Dan Andrei Iancu

Optimality of Affine Policies in Multistage Robust Optimization

In this paper, we prove the optimality of disturbance-affine control policies in the context of one-dimensional, constrained, multistage robust optimization. Our results cover the finite-horizon case, with minimax (worst-case) objective, and convex state costs plus linear control costs. We develop a new proof methodology, which explores the relationship between the geometrical properties of the feasible set of solutions and the structure of the objective function. Apart from providing an elegant and conceptually simple proof technique, the approach also entails very fast algorithms for the case of piecewise-affine state costs, which we explore in connection with a classical inventory management application.

A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization

In this paper, we propose a new tractable framework for dealing with linear dynamical systems affected by uncertainty, applicable to multistage robust optimization and stochastic programming. We introduce a hierarchy of near-optimal polynomial disturbance-feedback control policies, and show how these can be computed by solving a single semidefinite programming problem. The approach yields a hierarchy parameterized by a single variable (the degree of the polynomial policies), which controls the trade-off between the optimality gap and the computational requirements. We evaluate our framework in the context of three classical applications-two in inventory management, and one in robust regulation of an active suspension system-in which very strong numerical performance is exhibited, at relatively modest computational expense.

Supermodularity and Affine Policies in Dynamic Robust Optimization

This paper considers a particular class of dynamic robust optimization problems, where a large number of decisions must be made in the first stage, which consequently fix the constraints and cost structure underlying a one-dimensional, linear dynamical system. We seek to bridge two classical paradigms for solving such problems, namely, (1) dynamic programming (DP), and (2) policies parameterized in model uncertainties (also known as decision rules), obtained by solving tractable convex optimization problems. We show that if the uncertainty sets are integer sublattices of the unit hypercube, the DP value functions are convex and supermodular in the uncertain parameters, and a certain technical condition is satisfied, then decision rules that are affine in the uncertain parameters are optimal. We also derive conditions under which such rules can be obtained by optimizing simple (i.e., linear) objective functions over the uncertainty sets. Our results suggest new modeling paradigms for dynamic robust optimiz...

Optimality of affine policies in multi-stage robust optimization

In this paper, we prove the optimality of disturbance-affine control policies in the context of onedimensional, box-constrained, multi-stage robust optimization. Our results cover the finite horizon case, with minimax (worstcase) objective, and convex state costs plus linear control costs. Our proof methodology, based on techniques from polyhedral geometry, is elegant and conceptually simple, and entails efficient algorithms for the case of piecewise affine state costs, when computing the optimal affine policies can be done by solving a single linear program.

Disruption Risk and Optimal Sourcing in Multitier Supply Networks

We study sourcing in a supply chain with three levels: a manufacturer, tier 1 suppliers, and tier 2 suppliers prone to disruption from, e.g., natural disasters such as earthquakes or floods. The manufacturer may not directly dictate which tier 2 suppliers are used but may influence the sourcing decisions of tier 1 suppliers via contract parameters. The manufacturer’s optimal strategy depends critically on the degree of overlap in the supply chain: if tier 1 suppliers share tier 2 suppliers, resulting in a “diamond-shaped” supply chain, the manufacturer relies less on direct mitigation (procuring excess inventory and multisourcing in tier 1) and more on indirect mitigation (inducing tier 1 suppliers to mitigate disruption risk). We also show that while the manufacturer always prefers less overlap, tier 1 suppliers may prefer a more overlapped supply chain and hence may strategically choose to form a diamond-shaped supply chain. This preference conflict worsens as the manufacturer’s profit margin increases,...

Power generation management under time-varying power and demand conditions

A multi-period optimal power dispatching problem is considered for a network of energy utilities connected via multiple transmission lines, where the goal is to find the lowest operational-cost dispatching of diverse generation sources to satisfy demand over a time horizon comprised of multiple periods, and consisting of varying power and demand conditions. Our model captures various interactions among the time-varying periods including which generators should be allocated, when they should be brought into use, and the operational costs associated with each. An efficient algorithm is derived that exploits the structure inherent in this multi-period economic dispatch problem. The control options of our optimization model consist of the dispatching order and dispatching amount of available power generators. Our solutions are shown to be globally optimal under conditions that often arise in practice. Numerical experiments based on these solutions and analysis are presented to illustrate our findings.

A New Local Search Algorithm for Binary Optimization

We develop a new local search algorithm for binary optimization problems, whose complexity and performance are explicitly controlled by a parameter Q, measuring the depth of the local search neighborhood. We show that the algorithm is pseudo-polynomial for general cost vector c, and achieves a w2/2w-1 approximation guarantee for set packing problems with exactly w ones in each column of the constraint matrix A, when using Q = w2. Most importantly, we find that the method has practical promise on large, randomly generated instances of both set covering and set packing problems, as it delivers performance that is competitive with leading general-purpose optimization software CPLEX 11.2.

Is Operating Flexibility Harmful under Debt

We study the inefficiencies stemming from a firm’s operating flexibility under debt. We find that flexibility in replenishing or liquidating inventory, by providing risk-shifting incentives, could lead to borrowing costs that erase more than one-third of the firm’s value. In this context, we examine the effectiveness of practical and widely used covenants in restoring firm value by limiting such risk-shifting behavior. We find that simple financial covenants can fully restore value for a firm that possesses a midseason inventory liquidation option. In the presence of added flexibility in replenishing or partially liquidating inventory, financial covenants fail, but simple borrowing base covenants successfully restore firm value. Explicitly characterizing optimal covenant tightness for all these cases, we find that better market conditions, such as lower inventory depreciation rate, higher gross margins, or increased product demand, are typically associated with tighter covenants. Our results suggest that ...

Dynamic Learning of Patient Response Types: An Application to Treating Chronic Diseases

Currently available medication for treating many chronic diseases is often effective only for a subgroup of patients, and biomarkers accurately assessing whether an individual belongs to this subgroup typically do not exist. In such settings, physicians learn about the effectiveness of a drug primarily through experimentation, i.e., by initiating treatment and monitoring the patients response. Precise guidelines for discontinuing treatment are often lacking or left entirely to the physicians discretion. We introduce a framework for developing adaptive, personalized treatments for such chronic diseases. Our model is based on a continuous-time, multi-armed bandit setting where drug effectiveness is assessed by aggregating information from several channels: by continuously monitoring the state of the patient, but also by (not) observing the occurrence of particular infrequent health events, such as relapses or disease flare-ups. Recognizing that the timing and severity of such events provides critical information for treatment decisions is a key point of departure in our framework compared with typical (bandit) models used in healthcare. We show that the model can be analyzed in closed form for several settings of interest, resulting in optimal policies that are intuitive and may have practical appeal. We illustrate the effectiveness of the methodology by developing a set of efficient treatment policies for multiple sclerosis, which we then use to benchmark several existing treatment guidelines.

Fairness and Efficiency in Multiportfolio Optimization

We deal with the problem faced by a portfolio manager in charge of multiple accounts. We argue that because of market impact costs, this setting differs in several subtle ways from the classical single account case, with the key distinction being that the performance of each individual account typically depends on the trading strategies of other accounts, as well. We propose a novel, tractable approach for jointly optimizing the trading activities of all accounts and also splitting the associated market impact costs between the accounts. Our approach allows the manager to balance the conflicting objectives of maximizing the aggregate gains from joint optimization and distributing them across the accounts in an equitable way. We perform numerical studies that suggest that our approach outperforms existing methods employed in the industry or discussed in the literature.