A practical solution to a fuzzy two-dimensional cutting stock problem

An important implementation of the two-dimensional cutting stock problem is the application of cuttomer plate orders directly to surplus steel plates. In addition to the obvious desire to determine a high yield pattern, management is also interested in: (1) cutting few orders from a surplus plate (productivity reasons), (2) cutting mostly high priority orders from the plate (customer service considerations), and (3) cutting orders from a plate for as few distinct customers as possible (logistical concerns). This paper presents a problem formulation in a fuzzy environment which addresses the concerns listed above. Then, using α-cut sets, a sequence of crisp cutting stock problems are generated from the fuzzy formulation. A heuristic approach is developed to efficiently solve this sequence of problems. An example is solved to illustrate this approach which is used routinely at a Bethlehem Steel Corporation plant.