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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.

In the last 10 years, there have been major advances in the average-case analysis of bin packing, scheduling and similar partitioning problems in one and two dimensions. These problems are drawn from important applications throughout industry, often under the name of stock cutting. This article briefly surveys many of the basic results, as well as the probabilistic methods used to obtain them. The impact of the research discussed here has been twofold. First, analysis has shown that heuristic solutions often perform extremely well on average and hence can be recommended in practice, even though worst-case behavior can be quite poor. Second, the techniques of applied probability that have developed for the analysis of bin packing have found application in completely different arenas, such as statistics and stochastic models.