Abstract
This paper investigates the Score-Constrained Strip-Packing Problem (SCSPP), a combinatorial optimisation problem that generalises the one-dimensional bin-packing problem. In the construction of cardboard boxes, rectangular items are packed onto strips to be scored by knives prior to being folded. The order and orientation of the items on the strips determine whether the knives are able to score the items correctly. Initially, we detail an exact polynomial-time algorithm for finding a feasible alignment of items on a single strip. We then integrate this algorithm with a packing heuristic to address the multi-strip problem and compare with two other greedy heuristics, discussing the circumstances in which each method is superior.
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Notes
- 1.
Note that the left-hand score width of the first item and the right-hand score width of the last item on the strip are not adjacent to any other item, and can therefore be ignored.
- 2.
In the event of a tie, MBR selects the set with the lowest index.
- 3.
The average number of items per strip when \(n = 500\) for \(W = 5000\), 2500 and 1250 are 8.475, 4.310, and 2.165 respectively, and the average number of items per strip when \(n = 1000\) for \(W = 5000\), 2500 and 1250 are 8.621, 4.329, and 2.169 respectively.
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Hawa, A.L., Lewis, R., Thompson, J.M. (2018). Heuristics for the Score-Constrained Strip-Packing Problem. In: Kim, D., Uma, R., Zelikovsky, A. (eds) Combinatorial Optimization and Applications. COCOA 2018. Lecture Notes in Computer Science(), vol 11346. Springer, Cham. https://doi.org/10.1007/978-3-030-04651-4_30
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