# A Reinforcement Learning Approach to the Stochastic Cutting Stock Problem

arXiv: https://arxiv.org/abs/2109.09592 · HTML: https://mlsanity.com/paper/2109.09592/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 47 references that are in the map.
- First posted on arXiv 20 Sep 2021.

## Builds on (most cited first, 2 of 2)

- [Deep Reinforcement Learning for Robotic Manipulation with Asynchronous Off-Policy Updates](https://mlsanity.com/paper/1610.00633/) (2016)
- [Approximate Dynamic Programming for Planning a Ride-Sharing System using Autonomous Fleets of Electric Vehicles](https://mlsanity.com/paper/1810.08124/) (2018)

## Built on by (most cited first, 1 of 1)

- [Deep reinforcement learning for the dynamic vehicle dispatching problem: An event-based approach](https://mlsanity.com/paper/2307.07508/) (2023)

## Abstract (arXiv)

We propose a formulation of the stochastic cutting stock problem as a discounted infinite-horizon Markov decision process. At each decision epoch, given current inventory of items, an agent chooses in which patterns to cut objects in stock in anticipation of the unknown demand. An optimal solution corresponds to a policy that associates each state with a decision and minimizes the expected total cost. Since exact algorithms scale exponentially with the state-space dimension, we develop a heuristic solution approach based on reinforcement learning. We propose an approximate policy iteration algorithm in which we apply a linear model to approximate the action-value function of a policy. Policy evaluation is performed by solving the projected Bellman equation from a sample of state transitions, decisions and costs obtained by simulation. Due to the large decision space, policy improvement is performed via the cross-entropy method. Computational experiments are carried out with the use of realistic data to illustrate the application of the algorithm. Heuristic policies obtained with polynomial and Fourier basis functions are compared with myopic and random policies. Results indicate the possibility of obtaining policies capable of adequately controlling inventories with an average cost up to 80% lower than the cost obtained by a myopic policy.