Data-Driven Multi-Product Inventory Management: Substitution Effects and Customer Choices

Abstract

This thesis studies the multi-product inventory problems with substitution effects. It is common for real-world retailers to sell multiple products simultaneously. When making replenishment decisions, in addition to the individual demand for each product, retailers also need to care about the demand interaction among products. Customers may choose another available product as a substitute before their leaving when the preferred product is out of stock. This phenomenon is called stockout-based substitution, and the goal of retailers is to maximize the total profit with the existence of such a phenomenon. Many of the research works related to substitution effects focus on analyzing the properties of optimal inventory management policies by assuming full demand information, including the distribution of random demand and the structure of customer choices known to the retailer. In contrast, we consider the case where such demand information can only be learned (estimated) from historical data. Our research goal is to develop data-driven algorithms for the multi-product inventory management problem with substitution and show their good performances both in theory and in practice with actual data. Two models are considered in Chapters 2 and 3, respectively. Both works belong to the area of offline learning.

In Chapter 2, we consider the case where unsatisfied demands due to stockout translate into a request for the other product at a probability. Besides the already complex multi-product inventory management problem involving substitutions, we face further challenges in the absence of knowledge regarding demand distributions and substitution probabilities. In their stead, all we can rely on are the historical sales data that are compromised by censoring and substitution effects. We develop a method that carefully screens the data and subjects the useful portion to a Kaplan-Meier type of estimation. Notably, a very effective estimation of the substitution probabilities is also developed. Using large deviation tools, we establish guaranteed convergence rates of our estimates on top of consistency. The precision in parameter estimates also translates into accuracy in replenishment decisions. For inventory management, we take advantage of a submodularity property to obtain an exact algorithm for the two-product case and a good heuristic for the general multi-product problem. Computational studies based on simulated and actual data confirm the merits of our approach.

In Chapter 3, we study the problem where substitutions are associated with product features. A rank-based choice model incorporating product feature information is employed to tackle this problem. Customer's choice is ascertained under an unknown and nonparametric score function by their preferences and product features. The challenge mainly comes from two aspects: the estimation of the choice structure and the optimization of inventory levels. To overcome this challenge, we develop a preference learning method for choice structure estimation, which relies on a reformulation of kernel regression with considering the structure of choice models. Dynamic programming is formulated to link the segregated individual choice behavior with the aggregated inventory ordering decision. A prescriptive optimum is obtained by applying recursion algorithms to an intuitive integration of preference learning with dynamic programming. Using the large deviation theory and partitioning estimates theories in statistical learning, we show consistency results for both the learning algorithm and optimal policy. Approximation strategies are employed to combat the issue of high dimensionality. The efficacy of the proposed framework and solutions is tested using synthetic and real data, and the results are promising.

Date of Award	5 Jun 2023
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Youhua Frank CHEN (Supervisor)