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 concepts---the 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 Order-Up-To Policy.
Abstract: We model how a judge schedules cases as a multi-armed bandit problem. The model indicates that a first-in-first-out (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. This result convinced six judges of the Roman Labor Court of Appeals---a court that exhibits increasing hazard rates---to switch from hearing-level FIFO to case-level FIFO. Tracking these judges for eight years, we estimate that our intervention decreased the average case duration by 12% and the probability of a decision being appealed to the Italian supreme court by 3.8%, relative to a 44-judge control sample.
Abstract: We model a manufacturer's and regulator's joint recall decisions as an asymmetric dynamic discrete choice game. In each quarter, the agents observe a product's defect reports and update their beliefs about its failure rate. The agents face an optimal stopping problem: they decide whether or not to recall the product. The agents trade off between current recall costs and future failure costs; they respond to these intertemporal costs with Markov-perfect equilibrium. We estimate our model with auto industry data comprising 14,124 recalls and 976,062 defect reports. We reverse-engineer the structural primitives that underlie our model: (i) the evolution of the failure rates, and (ii) the failure and recall cost parameters. Since our model is a regenerative process---a recall resets the future failure rate---we implement a myopic policy estimator to circumvent the curse of dimensionality. Our counterfactual study establishes that both agents initiate recalls to avoid future failures but not to preempt the other agent's anticipated recalls. Indeed, we find that the regulator's recalls have no significant deterrence effect on the manufacturers.
Abstract: We explore the effect of supply chain proximity on product quality by merging four independent data sources from the automotive industry, collecting: (i) auto component defect rates, (ii) upstream component factory locations, (iii) downstream assembly plant locations, and (iv) product-level links connecting the upstream and downstream factories. Combining these four datasets allows us to trace the flow of 27,807 products through 529 supplier factories and 275 assembly plants. We estimate that increasing the distance between an upstream component factory and a downstream plant by an order of magnitude increases the componentâ€™s expected defect rate by 3.9%. We also find that shorter inter-factory spans are associated with more rapid product quality improvements, and that supply chain distance is more detrimental to quality when automakers: (i) produce early generation models or (ii) high-end products, (iii) when they buy components with more complex configurations, or (iv) when they source from suppliers who invest relatively little in research and development. Abstract: Morton (1971) and Morton and Wecker (1977) show that the policy function of an infinite-horizon, ergodic Markov decision process converges strictly faster with repeated Bellman contractions than the value function does; they call this phenomenon strong convergence. I show that exploiting strong convergence accelerates the classic algorithms for estimating Markov decision processes and calculating Markov perfect equilibria. The speed increase is especially pronounced for high-frequency models, with negligible discounting between decision epochs. I argue that the economic utility of strong convergence extends beyond the two applications I have considered. Abstract: I present two algorithms for solving dynamic programs with exogenous variables: endogenous value iteration and endogenous policy iteration. These algorithms are like relative value iteration and relative policy iteration, except they discard the variation in the value function that depends only on the exogenous variables (this variation doesn't affect the policy function). My algorithms are always at least as fast as relative value iteration and relative policy iteration, and are strictly faster when the exogenous variables are more persistent than the endogenous variables. My algorithms are well-suited for models in which an economic agent responds quickly to a slowly evolving exogenous environment. |
Teaching |