Solving the cutting-stock problem by using the Sequential Quadratic Programming optimization method

In operations research, the cutting-stock problem is an important issue in the manufacturing of textile, leather, paper, ship building, and sheet metal industries. This problem arranges the specific profiles on the material with minimum material wasted. It can increase the utility rate and reduce the cost of the stock. For example in the leather industry, the stock has irregular profiles, and the base material may also be irregular when using the remainders of the last cut. In this paper, the problem is formulated as a constrained optimization problem and solved by the Sequential Quadratic Programming (SQP) method. A global optimization algorithm is also proposed to avoid the local minimum point, which is helpful for the multi-stock problem.