Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Deep Generative Demand Learning for Newsvendor and Pricing

Shijin Gong, Huihang Liu, Xinyu Zhang

TL;DR

A novel approach leveraging conditional deep generative models (cDGMs) to address data-driven inventory and pricing decisions in the feature-based newsvendor problem, where demand is influenced by both price and contextual features and is modeled without any structural assumptions.

Abstract

We consider data-driven inventory and pricing decisions in the feature-based newsvendor problem, where demand is influenced by both price and contextual features and is modeled without any structural assumptions. The unknown demand distribution results in a challenging conditional stochastic optimization problem, further complicated by decision-dependent uncertainty and the integration of features. Inspired by recent advances in deep generative learning, we propose a novel approach leveraging conditional deep generative models (cDGMs) to address these challenges. cDGMs learn the demand distribution and generate probabilistic demand forecasts conditioned on price and features. This generative approach enables accurate profit estimation and supports the design of algorithms for two key objectives: (1) optimizing inventory for arbitrary prices, and (2) jointly determining optimal pricing and inventory levels. We provide theoretical guarantees for our approach, including the consistency of profit estimation and convergence of our decisions to the optimal solution. Extensive simulations-ranging from simple to complex scenarios, including one involving textual features-and a real-world case study demonstrate the effectiveness of our approach. Our method opens a new paradigm in management science and operations research, is adaptable to extensions of the newsvendor and pricing problems, and holds potential for solving other conditional stochastic optimization problems.

Deep Generative Demand Learning for Newsvendor and Pricing

TL;DR

A novel approach leveraging conditional deep generative models (cDGMs) to address data-driven inventory and pricing decisions in the feature-based newsvendor problem, where demand is influenced by both price and contextual features and is modeled without any structural assumptions.

Abstract

We consider data-driven inventory and pricing decisions in the feature-based newsvendor problem, where demand is influenced by both price and contextual features and is modeled without any structural assumptions. The unknown demand distribution results in a challenging conditional stochastic optimization problem, further complicated by decision-dependent uncertainty and the integration of features. Inspired by recent advances in deep generative learning, we propose a novel approach leveraging conditional deep generative models (cDGMs) to address these challenges. cDGMs learn the demand distribution and generate probabilistic demand forecasts conditioned on price and features. This generative approach enables accurate profit estimation and supports the design of algorithms for two key objectives: (1) optimizing inventory for arbitrary prices, and (2) jointly determining optimal pricing and inventory levels. We provide theoretical guarantees for our approach, including the consistency of profit estimation and convergence of our decisions to the optimal solution. Extensive simulations-ranging from simple to complex scenarios, including one involving textual features-and a real-world case study demonstrate the effectiveness of our approach. Our method opens a new paradigm in management science and operations research, is adaptable to extensions of the newsvendor and pricing problems, and holds potential for solving other conditional stochastic optimization problems.

Paper Structure

This paper contains 38 sections, 8 theorems, 49 equations, 6 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Feature-based newsvendor
  4. Joint Inventory and Pricing Decisions
  5. Deep Generative Models
  6. Organization
  7. Preliminaries: Newsvendor Problem
  8. Basic Newsvendor
  9. Feature-Based Newsvendor
  10. Feature-based Newsvendor and Pricing Problem
  11. Demand Modeling with Features and Price
  12. Feature-Based Newsvendor with Arbitrary Prices
  13. Sample Average Approximation (SAA).
  14. Empirical Risk Minimization (ERM).
  15. Kernel-Weights Optimization (KO).
  16. ...and 23 more sections

Key Result

proposition 1

For any $(\mathbf{x}, p, q) \in \mathcal{X} \times \mathcal{P} \times \mathbb{R}^+$, with equality only if $D | (\mathbf{X} = \mathbf{x}, P = p)$ is a degenerate distribution.

Figures (6)

  • Figure 1: The contour plot of $\pi(x,p,q^*(\hbox{\bf x},p))$ for model (a) in Example \ref{['example:2']} across Feature $\hbox{\bf x}$ and Price $p$ with a red line indicating the optimal pricing path for maximum profit.
  • Figure 2: Examples of cDGMs and the Decision Making Procedure
  • Figure 3: Inventory Results for DGP (c)
  • Figure 4: Inventory Results for (d)
  • Figure 5: Visualization of price versus demand for meal ID 1558 in different centers
  • ...and 1 more figures

Theorems & Definitions (8)

  • proposition 1
  • lemma 1
  • proposition 2
  • proposition 3
  • theorem 1
  • theorem 2
  • theorem 3
  • corollary 1