Full-cut promotion is a type of promotion where customers spend a minimum threshold amount in a single order to enjoy a fixed amount of discount for that order. In this paper, we propose a sequential choice model to model consumer’s choice of multiple items in a single transaction, which generalizes the traditional choice model which assumes at most one item chosen in one transaction. Base on the sequential choice model, we further propose a data driven approach to optimize the cut amount. We test the approach using both synthetic data and a real transaction data set from an e-commerce company
We study a single-server appointment scheduling problem with a fixed sequence of appointments, for which we must determine the arrival time for each appointment. We specifically examine two stochastic models. In the first model, we assume that all appointees show up at the scheduled arrival times yet their service durations are random. In the second model, we assume that appointees have random no-show behaviors and their service durations are random given that they show up at the appointments. In both models, we assume that the probability distribution of the uncertain parameters is unknown but can be partially observed via a set of historical observations. In view of the distributional ambiguity, we propose a data-driven distributionally robust optimization approach to determine an appointment schedule such that the worst-case (i.e., maximum) expectation of the system total cost is minimized. A key feature of this approach is that the optimal value and the set of optimal schedules thus obtained provably converge to those of the “true” model, i.e., the stochastic appointment scheduling model with regard to the true probability distribution of the stochastic parameters. While the resulting optimization problems are computationally intractable, we reformulate them to copositive programs, which are amenable to tractable semidefinite programming problems with high-quality approximations. Furthermore, under some mild conditions, we reformulate the distributioanlly robust appointment scheduling problems to polynomial-sized linear programs. Through an extensive numerical study, we demonstrate that our approach yields better out-of-sample performance than two state-of-the-art methods.
joint work with Chung-Piaw Teo, Huan Zheng
Large-scale natural disaster management is among the top list of worldwide challenges. One of the difficulties faced is that minimal historical information is present for future disaster prediction and risk assessment, making it challenging to construct proper ambiguity sets. In our paper, we model the natural disaster as an adversary and adopt a game theoretical framework to characterize the interactions between the adversarial nature and a decision maker. We show that the interaction can be fully captured by a conic program in general and obtain a closed-form solution to a symmetric problem.