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Deep Learning for Perishable Inventory Systems with Human Knowledge

Xuan Liao, Zhenkang Peng, Ying Rong

TL;DR

This paper addresses perishable inventory with finite lifetime $K$ and random lead times, where both demand and lead-time primitives are unknown. It develops end-to-end learning policies guided by marginal cost accounting, introducing two designs: E2E-BB (fully black-box) and E2E-PIL (structure-guided PIL), with an ODA-based boosting variant E2E-BPIL. The key contribution is embedding inventory-theoretic structure into DL policies, leveraging a marginal-cost loss and a PIL-based architecture to reduce learning complexity under limited data. Empirical results on real beverage data and diverse synthetic scenarios show that E2E-PIL and especially E2E-BPIL consistently outperform E2E-BB and PTO-PB benchmarks, highlighting the value of combining human knowledge with deep learning for robust, data-efficient decision-making in complex perishable systems.

Abstract

Managing perishable products with limited lifetimes is a fundamental challenge in inventory management, as poor ordering decisions can quickly lead to stockouts or excessive waste. We study a perishable inventory system with random lead times in which both the demand process and the lead time distribution are unknown. We consider a practical setting where orders are placed using limited historical data together with observed covariates and current system states. To improve learning efficiency under limited data, we adopt a marginal cost accounting scheme that assigns each order a single lifetime cost and yields a unified loss function for end-to-end learning. This enables training a deep learning-based policy that maps observed covariates and system states directly to order quantities. We develop two end-to-end variants: a purely black-box approach that outputs order quantities directly (E2E-BB), and a structure-guided approach that embeds the projected inventory level (PIL) policy, capturing inventory effects through explicit computation rather than additional learning (E2E-PIL). We further show that the objective induced by E2E-PIL is homogeneous of degree one, enabling a boosting technique from operational data analytics (ODA) that yields an enhanced policy (E2E-BPIL). Experiments on synthetic and real data establish a robust performance ordering: E2E-BB is dominated by E2E-PIL, which is further improved by E2E-BPIL. Using an excess-risk decomposition, we show that embedding heuristic policy structure reduces effective model complexity and improves learning efficiency with only a modest loss of flexibility. More broadly, our results suggest that deep learning-based decision tools are more effective and robust when guided by human knowledge, highlighting the value of integrating advanced analytics with inventory theory.

Deep Learning for Perishable Inventory Systems with Human Knowledge

TL;DR

This paper addresses perishable inventory with finite lifetime and random lead times, where both demand and lead-time primitives are unknown. It develops end-to-end learning policies guided by marginal cost accounting, introducing two designs: E2E-BB (fully black-box) and E2E-PIL (structure-guided PIL), with an ODA-based boosting variant E2E-BPIL. The key contribution is embedding inventory-theoretic structure into DL policies, leveraging a marginal-cost loss and a PIL-based architecture to reduce learning complexity under limited data. Empirical results on real beverage data and diverse synthetic scenarios show that E2E-PIL and especially E2E-BPIL consistently outperform E2E-BB and PTO-PB benchmarks, highlighting the value of combining human knowledge with deep learning for robust, data-efficient decision-making in complex perishable systems.

Abstract

Managing perishable products with limited lifetimes is a fundamental challenge in inventory management, as poor ordering decisions can quickly lead to stockouts or excessive waste. We study a perishable inventory system with random lead times in which both the demand process and the lead time distribution are unknown. We consider a practical setting where orders are placed using limited historical data together with observed covariates and current system states. To improve learning efficiency under limited data, we adopt a marginal cost accounting scheme that assigns each order a single lifetime cost and yields a unified loss function for end-to-end learning. This enables training a deep learning-based policy that maps observed covariates and system states directly to order quantities. We develop two end-to-end variants: a purely black-box approach that outputs order quantities directly (E2E-BB), and a structure-guided approach that embeds the projected inventory level (PIL) policy, capturing inventory effects through explicit computation rather than additional learning (E2E-PIL). We further show that the objective induced by E2E-PIL is homogeneous of degree one, enabling a boosting technique from operational data analytics (ODA) that yields an enhanced policy (E2E-BPIL). Experiments on synthetic and real data establish a robust performance ordering: E2E-BB is dominated by E2E-PIL, which is further improved by E2E-BPIL. Using an excess-risk decomposition, we show that embedding heuristic policy structure reduces effective model complexity and improves learning efficiency with only a modest loss of flexibility. More broadly, our results suggest that deep learning-based decision tools are more effective and robust when guided by human knowledge, highlighting the value of integrating advanced analytics with inventory theory.
Paper Structure (38 sections, 4 theorems, 55 equations, 12 figures, 10 tables, 1 algorithm)

This paper contains 38 sections, 4 theorems, 55 equations, 12 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Problem Formulation
  4. The End-to-End Policy Learning
  5. Marginal Cost Accounting Scheme and the Loss Function
  6. Marginal Cost Accounting Scheme
  7. Marginal Cost as the Loss Function
  8. The E2E Black-Box Policy without Enforcing Inventory Policy Structure
  9. The E2E Projected Inventory Level Policy
  10. The Projected Inventory Level Policy
  11. Embed the Projected Inventory Level Structure into the Network
  12. The Boosted E2E Projected Inventory Level Policy
  13. Numerical Study
  14. Primary Investigation based on a Real-World Dataset
  15. Data Description and Performance Metric
  16. ...and 23 more sections

Key Result

Proposition 1

The total cost $C(\{D_t\}_{t=1}^T,\{q^\pi_m\}_{m=1}^M)$ is homogeneous of degree $1$. That is, for any demand sequence $\{D_t\}_{t=1}^T$, any policy $\pi$ with decision sequence $\{q_m^\pi\}_{m=1}^M$, and for any $\gamma \in \mathbb R_+$, we have

Figures (12)

  • Figure 1: The deep neural network architecture of the E2E-BB policy.
  • Figure 2: The deep neural network architecture of the E2E-PIL policy.
  • Figure 3: Relative gap of all other policies against $\pi^{\text{E2E-BPIL}}$ in real-world data across different problem settings.
  • Figure 4: Boxplot of the average costs of all policies in synthetic data (SCR setting) across different problem settings.
  • Figure 5: The change of order quantities with remaining life time for both the E2E-BB (blue line, cross marker) and E2E-PIL (orange line, point marker) policy.
  • ...and 7 more figures

Theorems & Definitions (7)

  • Proposition 1
  • Lemma 1
  • Definition 1
  • Definition 2
  • Lemma 2
  • Proposition 2
  • Example 1