Robert L. Bray 
Kellogg School of Management Research Interests Supply Chaining and Empirical Operations Management Curriculum Vitae 
Articles 
Abstract: This work distinguishes between two related conceptsthe bullwhip effect and production smoothing. These phenomena appear antithetical because they share opposing empirical tests: production variability exceeding sales variability for bullwhip, and vice versa for smoothing. But this is a false dichotomy. We differentiate between the two with a new production smoothing measure, which estimates how much more volatile production would be absent production volatility costs. We apply this metric to an automotive manufacturing sample comprising 162 car models. We find 75% of our sample smooths production by at least 5%, despite the fact that 99% exhibits the bullwhip effect; indeed, we estimate both a strong bullwhip (on average, production is 220% as variable as sales) and a strong degree of smoothing (on average, production would be 22% more variable without deliberate stabilization). We find firms smooth both production variability and production uncertainty. We measure production smoothing with a structural econometric production scheduling model, based on the Generalized OrderUpTo Policy.
Abstract: We model how a judge schedules cases as a multiarmed bandit problem. The model indicates that a firstinfirstout (FIFO) scheduling policy is optimal when the case completion hazard rate function is monotonic. But there are two ways to implement FIFO in this context: at the hearing level or at the case level. Our model indicates that the former policy, prioritizing the oldest hearing, is optimal when the case completion hazard rate function decreases, and the latter policy, prioritizing the oldest case, is optimal when the case completion hazard rate function increases. Citing this result, we convince six judges of the Roman Labor Court of Appealsa court that exhibits increasing hazard ratesto switch from hearinglevel FIFO to caselevel FIFO. Tracking these judges for eight years, we estimate that our intervention decreased their case flow times by 19% and the likelihood that their decisions were appealed to the Italian supreme court by 3.8%, relative to a 44 judge control sample.
Abstract: Most supply chain works suppose retailers can credibly communicate costs with suppliers. But honest cost disclosure can be untenable because operational costs are opaque and stores have incentives to inflate marginal costs to shift the inventory burden upstream: e.g., stores can reduce their stockout rates by exaggerating the goodwill lost to unsatisfied demand. Accordingly, suppliers may not receive truthful cost estimates, preventing them from identifying globally optimal inventory policies. We develop an empirical means to resolve this supply chain cheap talk problemto compel the supplier and retailer to coordinate optimally, even when the latter is selfserving and dishonest. Rather than ask a retailer for its private costs, we estimate them directly with a dynamic discrete choice inventory model. We illustrate our approach with a 5,320SKU, 1,371day sample from a Chinese supermarket. We estimate that the distribution center stocking out of the median product costs as much to a store as .03 shipments, .51 lost sales, or 37 days of storage.

Teaching 