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A column generation on two-dimensional cutting stock problem with fixed-size usable leftover and multiple stock sizes

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  • Supphakorn Sumetthapiwat
  • Boonyarit Intiyot
  • Chawalit Jeenanunta

Abstract

We investigate a two-dimensional two-stage cutting stock problem (2D-2CP) with multiple stock sizes when fixed-size usable leftovers are considered. A fixed-size usable leftover is an object with the predefined size that could be used later. Fixed-size usable leftovers can reduce the waste area and therefore can help construct better cutting patterns. A mathematical model is proposed in a set-partitioning form where the sub-problems corresponding to two-dimensional knapsack problem (2DKP) with fixed-size usable leftovers are generated for optimality testing. A column generation technique is applied in an attempt to find a solution that minimises a total waste. Moreover, two different practical integer solution finding strategies are proposed. The algorithms are tested on a real-world dataset using various initial solution patterns and analysed. Additionally, the effect of the usable leftovers is investigated when compared with the prior literature that used the same dataset on the 2D-2CP problem without considering usable leftovers.

Suggested Citation

  • Supphakorn Sumetthapiwat & Boonyarit Intiyot & Chawalit Jeenanunta, 2020. "A column generation on two-dimensional cutting stock problem with fixed-size usable leftover and multiple stock sizes," International Journal of Logistics Systems and Management, Inderscience Enterprises Ltd, vol. 35(2), pages 273-288.
    • Handle: RePEc:ids:ijlsma:v:35:y:2020:i:2:p:273-288
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    Cited by:

    1. Teeradech Laisupannawong & Boonyarit Intiyot & Chawalit Jeenanunta, 2021. "Mixed-Integer Linear Programming Model and Heuristic for Short-Term Scheduling of Pressing Process in Multi-Layer Printed Circuit Board Manufacturing," Mathematics, MDPI, vol. 9(6), pages 1-25, March.
    2. Douglas Nogueira Nascimento & Adriana Cristina Cherri & José Fernando Oliveira, 2022. "The two-dimensional cutting stock problem with usable leftovers: mathematical modelling and heuristic approaches," Operational Research, Springer, vol. 22(5), pages 5363-5403, November.
    3. Hadj Salem, Khadija & Silva, Elsa & Oliveira, José Fernando & Carravilla, Maria Antónia, 2023. "Mathematical models for the two-dimensional variable-sized cutting stock problem in the home textile industry," European Journal of Operational Research, Elsevier, vol. 306(2), pages 549-566.

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