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...

Circular pieces are often cut from stainless steel roll to make common commodities such as pots and cups. The related factories are often make-to-order ones. The stock rolls usually have the same width. Each working order requires pieces of the same size. Pieces of different sizes cannot appear...

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...

Three-staged cutting patterns are often used in dividing large plates into small rectangular items. Vertical cuts separate the plate into segments in the first stage, horizontal cuts split each segment into strips in the second stage, and vertical cuts divide each strip into items in the third...