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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.

E ven though epidemiological evidence links specific workplace stressors to health outcomes, the aggregate contribution of these factors to overall mortality and health spending in the United States is not known. In this paper, we build a model to estimate the excess mortality and incremental health expenditures associated with exposure to the following 10 workplace stressors: unemployment, lack of health insurance, exposure to shift work, long working hours, job insecurity, work-family conflict, low job control, high job demands, low social support at work, and low organizational justice. Our model uses input parameters obtained from publicly accessible data sources. We estimated health spending from the Medical Expenditure Panel Survey and joint probabilities of workplace exposures from the General Social Survey, and we conducted a meta-analysis of the epidemiological literature to estimate the relative risks of poor health outcomes associated with exposure to these stressors. The model was designed to overcome limitations with using inputs from multiple data sources. Specifically, the model separately derives optimistic and conservative estimates of the effect of multiple workplace exposures on health, and uses optimization to calculate upper and lower bounds around each estimate, which accounts for the correlation between exposures. We find that more than 120,000 deaths per year and approximately 5%-8% of annual healthcare costs are associated with and may be attributable to how U.S. companies manage their work forces. Our results suggest that more attention should be paid to management practices as important contributors to health outcomes and costs in the United States.

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