A bi-integrated model for coupling lot-sizing and cutting-stock problems

TL;DR

This paper introduces a bi-integrated model combining lot-sizing and cutting-stock problems in papermaking, using heuristics to optimize production costs with significant improvements over existing strategies.

Contribution

The paper presents a novel integrated framework for the entire papermaking process, combining multiple optimization models with a heuristic solution approach.

Findings

Average cost reductions of 26.63% compared to other strategies

Effective heuristic using Simplex, column generation, and Relax-and-Fix techniques

Model behavior analyzed under various production scenarios

Abstract

In this paper, a framework that addresses the core of the papermaking process is proposed, starting from the production of jumbos and ending with the paper sheets used in daily life. The first phase of the process is modelled according to a lot-sizing problem, where the quantities of jumbos are determined in order to meet the demand of the entire chain. The second phase follows a one-dimensional cutting-stock formulation, where these jumbos are cut into smaller reels of predetermined lengths. Some of these are intended to fulfil a portfolio of orders, while others are used as raw material for the third phase of the process, when the reels are cut into sheets with specific dimensions and demands, following a two-dimensional cutting-stock problem. The model is called the Bi-Integrated Model, since it is composed of two integrated models. The heuristic method developed uses the Simplex Method with column generation for the two cutting-stock phases and applies the Relax-and-Fix technique to obtain the rounded-integer solution. Computational experiments comparing the solutions of the Bi-Integrated Model to other strategies of modelling the production process indicate average cost gains reaching 26.63%. Additional analyses of the model behaviour under several situations resulted in remarkable findings.