We study the problem when a firm sets prices for products based on the transaction data, i.e., which product past customers chose from an assortment and what were the historical prices that they observed. Our approach does not impose a model on the distribution of the customers' valuations and only assumes, instead, that purchase choices satisfy incentive-compatible constraints. The individual valuation of each past customer can then be encoded as a polyhedral set, and our approach maximizes the worst-case revenue assuming that new customers' valuations are drawn from the empirical distribution implied by the collection of such polyhedra. We show that the optimal prices in this setting can be approximated at any arbitrary precision by solving a compact mixed-integer linear program. Moreover, we study the single-product case and relate it to the traditional model-based approach. We also design three approximation strategies that are of low computational complexity and interpretable. Comprehensive numerical studies based on synthetic and real data suggest that our pricing approach is uniquely beneficial when the historical data has a limited size or is susceptible to model misspecification.
We propose to use Deep Neural Networks to solve data-driven stochastic optimization problems. Given the historical data of the observed covariate, taken decision, and the realized cost in past periods, we train a neural network to predict the objective value as a function of the decision and the covariate. Once trained, for a given covariate, we optimize the neural network over the decision variable using gradient-based methods because the gradient and the Hessian matrix can be analytically computed. We characterize the performance of our methodology based the generalization bound of the neural network. We show strong performance on two signature problems in operations management, the newsvendor problem and the assortment pricing problem.
Piece-rate compensation schemes, where workers are paid for each completed task regardless of the time spent on it, are common in practice. Detecting a potential negative impact on firm performance associated with their use adds to the literature on the challenges of piece-rate compensation schemes. We study a radiology workflow platform that connects off-site radiologists with hospitals. These radiologists select tasks from a common pool, and the service level is characterized by meeting priority-specific turnaround time targets. However, imbalances between pay and workload of different tasks could result in higher priority tasks with low pay relative to workload receiving poorer service than low priority tasks. Using a large dataset, we investigate whether low-priority tasks with a high pay-to-workload ratio have a shorter turnaround time. Then, using the same approach, we investigate whether having many low-priority tasks with high pay-to-workload increases the turnaround time and probability of delay of higher priority tasks. We show that turnaround time is decreasing in pay-to-workload for lower priority tasks, whereas it is increasing in workload for high priority tasks. More importantly, we find evidence of a spillover effect: Having many economically attractive tasks with low priority can lead to longer turnaround times for higher priority tasks, increasing the likelihood that those tasks are delayed. Our results suggest that organizations, where workers have task discretion from a common pool, need to carefully align their piece-rate compensation scheme with the workload of each task. Imbalances may lead to a degradation in the system service level provided to time-sensitive customers.
Works Under Preparation:
1. Data-driven Bundle Pricing. With Ningyuan Chen, Andre Cire and Ming Hu (Target: Operations Research).