  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.
