Assistant Professor of Business Administration
Joel Goh is an assistant professor of business administration in the Technology and Operations Management Unit, teaching the Technology and Operations course in the MBA required curriculum. He graduated with a PhD in Operations, Information, and Technology from the Stanford Graduate School of Business. In his research, he focuses on developing mathematical models that can provide insights into medical decision-making and recommendations for health policy. He has built models for detecting drug-related adverse events using health claims data, models to estimate the effect that workplace stressors have on health outcomes and costs, and models for assessing the effect of uncertainty in cost-effectiveness analyses for medical technology innovation. He has also made methodological contributions in the field of Operations Research, specifically in the areas of robust optimization and supply chain management. He is the co-creator of ROME (Robust Optimization Made Easy), a freely-distributed software for modeling robust optimization problems.
Total Cost Control in Project Management via Satisficing
We consider projects with uncertain activity times and the possibility of expediting, or crashing, them. Activity times come from a partially specified distribution within a family of distributions. This family is described by one or more of the following details about the uncertainties: support, mean, and covariance. We allow correlation between past and future activity time performance across activities. Our objective considers total completion time penalty plus crashing and overhead costs. We develop a robust optimization model that uses a conditional value-at-risk satisficing measure. We develop linear and piecewise-linear decision rules for activity start time and crashing decisions. These rules are designed to perform robustly against all possible scenarios of activity time uncertainty, when implemented in either static or rolling horizon mode. We compare our procedures against the previously available Program Evaluation and Review Technique and Monte Carlo simulation procedures. Our computational studies show that, relative to previous approaches, our crashing policies provide both a higher level of performance, i.e., higher success rates and lower budget overruns, and substantial robustness to activity time distributions. The relative advantages and information requirements of the static and rolling horizon implementations are discussed.
Keywords: project management;
time and cost control;
linear decision rule;
Robust Optimization Made Easy with ROME
We introduce ROME, an algebraic modeling toolbox for a class of robust optimization problems. ROME serves as an intermediate layer between the modeler and optimization solver engines, allowing modelers to express robust optimization problems in a mathematically meaningful way. In this paper, we discuss how ROME can be used to model (1) a service-constrained robust inventory management problem, (2) a project-crashing problem, and (3) a robust portfolio optimization problem. Through these modeling examples, we highlight the key features of ROME that allow it to expedite the modeling and subsequent numerical analysis of robust optimization problems. ROME is freely distributed for academic use at http://www.robustopt.com.
Keywords: robust optimization;
algebraic modeling toolbox;
Distributionally Robust Optimization and Its Tractable Approximations
In this paper we focus on a linear optimization problem with uncertainties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an approximate solution to the problem that is distributionally robust and more flexible than the standard technique of using linear rules. Our framework begins by first affinely extending the set of primitive uncertainties to generate new linear decision rules of larger dimensions and is therefore more flexible. Next, we develop new piecewise-linear decision rules that allow a more flexible reformulation of the original problem. The reformulated problem will generally contain terms with expectations on the positive parts of the recourse variables. Finally, we convert the uncertain linear program into a deterministic convex program by constructing distributionally robust bounds on these expectations. These bounds are constructed by first using different pieces of information on the distribution of the underlying uncertainties to develop separate bounds and next integrating them into a combined bound that is better than each of the individual bounds.