1. Cutting-2D Problem Specification¶
This page introduces the problem we would like to address with a Deep Reinforcement Learning agent: an online version of the Guillotine 2D Cutting Stock Problem.
Description of Problem:
In each step there is one new incoming customer order generated according to a certain demand pattern.
This customer order has to be fulfilled by cutting the exact x/y-dimensions from a set of available candidate pieces in the inventory.
A new raw piece is transferred to the inventory every time the current raw piece in inventory is used to cut and deliver a customer order.
The goal is to use as few raw pieces as possible throughout the episode, which can be achieved by following a clever cutting policy.
Agent-Environment Interaction Loop:
To make the problem more explicit from an RL perspective we formulate it according to the agent-environment interaction loop shown below.
The State contains the dimensions of the currently pending customer orders and all pieces on inventory.
The Reward is specified to discourage the usage of raw inventory pieces.
The Action is a joint action consisting of the following components (see image below for details):
Action \(a_0\): Cutting piece selection (decides which piece from inventory to use for cutting)
Action \(a_1\): Cutting orientation selection (decides the orientation of the customer)
Action \(a_2\): Cutting order selection (decides which cut to take first; x or y)
Given this description of the problem we will now proceed with implementing a corresponding simulation.