Dmitriy A. Katz-Rogozhnikov

Asymptotic Optimality of Constant-Order Policies for Lost Sales Inventory Models with Large Lead Times

Lost sales inventory models with large lead times, which arise in many practical settings, are notoriously difficult to optimize due to the curse of dimensionality. In this paper, we show that when lead times are large, a very simple constant-order policy, first studied by Reiman, performs nearly optimally. The main insight of our work is that when the lead time is very large, such a significant amount of randomness is injected into the system between when an order for more inventory is placed and when the order is received, that “being smart” algorithmically provides almost no benefit. Our main proof technique combines a novel coupling for suprema of random walks with arguments from queueing theory.

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.

MCMC inference of the shape and variability of time-response signals

Signals in response to time-localized events of a common phenomenon tend to exhibit a common shape, but with variable time scale, amplitude, and delay across trials in many domains. We develop a new formulation to learn the common shape and variables from noisy signal samples with a Bayesian signal model and a Markov chain Monte Carlo inference scheme involving Gibbs sampling and independent Metropolis-Hastings. Our experiments with generated and real-world data show that the algorithm is robust to missing data, outperforms the existing approaches and produces easily interpretable outputs.

Multiplicative regression via constrained least squares

This paper considers multiplicative models for predicting a response variable as a product of predictor variables. In the ideal case of known model parameters, the minimum mean squared error predictor is derived and its performance is shown to be fundamentally limited by the magnitude of the multiplicative error component. For estimating model parameters from data, the methods of logarithmically-transformed ordinary least squares (OLS) and nonlinear least squares (NLS) are discussed. We then propose a constrained least squares (CLS) regression method that combines the NLS objective function with a constraint based on the OLS solution. In experiments on log-normal and gamma-distributed data, CLS yields significant improvements in mean squared prediction error by avoiding large errors in parameter estimates and better accommodating model mismatch. We also compare the performances of the regression methods using real-world health care usage data.

Toward Comprehensive Attribution of Healthcare Cost Changes

Health insurance companies wish to understand themain drivers behind changes in their costs to enable targeted and proactive management of their operations. This paper presents a comprehensive approach to cost change attribution that encompasses a range of factors represented in insurance transaction data, including medical procedures, healthcare provider characteristics, patient features, and geographic locations. To allow consideration of such a large number of features and their combinations, we combine feature selection, using regularization and significance testing, with a multiplicative model to account for the nonlinear nature of multi-morbidities. The proposed regression procedure also accommodates real-world aspects of the healthcare domain such as hierarchical relationships among factors and the insurers differing abilities to address different factors. We describe deployment of the method for a large health insurance company in the United States. Compared to the companys expert analysis on the same dataset, the proposedmethod offers multiple advantages: 1) a unified view of themost significant cost factors across all categories, 2) discovery of smaller-scale anomalous factors missed by the experts, 3) early identification of emerging factors before all claims have been processed, and 4) an efficient automated process that can save months of manual effort.