Abstract
In paper production, a jumbo reel is cut into multiple intermediate rolls, and each intermediate roll is then sheeted as finished goods. This problem is called a cutting stock problem and is proven to be NP-hard. The objective is to minimize material waste or trim loss from all the cuttings. In the case that any intermediate roll is not entirely used for its associated order, the intermediate roll itself could turn to be a dead stock. We use the concept of universal sizes of intermediate rolls to eliminate the dead stock. A pre-defined number of universal sizes of intermediate rolls is to be used to serve all the orders. The problem is solved using Reinforcement Artificial Bee Colony algorithm with Integer Linear Programming subroutine. This proposed approach is then tested with a set of 1,055 orders and 127 different sizes of sheet papers from a paper manufacturer. The results reveal that our method outperforms other algorithms. Our method offers the total trim loss of 3.51%, compared to the trim loss reported by the industry of at least 5%. This approach not only reduces the number of partially cut rolls, but also decreases the number of the jumbo reels needed to serve all the orders. Therefore, both the inventory cost and material cost can be saved.
Highlights
To produce sheets of paper, the process typically starts from cutting large reels of paper stock—called jumbo reels— into smaller intermediate rolls of various widths on a cutting machine called winder
To evaluate the performance of the proposed method, we compare the quality of the solutions obtained from the R-Artificial Bee Colony (ABC) algorithm [29], [30] with those from the ABC algorithm [35] and two state-of-the-art ABC algorithms, which are aABC [17] and TMABC [18], as well as the randomly generating solutions
The code for ABC and R-ABC was provided by the original authors, whereas that of aABC and TMABC was rewritten based on published literature
Summary
To produce sheets of paper, the process typically starts from cutting large reels of paper stock—called jumbo reels— into smaller intermediate rolls of various widths on a cutting machine called winder. A common objective of paper cutting operations is to determine cutting patterns that minimize material waste or trim loss at both the winders and the sheet cutters while satisfying various sizes of paper sheets demanded by the customers. This type of problem is called the cutting stock problem which is among the most extensively studied problems due to its wide range of applications and possible extensions [1], [2]. A huge number of possible patterns makes this problem prohibitive to solve to optimality [3], and the problem is known to be NP-hard [4], [5].
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