Modeling and solution approaches for a one dimensional multi objective cutting problems

In this thesis, a one-dimensional cutting stock problem is studied. One of the main difficulties in formulating and solving mathematical models for one-dimensional cutting stock problems, is the use a set of cutting patterns as a parameter set. Since the total number of cutting patterns to be generated may be numerous, both the generation and the use of such a set, lead to computational difficulties in solution process. In this thesis, a new three-objective linear integer programming model that does not use a set of cutting patterns, is formulated. The objectives are related to the trim loss amount, the total number of different standard lengths used, and the production amount that exceeds the given demand for each cutting order. A solution algorithm for the presented mathematical model is given. Both the mathematical model and the solution algorithm are illustrated on test problems.