Exact methods in optimum disassembly sequence search for problems subject to sequence dependent costs
Disassembling complex products is formally approached via network representation and subsequent mathematical modeling, aimed at selecting a good or optimum sequence of disassembly operations. This is done via heuristics, metaheuristics or mathematical programming. In contrast with heuristics and met...
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| Vydáno v: | Omega (Oxford) Ročník 34; číslo 6; s. 538 - 549 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Oxford
Elsevier Ltd
01.12.2006
Elsevier Pergamon Press Inc |
| Edice: | Omega |
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| ISSN: | 0305-0483, 1873-5274 |
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| Abstract | Disassembling complex products is formally approached via network representation and subsequent mathematical modeling, aimed at selecting a good or optimum sequence of disassembly operations. This is done via heuristics, metaheuristics or mathematical programming. In contrast with heuristics and metaheuristics, which select a near-optimum solution, mathematical programming guarantees the selection of the global optimum. This problem is relatively simple if the disassembly costs can be assumed sequence independent. In practice, however, sequence dependent disassembly costs are frequently encountered, which causes NP-completeness of the problem. Although methods, e.g., based on the two-commodity network flow approach, are available to solve this constrained asymmetric Traveling Salesperson problem rigorously, this requires the introduction of integer variables. In this paper, a modification of the two-commodity network flow approach is proposed, which reduces the number of integer variables. This is applied to product structures that can be represented by a disassembly precedence graph. It is demonstrated that use of integer variables is completely avoided by iteratively solving a binary integer linear programming problem. This appears to be more efficient than solving the corresponding integer linear programming problem. It is demonstrated, on the basis of some cases, that this method might provide the exact solution of problems with increased complexity compared to those discussed so far in the literature. This appears particularly useful for evaluating heuristic and metaheuristic approaches. |
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| AbstractList | Disassembling complex products is formally approached via network representation and subsequent mathematical modeling, aimed at selecting a good or optimum sequence of disassembly operations. This is done via heuristics, metaheuristics or mathematical programming. In contrast with heuristics and metaheuristics, which select a near-optimum solution, mathematical programming guarantees the selection of the global optimum. This problem is relatively simple if the disassembly costs can be assumed sequence independent. In practice, however, sequence dependent disassembly costs are frequently encountered, which causes NP-completeness of the problem. Although methods, e.g., based on the two-commodity network flow approach, are available to solve this constrained asymmetric Traveling Salesperson problem rigorously, this requires the introduction of integer variables. In this paper, a modification of the two-commodity network flow approach is proposed, which reduces the number of integer variables. This is applied to product structures that can be represented by a disassembly precedence graph. It is demonstrated that use of integer variables is completely avoided by iteratively solving a binary integer linear programming problem. This appears to be more efficient than solving the corresponding integer linear programming problem. Disassembling complex products is formally approached via network representation and subsequent mathematical modeling, aimed at selecting a good or optimum sequence of disassembly operations. This is done via heuristics, metaheuristics or mathematical programming. In contrast with heuristics and metaheuristics, which select a near-optimum solution, mathematical programming guarantees the selection of the global optimum. This problem is relatively simple if the disassembly costs can be assumed sequence independent. In practice, however, sequence dependent disassembly costs are frequently encountered, which causes NP-completeness of the problem. Although methods, e.g., based on the two-commodity network flow approach, are available to solve this constrained asymmetric Traveling Salesperson problem rigorously, this requires the introduction of integer variables. In this paper, a modification of the two-commodity network flow approach is proposed, which reduces the number of integer variables. This is applied to product structures that can be represented by a disassembly precedence graph. It is demonstrated that use of integer variables is completely avoided by iteratively solving a binary integer linear programming problem. This appears to be more efficient than solving the corresponding integer linear programming problem. It is demonstrated, on the basis of some cases, that this method might provide the exact solution of problems with increased complexity compared to those discussed so far in the literature. This appears particularly useful for evaluating heuristic and metaheuristic approaches. |
| Author | Lambert, A.J.D. |
| Author_xml | – sequence: 1 givenname: A.J.D. surname: Lambert fullname: Lambert, A.J.D. email: a.j.d.lambert@tm.tue.nl organization: Department of Technology Management, Technische Universiteit Eindhoven, TM/AW Pav. H.03, P.O. Box 513, 5600 MB Eindhoven, The Netherlands |
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| Cites_doi | 10.1109/70.54734 10.1109/ISATP.2003.1217203 10.1080/002075498192049 10.1016/S0360-8352(97)00104-6 10.1016/B978-0-444-81901-7.50130-4 10.1109/70.68072 10.1142/S0960313102000436 10.1109/70.75905 10.1109/70.964670 10.1109/ISATP.2003.1217182 10.1080/00207540010002838 10.1016/S0278-6125(99)80032-6 10.1109/IROS.1993.583945 10.1016/S0007-8506(07)62136-2 10.1016/S0360-8352(99)00167-9 10.1016/S0360-8352(99)00162-X 10.1080/0020754031000120078 10.1109/JRA.1987.1087132 |
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| References_xml | – volume: 33 start-page: 329 year: 1997 end-page: 332 ident: bib15 article-title: An evaluation methodology for disassembly processes publication-title: Computers and Industrial Engineering – year: 1993 ident: bib22 article-title: AIMMS, the modeling system – volume: 6 start-page: 188 year: 1990 end-page: 189 ident: bib6 article-title: And/or graph representation of assembly plans publication-title: IEEE Transactions on Robotics and Automation – volume: 36 start-page: 723 year: 1999 end-page: 738 ident: bib10 article-title: Linear programming in disassembly/clustering sequence generation publication-title: Computers and Industrial Engineering – volume: 7 start-page: 228 year: 1991 end-page: 240 ident: bib7 article-title: A correct and complete algorithm for the generation of mechanical assembly sequences publication-title: IEEE Transactions on Robotics and Automation – volume: 41 start-page: 3721 year: 2003 end-page: 3759 ident: bib2 article-title: Disassembly sequencing publication-title: International Journal of Production Systems – reference: Boothroyd G, Poli C, Murch LE. 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| SubjectTerms | Assembly planning Assembly planning Disassembly planning Mathematical programming Network Traveling salesperson problem Optimization Disassembly planning Linear programming Mathematical models Mathematical programming Network Network flow problem Optimization Studies Traveling salesman problem Traveling salesperson problem |
| Title | Exact methods in optimum disassembly sequence search for problems subject to sequence dependent costs |
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