📚 Documentation

Technical overview of the Inventory Quantum system

Overview

Inventory Quantum is a research-grade inventory optimization system combining:

  • Temporal Fusion Transformer (TFT) - Google's state-of-the-art forecasting model
  • Conformal Prediction - Distribution-free uncertainty quantification
  • QAOA - Quantum Approximate Optimization Algorithm simulation
  • Conservative Q-Learning - Offline reinforcement learning

Data Requirements

The system adapts to available features. Minimum required:

Column Type Required Description
date Date ✓ Date of observation (YYYY-MM-DD)
sku String ✓ Product identifier
quantity_sold Integer ✓ Units sold
quantity_on_hand Integer Current inventory level
price Float Unit price
lead_time_days Integer Supplier lead time
holding_cost Float Cost per unit per period
ordering_cost Float Fixed cost per order
promotion Binary Promotion indicator (0/1)
category String Product category
region String Geographic region

Note: More features = higher accuracy. System gracefully degrades with missing features.

Forecasting Methods

Temporal Fusion Transformer (TFT)

Key components:

  • Variable Selection Network (VSN) - Learns feature importance automatically
  • Gated Residual Network (GRN) - Flexible nonlinear transformations
  • Multi-Head Attention - Interpretable temporal patterns
  • Quantile Regression - Probabilistic outputs

Conformal Prediction

Provides guaranteed coverage: P(Y ∈ [L, U]) ≥ 1 - α

  • Split Conformal - Simple calibration-based
  • CQR - Conformalized Quantile Regression
  • Adaptive - Adjusts for non-exchangeable data

Optimization

QUBO Formulation

Inventory decisions are encoded as Quadratic Unconstrained Binary Optimization problems:

min xTQx where x ∈ {0,1}n

Binary encoding allows for exact order quantities using positional representation.

QAOA

Variational quantum algorithm with classical optimization loop:

  1. Initialize in superposition |+⟩⊗n
  2. Apply cost unitary UC(γ) = exp(-iγC)
  3. Apply mixer unitary UM(β) = exp(-iβB)
  4. Measure and optimize (γ, β) classically

Drift Detection

Detection methods that work without ground truth labels:

  • PSI - Population Stability Index for binned distributions
  • KS Test - Kolmogorov-Smirnov for continuous distributions
  • JS Divergence - Jensen-Shannon for symmetric comparison

References

  1. Lim et al. (2021) - Temporal Fusion Transformers
  2. Romano et al. (2019) - Conformalized Quantile Regression
  3. Farhi et al. (2014) - QAOA
  4. Kumar et al. (2020) - Conservative Q-Learning