One Dimensional Cutting Stock Problem (1D-CSP): A New approach for Sustainable Trim Loss
DOI:
https://doi.org/10.26438/ijcse/v6i10.265271Keywords:
Pre-Defined Sustainable Trim, Loss, Sustainable Trim Loss, Lagrange interpolation approximation, Total Trim LossAbstract
Given the stock lengths , this paper computes the total trim loss of One-dimensional-cutting stock problem (1D-CSP) by considering the cutting plan of at most two order lengths at a time of the required order lengths . The Total Trim Loss (TTL) is computed by fixing a variable as the percentage of the Pre-Defined Sustainable Trim Loss(PDSTL) on the given stock by the industry. In view of the past experience, it has been noticed that the trim loss up to 3% is viable for the smooth running of the industry. Hence, we consider 3 as the upper bound of the pre-defined sustainable trim t. Considering the variable with the stepping of as the nodal points in the domain, we have first computed the corresponding TTL and plotted these points in the range. With this information, Lagrange Interpolation method has been applied to predict the TTL at any arbitrary point .
References
[1]. Alem Douglas José, Munari Pedro Augusto, Arenales Marcos Nereu, Ferreira Paulo Augusto Valente, “On the cutting stock problem under stochastic demand”, Annals of Operations Research, vol. 179 (1), pp. 169-186, 2010.
[2]. Araujo Silvio Alexandre de, Poldi Kelly Cristina, Smith Jim, “A Genetic Algorithm for the One-Dimensional Cutting Stock Problem with Setups”, Pesquisa Operacional, vol. 34(2) pp. 165-187, 2014.
[3]. Arenales, M. N., Cherri, A. C., Nascimento, D. N. do, & Vianna, A., “A New Mathematical Model for the Cutting Stock/Leftover Problem”, Pesquisa Operacional, vol. 35(3), pp. 509–522, 2015.
[4]. Dikili Ahmet Cemil, Barlas Baris, “A Generalized approach to the solution of One-Dimensional Stock-Cutting Problem for Small Shipyards”, Journal of Marine Science and Technology, vol. 19, no. 4, pp. 368-376, 2011.
[5]. Erjavec, J., Miro Gradišar, Trkman Peter, “Renovation of the Cutting Stock Process”, International Journal of Production Research, vol. 47(14), pp. 3979-3996, 2009.
[6]. Gilmore, P. C. and Gomory, R. E., “A linear programming approach to the cutting-stock problem”, Operations Research, vol. 9, pp. 849-859, 1961.
[7]. Gilmore, P. C. and Gomory, R. E., “A linear programming approach to the cutting-stock problem Part II”, Operations Research, vol. 11, pp. 863-888, 1963.
[8]. Gilmore, P. C. and Gomory, R. E., “Multi-stage cutting-stock problems of two or more dimensions”, Operations Research, vol. 13, pp. 94-120, 1965.
[9]. Ibrahim Muter, Zeynep Sezer “Algorithms for the One-Dimensional Two-Stage Cutting Stock Problem”, European Journal of Operational Research, vol 271(1), pp. 20-32, 2018.
[10]. Mobasher A.,Ekici A., “Solution approaches for the cutting stock problem with setup cost”, Journal Computers and Operations Research, vol. 40(1), pp. 225-235, 2013.
[11]. Powar P.L., Jain V., Saraf M., Vishwakarma R., “One-Dimensional Cutting Stock Problem with First Order Sustainable Trim: A Practical Approach,” International Journal of Computer Science Engineering and Information Technology Research, vol. 3(3), pp. 227-240, 2013.
[12]. Rodrigo N., Shashikala S., “One-Dimensional Cutting Stock Problem with Cartesian Coordinate Points”, International Journal of Systems Science and Applied Mathematics, vol 2(5), pp: 99-104, 2017.
[13]. Suliman S. M. A., “An Algorithm for Solving Lot Sizing and Cutting Stock Problem within Aluminum Fabrication Industry”, Proceedings of the International Conference on Industrial Engineering and Operations Management Istanbul, Turkey, July 3 –6, pp. 783-789, 2012.
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