatorial optimization), but also new topics (such as conic, semidefinite, polynomial or robust optimization), covering theoretical, as well as computational and implementation issues.

Bibliography:

1. “Fairness and Efficiency in Multiportfolio Optimization,” D. A. Iancu and N. Trichakis, Forthcoming in Operations Research.

2. “Pareto Efficiency in Robust Optimization,” D. A. Iancu and N. Trichakis, Management Science, vol. 60, No. 1, pp. 130-147, 2014.

3. “Tight Approximations of Dynamic Risk Measures,” D. A. Iancu, M. Petrik, and D. Subramanian, Forthcoming in Mathematics of Operations Research.

4. “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.

5. “A General Purpose Local Search Algorithm for Binary Optimization,” D. Bertsimas, D. A. Iancu, and D. Katz-Rogozhnikov, INFORMS Journal on Computing, vol. 25, No. 2, pp. 208-221, 2013.

6. “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.

7. “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.

8. “Operationalizing Financial Covenants,” D. A. Iancu, N. Trichakis, and G. Tsoukalas. Submitted to Management Science.

9. “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.

10. “Disruption Risk and Optimal Sourcing in Multi-tier Supply Networks,” E. Ang, D. A. Iancu, and R. Swinney. Revise and Resubmit, Management Science.

11. “Long-Term Management of Loyalty and Reward Programs,” S-Y. Chun, D. A. Iancu, and N. Trichakis.

12. “Dynamic Pricing Under Financial Covenants,” O. Besbes, D. A. Iancu, and N. Trichakis.

13. “Sustainability, Climate Risk, and Optimal Sourcing in Coffee Supply Chains,” D. A. Iancu and Joann de Zegher.

14. “Planning for Disaster Recovery and Relief in the Philippines,” D. A. Iancu and J. Uichanco.

15. “Optimal Monitoring and Liquidation in Long-Term Debt Agreements,” D. A. Iancu, D.-Y. Yoon, and N. Trichakis.

16. “Robust Contracting and Revolver Management in Asset-Based Lending,” D. A. Iancu, S. Moazeni, and N. Trichakis.

17. “Optimal Growth Policies in Online Advertising,” D. A. Iancu, and J. Turner.

18. “Dynamic Pricing and Customer Choice in the Theater Industry,” S.-Y. Chun, D. A. Iancu, and Y. Yang.