A two-objective mathematical model without cutting patterns for one-dimensional assortment problems

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Atıf İçin Kopyala

Kasimbeyli N., SARAÇ T., Kasimbeyli R.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.235, sa.16, ss.4663-4674, 2011 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 235 Sayı: 16
• Basım Tarihi: 2011
• Doi Numarası: 10.1016/j.cam.2010.07.019
• Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.4663-4674
• Anahtar Kelimeler: One-dimensional assortment problem, Cutting stock problem, Stock size selection, Trim loss minimization, Heuristic algorithm, Multi-objective optimization, MULTIPLE STOCK LENGTHS, STANDARD LENGTHS, PACKING PROBLEMS, ALGORITHM, TYPOLOGY
• Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

This paper considers a one-dimensional cutting stock and assortment problem. One of the main difficulties in formulating and solving these kinds of problems is the use of the set of cutting patterns as a parameter set in the mathematical model. Since the total number of cutting patterns to be generated may be very huge, both the generation and the use of such a set lead to computational difficulties in solution process. The purpose of this paper is therefore to develop a mathematical model without the use of cutting patterns as model parameters. We propose a new, two-objective linear integer programming model in the form of simultaneous minimization of two contradicting objectives related to the total trim loss amount and the total number of different lengths of stock rolls to be maintained as inventory, in order to fulfill a given set of cutting orders. The model does not require pre-specification of cutting patterns. We suggest a special heuristic algorithm for solving the presented model. The superiority of both the mathematical model and the solution approach is demonstrated on test problems. (C) 2010 Elsevier B.V. All rights reserved.