In This Issue
Clinician Decision Support Models for Monitoring Glaucoma Patients
In managing chronic diseases, the timing of successive examinations is important to patients’ outcomes and the cost of care. In “Dynamic Forecasting and Control Algorithms of Glaucoma Progression for Clinician Decision Support,” J. Helm, M. Lavieri, M. Van Oyen, J. Stein, and D. Musch integrate a dynamic, stochastic state space system model of disease evolution with novel optimization approaches. Their methods optimize the question of when to take tests to monitor each glaucoma patient based on individual disease state information that is learned through a series of noisy medical tests. The authors develop closed form solutions and study structural properties of their algorithm. Based on data from large scale clinical trials, the authors show that these personalized methods significantly outperform current practice by achieving greater accuracy in identifying progression with fewer examinations. The methodology is applicable to other chronic diseases with implications for cost and quality of chronic disease care.
Mechanism Design by Automatically Searching within a Parametric Family, and Application to Revenue-Maximizing Combinatorial Auctions
In “Automated Design of Revenue-Maximizing Combinatorial Auctions,” T. Sandholm and A. Likhodedov introduce an automated approach to mechanism design via searching within a parametric family of mechanisms, all of which satisfy incentive properties. They apply it to designing revenue-maximizing combinatorial auctions (CAs)—an important elusive problem that is open even for just two items for sale. They introduce a family based on bidder weighting and allocation boosting: virtual valuations combinatorial auctions (VVCAs). VVCAs are the VCG mechanism executed on virtual valuations that are affine transformations of the bidders’ valuations. They also study the broader family of affine maximizer auctions. The paper first constructs VVCAs with logarithmic approximation guarantees in canonical special settings: (1) limited supply with additive valuations and (2) unlimited supply. The main part of the paper develops algorithms for designing high-revenue CAs for general valuations using samples from the prior. The algorithms created mechanisms that yield significantly higher revenue than the VCG and scale dramatically better than prior automated mechanism design approaches. They yielded deterministic mechanisms with the highest known revenues for the settings tested, including the canonical setting with two bidders, two items, and uniform additive valuations.
Theory of Unbiased Estimation with Biased Samplers and its Application in Finance
In mathematical finance, continuous-time modeling is widely used, and stochastic differential equations (SDEs) arise frequently as a means of modeling the underlying processes in financial markets. While stochastic simulation has become a popular tool for computations—derivative pricing, hedging, model calibration, etc.—the numerical simulation of such models has historically relied on discrete approximations of SDEs. These approximations are biased, and the presence of this bias can greatly inhibit the convergence rate of such simulation-based algorithms. In “Unbiased Estimation with Square Root Convergence for SDE Models,” C.-H. Rhee and P. W. Glynn develop a general theory for creating unbiased estimators from biased samplers and achieving optimal performance with the new estimators. Applying this general theory to the SDE context, they produce unbiased estimators for SDEs and achieve a square root convergence rate, the best convergence rate one can expect from simulation estimator.
Optimal Government Debt Portfolio and Payments, Debt Aversion, and Exchange Rates
Governments in many countries have been reducing their proportion of foreign currency in their debt portfolio. Surprisingly, this trend has been taken place in a context in which they have access to the international markets to issue debt in foreign currencies. In “Government Debt Control: Optimal Currency Portfolio and Payments,” R. Huamán-Aguilar and A. Cadenillas build a stochastic control model to study the optimal currency portfolio and payments for government debt. First, they derive a realistic stochastic dynamics for government debt. Then, they obtain the optimal policies for currency portfolio and payments explicitly. They find that debt aversion and jumps in the exchange rates reduce the optimal proportion of foreign currency in the government debt portfolio. In addition, they show that for a government with extreme debt aversion it is optimal not to issue debt in foreign currencies.
Efficient Learning of Price Impact
Impact of trades on the market price of assets, called price impact, is responsible for a large fraction of transaction costs and thus it is important to design trading strategies that effectively manage it. However, it is known to be elusive to estimate and requires retuning over time due to continual evolution of trading venues, regulations and population of market participants. In “Adaptive Execution: Exploration and Learning of Price Impact,” B. Park and B. Van Roy develop an algorithm that learns a price impact model while guiding trading decisions to maximize risk-adjusted profits using the model being learned. The algorithm balances the short-term costs of accelerated learning against the long term benefits of an accurate model. The authors establish a finite-time regret bound that exhibits a poly-logarithmic dependence on time and demonstrate via Monte Carlo simulation that the algorithm dramatically outperforms benchmark algorithms.
Regression Methods for the Efficient Risk Estimation
The estimation of risk in complex derivative portfolios is a challenging problem. In fact, risk-related computations are the single largest computational burden for many large financial institutions. Standard techniques involve nested simulation, where future scenarios are first sampled and then, within each scenario, additional sampling is performed to value the portfolio. In “Risk Estimation via Regression,” M. Broadie, Y. Du, and C. Moallemi suggest a novel alternative based on regression. Intuitively, regression combines combine coarse information about portfolio losses across different scenarios into a good approximation of the portfolio loss function, which can then be used to construct an estimate of risk. They establish that the regression method converges at a faster rate than nested simulation until reaching an asymptotic bias level, which depends on the quality of the regression model. Numerical results in practical examples demonstrate the advantage of the regression method over other approaches.
Integration of Material and Financial Flows in Supply Chains
When financial markets are imperfect, operations and financial decisions cannot be decoupled. This view is supported by an observation that many multi-divisional supply chain firms experienced a significant increase on their intra-group financial transactions during the recent financial crisis. In the supply chain literature, the discussion of integrating material and financial flows is relatively sparse. In “Joint Inventory and Cash Management for Multidivisional Supply Chains,” W. Luo and K. Shang incorporate cash flows into a supply chain model. They investigate the value of financial integration by comparing systems with different levels of financial integration. They obtain the optimal control policy for systems under cash pooling and a lower bound cost for systems under transfer pricing. Their study characterizes the conditions under which a fully integrated system, i.e., the cash pooling system, is most beneficial. They also introduce an important concept of system working capital to manage the supply chain in this study.
Meeting Consumption Targets Dynamically
It is well documented that target attainment is an important concern for managers in decision making processes. In the paper “On Dynamic Decision Making to Meet Consumption Targets,” L. G. Chen, D. Z. Long, and M. Sim propose a dynamic decision criterion to evaluate the prospect of a consumption profile in achieving consumption targets over time. If borrowing and saving are unrestricted, they show that in a finite horizon, the optimal policy that optimizes the criterion is to finance consumption at the target level for all periods except the last. For convex dynamic decision problems, the optimal policies correspond to those that optimize an expected additive utility. Through the choice of targets, the proposed approach determines the weights and parameters of the utility functions by solving an optimization problem.
Merchant Commodity Storage Practice
The valuation of commodity storage contracts as real options is an important practical problem. Commodity storage merchants use various heuristics for this purpose. In “Commodity Storage Practice Revisited,” N. Secomandi considers two such heuristics that are available in commercial software and have been observed to be near optimal in prior work. He provides theoretical support and numerical evidence for this performance, also emphasizing when one heuristic performs better than the other. He also proposes dual bounds to assess the quality of merchant commodity storage heuristics, which are simpler to implement than known dual bounds for this problem but equally effective. These bounds are particularly pertinent to the developers and users of the two studied heuristics.
Creating Better Alternatives
Operations research uses analysis to provide information and insights about the pros and cons of alternatives to help organizations and individuals make better decisions. However, the selected alternative can be no better than the best of the available alternatives. In “Creating More and Better Alternatives for Decisions Using Objectives,” J. Siebert and R. Keeney indicate for decisions where many alternatives are not readily apparent, creating alternatives has a high potential value. They investigate the decision of how operations researchers can best help decision-makers create better alternatives. In experiments, individuals facing important personal decisions are shown to omit at least half of the best alternatives when asked to list their available alternatives. Using the objectives of decision-makers to stimulate their thought processes can often identify alternatives subsequently identified as the best. An operational thought-provoking procedure for operations researchers to facilitate decision-makers in creating alternatives is presented.
A New Classes of Flexibility Structures
Process flexibility has been an important operational strategy to enable firms to better fulfill uncertain product demand. While most existing literature studies either average or worst-case performance of various flexibility structures, it is of interest to design a flexible structure, whose performance is more robust than average performance but less conservative than worst-case performance. In “Optimal Sparse Designs for Process Flexibility via Probabilistic Expanders,” X. Chen, J. Zhang and Y. Zhou introduce a new class of flexibility structures called probabilistic expanders. The authors show that such structures, even with very limited flexibility, perform almost as well as fully flexible structures for almost all demand realizations.
Solving Ranking-and-Selection Problems using Parallel Simulation
With the fast development of technology, parallel computing environments, from multi-core personal computers to many-core servers, from commercial cloud computing services to smart phones, are ubiquitous and easily accessible to ordinary users. In “Fully Sequential Procedures for Large-Scale Ranking-and-Selection Problems in Parallel Computing Environments,” J. Luo, L. J. Hong, B. L. Nelson and Y. Wu consider how to use parallel computing to solve traditional ranking-and-selection problems effectively and efficiently. In particular, they use a queueing analogy to show that statistical issues may arise if one simply implements existing fully sequential procedures on multiple processors. They then propose two types of procedures, called the Vector Filling Procedure and the Asymptotic Parallel Selection Procedure, which are statistically valid and computationally efficient in parallel computing environments. Extensive numerical experiments show that the proposed procedures can take advantage of multiple parallel processors to solve large-scale ranking-and-selection problems.
Handling Stochastic Constraints in Discrete Simulation Optimization
In discrete optimization via simulation (DOvS), stochastic constraints on secondary performance measures often exist and it makes finding an optimal feasible solution difficult when both objective and secondary performance measures need to be estimated by stochastic simulation. In “Penalty Function with Memory for Discrete Optimization via Simulation with Stochastic Constraints,” C. Park and S.-H. Kim develop a new method called the Penalty Function with Memory (PFM). It is similar to an existing penalty-type method but uses a different penalty parameter, called a penalty sequence, determined by the past history of feasibility checks on a solution. Specifically, assuming a minimization problem, a penalty sequence diverges to infinity for any infeasible solution but converges to zero for any feasible solution under certain conditions. As a result, a DOvS algorithm combined with PFM performs well even when an optimal feasible solution is a boundary solution with one or more active constraints.
Better Admission Control Requires Ample Predictive Information
Predictive models and forecasting methods are increasingly employed by system managers to improve operations, but how much predictive information is enough to achieve good performance? In “Necessity of Future Information in Admission Control,” K. Xu shows that a large amount of predictive information is necessary in order to significantly improve the delay performance in a certain queueing admission control system: unless the future arrivals and services are predicted sufficiently in advance, the average delay cannot be much smaller than that under a simple online threshold policy. Our impossibility result compliments the delay improvement reported in an earlier paper of Spencer et al. 2014, obtained by leveraging predictions. Together, they point to the existence of a critical threshold of predictive information, which is both sufficient and necessary for achieving good performance in this family of admission control problems.
Sequential Decision-Making in Changing Environments
Most methods that address sequential optimization problems have been developed under the assumption that the underlying environment, while unknown, is not changing over time. In “Non-stationary Stochastic Optimization,” O. Besbes, Y. Gur, and A. Zeevi consider a general, non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. They propose a measure, termed variation budget, that controls the extent of said change, and study how restrictions on this budget impact achievable performance, in terms of regret relative to the dynamic sequence of best actions. In doing so, a strong connection is established between two strands of literature: (adversarial) online convex optimization, and the more traditional stochastic approximation paradigm.
