Unequal individual genetic algorithm with intelligent diversification for the lot-scheduling problem in integrated mills using multiple-paper machines

Abstract

This paper addresses the lot-sizing and scheduling problem of pulp and paper mills involving multiple paper machines. The underlying multi-stage integrated production process considers the following critical units: continuous digester, intermediate stocks of pulp and liquor, multiple paper machines and a recovery line to treat by-products. This work presents a mixed integer programming (MIP) model to represent the problem, as well as a solution approach based on a customized genetic algorithm (GA) with an embedded residual linear programming model. Some GA tools are explored, including literature and new operators, a novel diversification process and other features. In particular, the diversification process uses a new allele frequency measure to change between diversification and intensification procedures. Computational results show the effectiveness of the method to solve relatively large instances of the single paper machine problem when compared to other single paper machine solution methods found in the literature. For multiple paper machine settings, in most runs the GA solutions are better than those obtained for the MIP model using an optimization software.

A Description of Supply Chain Planning Problems in the Paper Industry with Literature Review

“…Lot-sizing, scheduling, cutting stock, distribution and inventory planning are topics in several publications (Tables 5-9). Part of the researches contain integrated models covering more than one of the topics (Figueira et al, 2013(Figueira et al, , 2015Furlan et al, 2015;Geismar and Murthy, 2015;Keskinocak et al, 2002;Liu, 2014;Martel et al, 2005b;Santos and Almada-Lobo, 2012;Yin et al, 2003). Practical difficulties of embedding load planning into the models were addressed in none of the studies.…”

“…Both models consider the sequence dependency by including the grade change costs in the objective and the dependency in the restrictions. Furlan et al (2015) utilize genetic algorithms in a similar model.…”

A decision support system for the operational production planning and scheduling of an integrated pulp and paper mill

“…The proposed model was based on the general lot-sizing and scheduling problem (GLSP), presented by Fleischmann and Meyr (1997), and considered sequence dependent setup times and costs. Figueira et al (2013) then improved the resolution of the problem with a variable neighbourhood search, whereas Furlan et al (2015) developed a genetic algorithm for the multi-machine scenario.…”

Optimization Algorithm in Supply Chain Management

“…An enhanced approach of GA for optimization of production planning along with supplier selection taking into account flexibility of customer was presented by Cui [24]. In [35]a lot-scheduling problem was worked on using GA and in [22] a hybrid GA which combined features of random sampling search with GA was used to solve a scheduling problem.…”