Matheuristic for the lot-sizing and scheduling problem in integrated pulp and paper production

Abstract

Vertical pulp and paper production is challenging from a process point of view. Managers must deal with floating bottlenecks, intermediate storage levels, and by-product production to control the whole process while reducing unexpected downtimes. Thus, this paper aims to address the integrated lot sizing and scheduling problem considering continuous digester production, multiple paper machines, and a chemical recovery line to treat by-products. The aim is to minimize the total production cost to meet customer demands, considering all productive resources and encouraging steam production (which can be used in power generation). Production planning should define the sizes of production lots, the sequence of paper types produced in each machine, and the digester working speed throughout the planning horizon. Furthermore, it should indicate the rate of by-product treatment at each stage of the recovery line and ensure the minimum and maximum storage limits. Due to the difficulty of exactly solving the mixed integer programming model representing this problem for real-world instances, mainly with planning horizons of over two weeks, constructive and improvement heuristics are proposed in this work. Different heuristic combinations are tested on hundreds of instances generated from data collected from the industry. Comparisons are made with a commercial Mixed-Integer and Linear Programming solver and a hybrid metaheuristic. The results show that combining the greedy constructive heuristic with the new variation of a fix-and-optimize improvement method delivers the best performance in both solution quality and computational time and effectively solves realistic size problems in practice. The proposed method achieved 69.41% of the best solutions for the generated set and 55.40% and 64.00% for the literature set for 1 and 2 machines, respectively, compared with the best solution method from the literature and a commercial solver.