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Stochastic Optimization of Inventory at Large-scale Supply Chains

Zhaoyang Larry Jin, Mehdi Maasoumy, Yimin Liu, Zeshi Zheng, Zizhuo Ren

TL;DR

This work reframes inventory management in large-scale supply chains as a constrained stochastic optimization problem solvable within an MPC framework. By integrating forward-looking simulations with an uncertainty-aware, data-driven search for reorder parameters, the approach delivers robust reductions in inventory and safety-stock costs while preserving service levels, and it scales to enterprise-level SKUs via the C3 AI Suite. Key contributions include a detailed stochastic model of demand and supply uncertainties, a k-iteration procedure to adapt safety stock dynamically, and a practical deployment pipeline that couples with legacy MRP systems. The method demonstrates substantial operational impact (10–35% inventory reductions) and broad applicability across industries, enabling lean, resilient supply chains without sacrificing service reliability.

Abstract

Today's global supply chains face growing challenges due to rapidly changing market conditions, increased network complexity and inter-dependency, and dynamic uncertainties in supply, demand, and other factors. To combat these challenges, organizations employ Material Requirements Planning (MRP) software solutions to set inventory stock buffers - for raw materials, work-in-process goods, and finished products - to help them meet customer service levels. However, holding excess inventory further complicates operations and can lock up millions of dollars of capital that could be otherwise deployed. Furthermore, most commercially available MRP solutions fall short in considering uncertainties and do not result in optimal solutions for modern enterprises. At C3 AI, we fundamentally reformulate the inventory management problem as a constrained stochastic optimization. We then propose a simulation-optimization framework that minimizes inventory and related costs while maintaining desired service levels. The framework's goal is to find the optimal reorder parameters that minimize costs subject to a pre-defined service-level constraint and all other real-world operational constraints. These optimal reorder parameters can be fed back into an MRP system to drive optimal order placement, or used to place optimal orders directly. This approach has proven successful in reducing inventory levels by 10-35 percent, resulting in hundreds of millions of dollars of economic benefit for major enterprises at a global scale.

Stochastic Optimization of Inventory at Large-scale Supply Chains

TL;DR

This work reframes inventory management in large-scale supply chains as a constrained stochastic optimization problem solvable within an MPC framework. By integrating forward-looking simulations with an uncertainty-aware, data-driven search for reorder parameters, the approach delivers robust reductions in inventory and safety-stock costs while preserving service levels, and it scales to enterprise-level SKUs via the C3 AI Suite. Key contributions include a detailed stochastic model of demand and supply uncertainties, a k-iteration procedure to adapt safety stock dynamically, and a practical deployment pipeline that couples with legacy MRP systems. The method demonstrates substantial operational impact (10–35% inventory reductions) and broad applicability across industries, enabling lean, resilient supply chains without sacrificing service reliability.

Abstract

Today's global supply chains face growing challenges due to rapidly changing market conditions, increased network complexity and inter-dependency, and dynamic uncertainties in supply, demand, and other factors. To combat these challenges, organizations employ Material Requirements Planning (MRP) software solutions to set inventory stock buffers - for raw materials, work-in-process goods, and finished products - to help them meet customer service levels. However, holding excess inventory further complicates operations and can lock up millions of dollars of capital that could be otherwise deployed. Furthermore, most commercially available MRP solutions fall short in considering uncertainties and do not result in optimal solutions for modern enterprises. At C3 AI, we fundamentally reformulate the inventory management problem as a constrained stochastic optimization. We then propose a simulation-optimization framework that minimizes inventory and related costs while maintaining desired service levels. The framework's goal is to find the optimal reorder parameters that minimize costs subject to a pre-defined service-level constraint and all other real-world operational constraints. These optimal reorder parameters can be fed back into an MRP system to drive optimal order placement, or used to place optimal orders directly. This approach has proven successful in reducing inventory levels by 10-35 percent, resulting in hundreds of millions of dollars of economic benefit for major enterprises at a global scale.

Paper Structure

This paper contains 25 sections, 34 equations, 24 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Problem formulation
  5. Algorithm overview
  6. Inventory simulation with MRP
  7. Safety Stock MRP
  8. Order cancellation
  9. Modeling of the uncertainties
  10. Optimization of the hyper-parameters
  11. Forward-looking simulations
  12. The k-iteration algorithm
  13. Other algorithm treatments
  14. Batched uncertainty realizations with MRP
  15. "Steady-state" initial inventory
  16. ...and 10 more sections

Figures (24)

  • Figure 1: Common issues in manufacturing ranging from suppliers to customers
  • Figure 2: MRP follows a deterministic logic to place orders based on demand forecast, current day inventory, planning calendar, order parameters and previously scheduled arrivals (ELT: expedited lead time, LT: lead time, PTF: planning time fence)
  • Figure 3: Workflow of the C3 AI Stochastic Inventory Optimization algorithm
  • Figure 4: Comparison of high versus low service level percentiles
  • Figure 5: Safety time percentile is the percentile on the supplier time uncertainty
  • ...and 19 more figures