A Heuristic Approach for Two-Dimensional Rectangular Cutting Stock Problem considering Balance for Material Utilization and Cutting Complexity

The common staged patterns are always required during the cutting process for separating a set of rectangular items from rectangular plates in manufacturing industries. Two-staged patterns can reduce cutting complexity at the expense of material utilization; three-staged patterns do the opposite. Combining these two types of staged patterns may be a good balance for two contradictory objectives of material utilization and cutting complexity. A heuristic approach is proposed to solve the two-dimensional rectangular cutting stock problem with a combination of two-staged general patterns (2SGP) and three-staged homogenous patterns (3SHP). Firstly, the 2SGP and 3SHP are constructed by using recursive techniques. The pattern with the larger value is selected as the candidate pattern. Then, the value of each item is corrected according to the current candidate pattern. A cutting plan accurately satisfying all items demand is obtained by using the sequential heuristic algorithm. Finally, the cutting plan with a minimum number of used plates is achieved by applying the iterative algorithm. The computational results indicate that the proposed heuristic approach is more effective in material utilization and cutting complexity than the two published algorithms with staged patterns.

Manufacturing-oriented silicon steel coil lengthwise cutting stock problem with useable leftover

PurposeThis paper propose an algorithm for the multiple silicon steel coils multiperiod two-dimensional lengthwise cutting stock problem (m2DLCSP), so as to minimize the total cost of materials and production.Design/methodology/approachThe authors propose a sequential leftovers utilization correction (SLUC) algorithm for the m2DLCSP. The algorithm primarily considers three optimization strategies. First, it considers usable leftovers to simplify the cutting process and improve material utilization. The total quantity and types of leftovers should be limited in order to avoid leftover overstock. Second, it uses a splice method of items to improve the generated cutting plan. Third, it takes into account operational restrictions in the cutting operations. Operational restrictions include imposing maximum and minimum lengths on the cutting patterns, and the limitation of cutting knives at the slitting machines.FindingsSeveral sets of benchmark with real-world and randomly generated instances are provided to evaluate the algorithm. Compared with literature algorithm and current procedure applied in enterprises, the computational results indicate that proposed algorithm can effectively reduce the total cost, and the computation time is reasonable for practical use.Social implicationsThis algorithm can effectively reduce the total cost.Originality/valueThe proposed method can effectively applied to solve the m2DLCSP and improve the economic efficiency of enterprises.

Solution to Solid Wood Board Cutting Stock Problem

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 (AC-IGA) 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 AC-IGA, and the experimental results show that the AC-IGA 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.

Analysis of cutting stock problem metaheuristic algorithms

The analysis of cutting stock problem and heuristic and metaheuristic algorithms for solving it are presented in this paper.

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

This paper presents a new class of multiple-follower bilevel problems and a heuristic approach to solving them. In this new class of problems, the followers may be nonlinear, do not share constraints or variables, and are at most weakly constrained. This allows the leader variables to be partitioned among the followers. We show that current approaches for solving multiple-follower problems are unsuitable for our new class of problems and instead we propose a novel analytics-based heuristic decomposition approach. This approach uses Monte Carlo simulation and k-medoids clustering to reduce the bilevel problem to a single level, which can then be solved using integer programming techniques. The examples presented show that our approach produces better solutions and scales up better than the other approaches in the literature. Furthermore, for large problems, we combine our approach with the use of self-organising maps in place of k-medoids clustering, which significantly reduces the clustering times. Finally, we apply our approach to a real-life cutting stock problem. Here a forest harvesting problem is reformulated as a multiple-follower bilevel problem and solved using our approach.