Logistics, Bin Packing

The name of the paper is solving one dimensional cutting stock problem with discrete demands and capacitated planning objective. Cutting stock problems are NP-hard problems and mentioned about what is NP-hard problems. One of classical NP-hard problems which could not be solved within the polynomial computation time is a cutting stock problem. Wongprakornkul and Charnsethikul said that the most powerful algorithm for solving linear problems with many columns is the column generation procedure and after they give some information about large size of the pattern in cutting stock problems. In the study, they proposed to approach; first one is column generation technique for searching effective cutting patterns with a mathematical model of one dimensional cutting stock problem with discrete random demands. Other approach is a heuristic method based on the first fit decreasing method. After that they compare the results of the solutions. They coded algorithms in C++ programming language and solved with same computer. After this information they explain the methodologies. For the mathematical programming with column generation technique, they made five assumptions and give notations with the mathematical model. They develop the following procedure for the column generation.

Fig. 1: Flow chart of column-generation procedure for the problem

They claimed that the column generation approach provides the nearly optimal solution but approach is not always attainable within the allowable time.

The proposed heuristic is based on first fit decreasing method of Bin Packing problem. They sorted items in such a way that the longer item is selected before others. The outline of the algorithm has been shown in following figure in the article.

Fig. 2: Flow chart of the heuristic for the problem

They compared the results. They made three scenarios for comparing the results and discovered that various retail items and choices of demands sometimes not related with the