Dynamic Inventory Control with Stockout Substitution and Demand Learning

Abstract

We consider an inventory control problem with multiple products and stockout substitution. The firm knows neither the primary demand distribution for each product nor the customers’ substitution probabilities between products a priori, and it needs to learn such information from sales data on the fly. One challenge in this problem is that the firm cannot distinguish between primary demand and substitution (overflow) demand from the sales data of any product, and lost sales are not observable. To circumvent these difficulties, we construct learning stages with each stage consisting of a cyclic exploration scheme and a benchmark exploration interval. The benchmark interval allows us to isolate the primary demand information from the sales data, and then this information is used against the sales data from the cyclic exploration intervals to estimate substitution probabilities. Because raising the inventory level helps obtain primary demand information but hinders substitution demand information, inventory decisions have to be carefully balanced to learn them together. We show that our learning algorithm admits a worst-case regret rate that (almost) matches the theoretical lower bound, and numerical experiments demonstrate that the algorithm performs very well. This paper was accepted by J. George Shanthikumar, big data analytics.

The First Half-Century of Decision Modelling for Substitutable Products: A Literature Review and Bibliographic Analysis

“…Kok and Fisher (2007) proposed an approach to modelling the assortment decisions in which the customer may buy a substitute in the event of unavailability of his/her favourite product. Chen and Plambeck (2008) proved that inventory levels can be reduced by incorporating the learnings of substitution probabilities in the demand model. Li and Ha (2008) studied how the reactive capacity can help reduce the deviation between the supply and uncertain demand in case of substitutable products.…”

“…Netessine and Rudi (2003) discussed an optimal stocking of substitutable products using a consumer-driven substitution model under competition for a random number of products. Chen and Plambeck (2008) suggested that the inventory level of substitutable products also affects the demand and buying behaviour and hence it is important to know the demand distribution and substitution pattern. Thus store footprint can be reduced and assortment can be downsized by estimating the substitution effects in a retail basket.…”

An efficient learning framework for multiproduct inventory systems with customer choices

“…To the best of our knowledge, B. Chen and Chao (2020) is the only paper that studies the joint learning and optimization of inventory control problem with stock‐out substitution. In B. Chen and Chao (2020), the authors considered a one‐time or a Markov‐chain‐based stock‐out substitution, in which the substitution behavior is specified by the substitution probabilities between each pair of product and demand. Furthermore, their algorithm has predetermined separated learning and earning cycles, and in the learning cycle the algorithm allocates dedicated periods to learn the substitution probabilities.…”

“…Note that the existing literature that mainly focuses on analyzing the structural properties and proposing efficient solution methods for the optimization problem. To the best of our knowledge, B. Chen and Chao (2020) is the only paper that studies the joint learning and optimization of inventory control problem with stock‐out substitution. In B. Chen and Chao (2020), the authors considered a one‐time or a Markov‐chain‐based stock‐out substitution, in which the substitution behavior is specified by the substitution probabilities between each pair of product and demand.…”

Data‐Driven Inventory Control with Shifting Demand

“…(2018), systems with fixed setup cost is studied in Yuan et al. (2019), inventory control with stockout substitution is considered in Chen and Plambeck (2008) and Chen and Chao (2020), the big data newsvendor model with feature information is studied in Ban and Rudin (2018), and learning in the dual sourcing inventory system is considered by Chen and Shi (2019). All of the studies here consider stationary environment, that is, the demand distribution stays the same throughout the planning horizon.…”