Reducing uncertainty in operational problems

Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2016.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 205-207).Motivated by several core operational applications, we introduce a class of multistage stochastic optimization models that capture a fundamental tradeoff between performing work under uncertainty (exploitation) and investing resources to reduce the uncertainty in the decision making (exploration/testing). Unlike existing models, in which the exploration-exploitation tradeoffs typically relate to learning the underlying distributions, the models we introduce assume a known probabilistic characterization of the uncertainty, and focus on the tradeoff of learning exact realizations. In the first part of the thesis (Chapter 2), we study a class of scheduling problems that capture common settings in service environments in which the service provider must serve a collection of jobs that have a-priori uncertain processing times and priorities (modeled as weights). In addition, the service provider must decide how to dynamically allocate capacity between processing jobs and testing jobs to learn more about their respective processing times and weights. We obtain structural results of optimal policies that provide managerial insights, efficient optimal and near-optimal algorithms, and quantification of the value of testing. In the second part of the thesis (Chapter 3), we generalize the model introduced in the first part by studying how to prioritize testing when jobs have different uncertainties. We model difference in uncertainties using the convex order, a general relation between distributions, which implies that the variance of one distribution is higher than the variance of the other distribution. Using an analysis based on the concept of mean preserving local spread, we show that the structure of the optimal policy generalizes that of the initial model where jobs were homogeneous and had equal weights. Finally, in the third part of the thesis (Chapter 4), we study a broad class of stochastic combinatorial optimization that can be formulated as Linear Programs whose objective coefficients are random variables that can be tested, and whose constraint polyhedron has the structure of a polymatroid. We characterize the optimal policy and show that similar types of policies optimally govern testing decisions in this setting as well.by Yaron Shaposhnik.Ph. D

Mining Optimal Policies: A Pattern Recognition Approach to Model Analysis

This project spawned from an admission control problem we were working on for a major hospital in the Boston area. We tried to incorporate various aspects of the problem in a model, which resulted in a complex optimization problem that was difficult to solve analytically. Although numerical solutions could be computed, we were looking for insights to characterize simple policies that could be used in practice. We then came up with the idea of using machine learning to analyze solutions as a mean for obtaining such insights, an idea we thought could be interesting by itself. The motivating problem is an ongoing separate work

Scheduling with Testing

We study a new class of scheduling problems that capture common settings in service environments, in which one has to serve a collection of jobs that have a priori uncertain attributes (e.g., processing times and priorities) and the service provider has to decide how to dynamically allocate resources (e.g., people, equipment, and time) between testing (diagnosing) jobs to learn more about their respective uncertain attributes and processing jobs. The former could inform future decisions, but could delay the service time for other jobs, while the latter directly advances the processing of the jobs but requires making decisions under uncertainty. Through novel analysis we obtain surprising structural results of optimal policies that provide operational managerial insights, efficient optimal and near-optimal algorithms, and quantification of the value of testing. We believe that our approach will lead to further research to explore this important practical trade-off