Integrating irregular strip packing and cutting path determination problems: A discrete exact approach
The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What di...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Oliveira, Larissa Tebaldi [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020transfer abstract |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Exploring the drying behaviors of microencapsulated noni juice using reaction engineering approach (REA) mathematical modelling - Zhang, Chuang ELSEVIER, 2018, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:149 ; year:2020 ; pages:0 |
| Links: |
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| DOI / URN: |
10.1016/j.cie.2020.106757 |
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ELV051830507 |
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| 520 | |a The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. | ||
| 520 | |a The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. | ||
| 650 | 7 | |a Integrated model |2 Elsevier | |
| 650 | 7 | |a Cutting path determination problem |2 Elsevier | |
| 650 | 7 | |a Irregular strip packing problem |2 Elsevier | |
| 700 | 1 | |a Silva, Everton Fernandes |4 oth | |
| 700 | 1 | |a Oliveira, José Fernando |4 oth | |
| 700 | 1 | |a Toledo, Franklina Maria Bragion |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier Science |a Zhang, Chuang ELSEVIER |t Exploring the drying behaviors of microencapsulated noni juice using reaction engineering approach (REA) mathematical modelling |d 2018 |g Amsterdam [u.a.] |w (DE-627)ELV00175033X |
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10.1016/j.cie.2020.106757 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001186.pica (DE-627)ELV051830507 (ELSEVIER)S0360-8352(20)30472-1 DE-627 ger DE-627 rakwb eng 630 640 VZ 58.34 bkl Oliveira, Larissa Tebaldi verfasserin aut Integrating irregular strip packing and cutting path determination problems: A discrete exact approach 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. Integrated model Elsevier Cutting path determination problem Elsevier Irregular strip packing problem Elsevier Silva, Everton Fernandes oth Oliveira, José Fernando oth Toledo, Franklina Maria Bragion oth Enthalten in Elsevier Science Zhang, Chuang ELSEVIER Exploring the drying behaviors of microencapsulated noni juice using reaction engineering approach (REA) mathematical modelling 2018 Amsterdam [u.a.] (DE-627)ELV00175033X volume:149 year:2020 pages:0 https://doi.org/10.1016/j.cie.2020.106757 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 58.34 Lebensmitteltechnologie VZ AR 149 2020 0 |
| spelling |
10.1016/j.cie.2020.106757 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001186.pica (DE-627)ELV051830507 (ELSEVIER)S0360-8352(20)30472-1 DE-627 ger DE-627 rakwb eng 630 640 VZ 58.34 bkl Oliveira, Larissa Tebaldi verfasserin aut Integrating irregular strip packing and cutting path determination problems: A discrete exact approach 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. Integrated model Elsevier Cutting path determination problem Elsevier Irregular strip packing problem Elsevier Silva, Everton Fernandes oth Oliveira, José Fernando oth Toledo, Franklina Maria Bragion oth Enthalten in Elsevier Science Zhang, Chuang ELSEVIER Exploring the drying behaviors of microencapsulated noni juice using reaction engineering approach (REA) mathematical modelling 2018 Amsterdam [u.a.] (DE-627)ELV00175033X volume:149 year:2020 pages:0 https://doi.org/10.1016/j.cie.2020.106757 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 58.34 Lebensmitteltechnologie VZ AR 149 2020 0 |
| allfields_unstemmed |
10.1016/j.cie.2020.106757 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001186.pica (DE-627)ELV051830507 (ELSEVIER)S0360-8352(20)30472-1 DE-627 ger DE-627 rakwb eng 630 640 VZ 58.34 bkl Oliveira, Larissa Tebaldi verfasserin aut Integrating irregular strip packing and cutting path determination problems: A discrete exact approach 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. Integrated model Elsevier Cutting path determination problem Elsevier Irregular strip packing problem Elsevier Silva, Everton Fernandes oth Oliveira, José Fernando oth Toledo, Franklina Maria Bragion oth Enthalten in Elsevier Science Zhang, Chuang ELSEVIER Exploring the drying behaviors of microencapsulated noni juice using reaction engineering approach (REA) mathematical modelling 2018 Amsterdam [u.a.] (DE-627)ELV00175033X volume:149 year:2020 pages:0 https://doi.org/10.1016/j.cie.2020.106757 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 58.34 Lebensmitteltechnologie VZ AR 149 2020 0 |
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10.1016/j.cie.2020.106757 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001186.pica (DE-627)ELV051830507 (ELSEVIER)S0360-8352(20)30472-1 DE-627 ger DE-627 rakwb eng 630 640 VZ 58.34 bkl Oliveira, Larissa Tebaldi verfasserin aut Integrating irregular strip packing and cutting path determination problems: A discrete exact approach 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. Integrated model Elsevier Cutting path determination problem Elsevier Irregular strip packing problem Elsevier Silva, Everton Fernandes oth Oliveira, José Fernando oth Toledo, Franklina Maria Bragion oth Enthalten in Elsevier Science Zhang, Chuang ELSEVIER Exploring the drying behaviors of microencapsulated noni juice using reaction engineering approach (REA) mathematical modelling 2018 Amsterdam [u.a.] (DE-627)ELV00175033X volume:149 year:2020 pages:0 https://doi.org/10.1016/j.cie.2020.106757 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 58.34 Lebensmitteltechnologie VZ AR 149 2020 0 |
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10.1016/j.cie.2020.106757 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001186.pica (DE-627)ELV051830507 (ELSEVIER)S0360-8352(20)30472-1 DE-627 ger DE-627 rakwb eng 630 640 VZ 58.34 bkl Oliveira, Larissa Tebaldi verfasserin aut Integrating irregular strip packing and cutting path determination problems: A discrete exact approach 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. Integrated model Elsevier Cutting path determination problem Elsevier Irregular strip packing problem Elsevier Silva, Everton Fernandes oth Oliveira, José Fernando oth Toledo, Franklina Maria Bragion oth Enthalten in Elsevier Science Zhang, Chuang ELSEVIER Exploring the drying behaviors of microencapsulated noni juice using reaction engineering approach (REA) mathematical modelling 2018 Amsterdam [u.a.] (DE-627)ELV00175033X volume:149 year:2020 pages:0 https://doi.org/10.1016/j.cie.2020.106757 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 58.34 Lebensmitteltechnologie VZ AR 149 2020 0 |
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integrating irregular strip packing and cutting path determination problems: a discrete exact approach |
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Integrating irregular strip packing and cutting path determination problems: A discrete exact approach |
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The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. |
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The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. |
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The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors’ knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems. |
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