Two-staged patterns are often used in manufacturing industries to divide stock plates into rectangular items. A heuristic algorithm is presented to solve the rectangular two-dimensional single stock size cutting stock problem with two-staged patterns. It uses the column-generation method to...

The primary objective in the one-dimensional cutting stock problem is to minimize material cost. In real applications it is often necessary to consider auxiliary objectives, one of which is to reduce the number of different cutting patterns (setups). This paper first presents an integer linear...

A heuristic algorithm for the one-dimensional cutting stock problem with usable leftover (residual length) is presented. The algorithm consists of two procedures. The first is a linear programming procedure that fulfills the major portion of the item demand. The second is a sequential heuristic...

Three-staged guillotine patterns are widely used in the manufacturing industry to cut stock plates into rectangular items. The cutting cost often increases with the number of cuts required. This paper focuses on the rectangular two-dimensional cutting stock problem, where three-staged guillotine...

A heuristic approach for the two-dimensional bin-packing problem is proposed. The algorithm is based on the sequential heuristic procedure that generates each pattern to produce some items and repeats until all items are produced. Both guillotine and non-guillotine patterns can be used. Each...