Real time multiple-grade cutting stock optimization using adaptive fuzzy and recursive algorithms

In the production of commodities there exist many instances of cutting processes whereby decisions have to be made on how the cuts can be performed optimally. In other words, the question arises that " in what sequence should cutting o f a workpiece into smaller items be conducted so that the raw material used is minimized?" This is often synonymous to generating the "minimum waste". In its simplest form, this is referred to as the Classical One-dimensional Cutting Stock Problem or Classical 1D-CSP, for which very effective solutions for static off-line cases exist. The 1D-CSP is present in such industries as steel, apparel, paper, wood and food. A cut sequence is commonly referred to as a pattern. A n investigation into 1D-CSP reveals that many patterns or combinations must be evaluated before an optimal solution is found. Further, the number of such combinations dramatically rises with the number of problem parameters and operational features, making the solution computationally extensive. For this reason, beyond the classical 1D-CSP and in particular when real time online applications are involved, developing practical optimization solutions is a major challenge. In a high volume wood product manufacturing plant encountered in this research, a major production phase involves online inspection o f wood strips, for removing defects and quality grading, and subsequent chopping of the useful pieces to build up the inventory needed for the product on orders received. Specifically, the production line is to use wood as a defect-sensitive raw material, make decisions one strip at a time, deal with all non-identical pieces, use multiple grades of wood, cut strips to pieces, and at the same time satisfy objectives such as meeting customer due dates and generating least waste. This turns out to be is a complex case of dynamic 1D-CSP and a new solution approach needs to be instigated. In this work, in an attempt to develop an effective optimization tool, a mathematical formulation for an exact solution with multiple material grades is derived and it is demonstrated that even for small problems the computational times are prohibitive for online applications. Hence, an adaptive fuzzy algorithm is developed and tested which is able to produce results comparable to the exact solution for C S P . This fuzzy algorithm is then integrated with an innovative recursive pattern generation module into an optimization algorithm for real time problem. The combined optimization structure is examined with various objective functions, constraints and input data, and results are discussed. It is concluded that the developed optimization approach has an excellent performance and can adapt itself to extreme variations in raw material quality and most of all is applicable to real time decision-making.