Solving a Hard Cutting Stock Problem by Machine Learning and Optimisation

Abstract

We are working with a company on a hard industrial optimisation problem: a version of the well-known Cutting Stock Problem in which a paper mill must cut rolls of paper following certain cutting patterns to meet customer demands. In our problem each roll to be cut may have a different size, the cutting patterns are semi-automated so that we have only indirect control over them via a list of continuous parameters called a request, and there are multiple mills each able to use only one request. We solve the problem using a combination of machine learning and optimisation techniques. First we approximate the distribution of cutting patterns via Monte Carlo simulation. Secondly we cover the distribution by applying a k-medoids algorithm. Thirdly we use the results to build an ILP model which is then solved.

Cutting uncertain stock and vehicle routing in a sustainability forestry harvesting problem

“…To calculate values, the ILP model was run only once with the sampled data. We would like to note that this "static" way of solving the problem is very similar to those in Prestwich et al (2015) and Dems et al (2017). However, real-life applications typically have associated uncertainty which it is unrealistic to ignore.…”

“…Furthermore, Dems et al (2017) only handle 16 cutting instructions, while we can handle several hundred. The other improvement of our technique over Dems et al (2017) and also Prestwich et al (2015) is that we address the dynamic on-line cutting process: we re-calculate targeted amounts and re-compute solutions at the end of each cutting stage. Moreover, these two previous works do not compare themselves with a previous and popular metaheuristic approach while we do (see Sect.…”

“…In this section, we explain the ILP model from Prestwich et al (2015) that handles the MSSCSP. We denote it as h( ⃗ d, ⃗ u, ⃗ c, K) and it is defined as follows:…”

An analytics-based heuristic decomposition of a bilevel multiple-follower cutting stock problem

“…A smaller evaluation using 8 blocks (Q = 8) with each block’s trees partitioned into a maximum of 4 different types of products was done in Prestwich et al. ( 2015 ). Results showed that the approach came to within of optimality bound (see Fig.…”