Mathematical models and solution approaches for two dimensional cutting and assortment problems

According to predefined demand list cutting smaller items from larger one or more dimensional stocks, by minimizing the number of used stock or trim loss is described as cutting stock problem. In this study we consider two-dimensional cutting stock and assortment problems under various assumptions and constraints. In order to solve two-dimensional two-stage guillotine cutting stock and assortment problem and two-dimensional cutting stock and assortment problem, two-objective mixed integer mathematical models are proposed. By formulating these problems two-objective, we minimize trim loss and also reduce storage costs, which we may have to deal with because of using different stock materials. Also for this problem, we propose metaheuristic methods that are proven as efficient in the literature. Some test problems are solved with biased random key genetic algorithm; simulated annealing and tabu search and we obtained optimal solutions for some of these problems. Finally for larger problems, a mixed integer mathematical model based two-phased heuristic method that aimed to obtain feasible solutions in a shorter time, has been developed.