Solution to Solid Wood Board Cutting Stock Problem

Abstract

In the production process for wooden furniture, the raw material costs account for more than 50% of furniture costs, and the utilization rate of raw materials depends mainly on the layout scheme. Therefore, a reasonable layout is an important measure to reduce furniture costs. This paper investigates the solid wood board cutting stock problem (CSP) and establishes an optimization model, with the goal of the highest possible utilization rate for original boards. An ant colony-immune genetic algorithm (AC­IGA) is designed to solve this model. The solutions of the ant colony algorithm are used as the initial population of the immune genetic algorithm, and the optimal solution is obtained using the immune genetic algorithm after multiple iterations are transformed into the accumulation of global pheromones, which improves the search ability and ensures the solution quality. The layout process of the solid wood board is abstracted into the construction process of the solution. At the same time, in order to prevent premature convergence, several improved methods, such as a global pheromone hybrid update and adaptive crossover probability, are proposed. Comparative experiments are designed to verify the feasibility and effectiveness of the AC­IGA, and the experimental results show that the AC­IGA has better solution precision and global search ability compared with the ant colony algorithm (ACA), genetic algorithm (GA), grey wolf optimizer (GWO), and polar bear optimization (PBO). The utilization rate increased by more than 2.308%, which provides effective theoretical and methodological support for furniture enterprises to improve economic benefits.

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“…Second, timber transshipment is key to solving the "last mile" problem of raw materials from the source to wood furniture producers, hence the gross value of timber harvesting as an indicator [44]. In addition, current research indicates that raw material supply is supplemented by the production of manmade boards and the import of logs and sawn timber [45]. The details are presented in Table 1.…”

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“…In Tang et al (2021) , ACO is used together with the immune genetic algorithm to maximize the use of boards in the production process for wooden furniture. Also, they had to improve the pheromone update method in order to avoid the premature convergence.…”

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“…The elastic constant of wood and its solid wood composite material is the quantity that characterizes the elasticity of the material (Yi 1996;Wang et al 2014;Li et al 2016;Li et al 2020;Li et al 2021;Li et al 2021;Ponzo et al 2021). Many researchers have studied the mechanical properties of wood (Ma 1996;Zhou et al 2007;Cheng and Wang 2015;Wang et al 2019;Felice et al 2021), and static and dynamic methods have yielded results in testing its modulus of elasticity, shear modulus, and Poisson's ratio Wang et al 2016;Zahedi et al 2020;Li et al 2021a,b;Tang et al 2021;Wang and Ghanem 2021;Meng et al 2021;Zhou et al 2021). Many research studies used probabilistic methods to study the mechanical properties of materials (Fan and Shen 1992;Thomas 2003; Kumpenza et al 2018;Peng et al 2018; Wang and Roger 2021; Wang and Roger 2022).…”