Events & Seminars

Classical statistical learning distinguishes between offline learning and online learning. Motivated by the idea of bridging the gap between these two different types of learning tasks, this work investigates the impact of pre-existing offline data on the online learning in the context f a dynamic pricing problem. We consider a seller offering a single product with an infinite amount of inventory over a selling horizon. The demand in each period is determined by the price of the product according to a linear demand model with unknown parameters. We assume that the seller has some pre-existing offline data before the start of the selling horizon, and wants to utilize both the preexisting offline data and the sequentially-revealed online data to minimize the regret of the online learning process. We characterize the joint effect of the size, location and dispersion of the offline data on the optimal regret of the online learning. Our results reveal surprising transformations of the optimal regret rate with respect to the size of the offline data, which we refer to as phase transitions. In addition, our results also demonstrate that the location and dispersion of the offline data have an intrinsic effect on the optimal regret, which is quantified via the inverse-square law.

We consider the assortment optimization problem of a retailer who operates both a physical store and an online store. Products are described by their features and we capture the relationship between the products and the features with a tree. Non-leaf vertices correspond to features and leaf vertices correspond to products, so that the path from the root to a leaf describes the features that make up a product. A customer observes a feature if any product with that feature is offered in the physical store. A customer is either a physical store customer or an online store customer, and each customer chooses amongst the products offered in her respective store. However, an online store customer also visits the physical store to try out the products. The utilities of products in the online store are revised based on the features that an online customer sees in the physical store. The retailer offers the full assortment of products in the online store, and the goal is to find an assortment to offer in the physical store that maximizes the total expected revenue from both types of customers.

First, we consider the case with only online store customers, so that the physical store serves as a showroom for customers to try out products. We give an efficient algorithm to find the optimal assortment to display in the physical store. Second, we consider a mix of customers. The assortment optimization problem is NP-hard and we give a fully polynomial-time approximation scheme (FPTAS). Via numerical experiments, we demonstrate that our model can approximate the case where the products are arbitrary combinations of features without a tree structure and our FPTAS performs much better than its theoretical guarantee.

This is joint work with Professor Huseyin Topaloglu at Cornell University

3D printing, as a production technology, distinguishes from conventional technologies in three characteristics: design freedom, i.e., it can handle certain product designs that conventional technologies cannot; quality differentiation, i.e., for the same product design, it might achieve a different quality, higher or lower than that of conventional technologies; and natural flexibility, i.e., it is endowed with capacity flexibility without sacrificing operational efficiency. This paper investigates the joint impact of these characteristics when a firm selects conceptual designs to form its product assortment, taking into account each design's production technology choice from 3D printing and two conventional technologies: dedicated and traditional flexible. Some designs can be handled by any technology (generic), whereas the others are specific to 3D printing (3D-specific). The firm selects designs to be handled by each technology and then invests accordingly in technology adoption, product development, capacity, and production. We characterize the structure of the optimal assortment based on the popularity of each design. Within the sets of generic designs and 3D-specific designs, respectively, the most popular designs should be selected into the assortment; under a mild condition, the optimal assortment comprises the most popular ones among all the designs. Within the optimal assortment, 3D printing should handle the less popular generic designs than conventional technologies. We further demonstrate that a greater design freedom or higher quality of 3D printing may reduce product variety. In the absence of design freedom and quality differentiation, natural flexibility by itself always enhances product variety; by contrast, the traditional flexible technology may reduce product variety. Numerical study shows that 3D printing tends to be more valuable when popularities of the generic designs have a lower Gini index and when popularities of the 3D- specific designs have a higher Gini index.