Application of the surrogate gradient method for a multi-item single-machine dynamic lot size scheduling problem
Abstract This study treats a multi-item single-machine dynamic lot size scheduling problem with sequence-independent setup cost and setup time. This problem has various heterogeneous decision features, such as lot sizing and lot sequencing. Traditionally, the problem has been treated by putting arti...
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| Format: | Article |
| Language: | English |
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Springer
2021-06-01
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| Series: | SN Applied Sciences |
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| Online Access: | https://doi.org/10.1007/s42452-021-04669-3 |
| _version_ | 1818907260993142784 |
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| author | Minoru Kobayashi |
| author_facet | Minoru Kobayashi |
| author_sort | Minoru Kobayashi |
| collection | DOAJ |
| description | Abstract This study treats a multi-item single-machine dynamic lot size scheduling problem with sequence-independent setup cost and setup time. This problem has various heterogeneous decision features, such as lot sizing and lot sequencing. Traditionally, the problem has been treated by putting artificial constraints on the other feature in order to determine one of them. The proposed model is a Lagrange decomposition and coordination method that aims at simultaneous optimization of these decision features; however, smooth convergence to a feasible near-optimal solution has been a problem. So, in this paper, we propose a model that improves the constraint equation of the existing model and showed that it satisfies the Karush–Kuhn–Tucker (KKT) condition when we obtained a feasible solution. In addition, by applying the surrogate gradient method, which has never been applied to this problem before, it was shown that smoother convergence than before can be achieved through actual example of printed circuit board. |
| first_indexed | 2024-12-19T21:52:18Z |
| format | Article |
| id | doaj.art-6210d4793bf544ed9e389969b5642557 |
| institution | Directory Open Access Journal |
| issn | 2523-3963 2523-3971 |
| language | English |
| last_indexed | 2024-12-19T21:52:18Z |
| publishDate | 2021-06-01 |
| publisher | Springer |
| record_format | Article |
| series | SN Applied Sciences |
| spelling | doaj.art-6210d4793bf544ed9e389969b56425572022-12-21T20:04:23ZengSpringerSN Applied Sciences2523-39632523-39712021-06-01371910.1007/s42452-021-04669-3Application of the surrogate gradient method for a multi-item single-machine dynamic lot size scheduling problemMinoru Kobayashi0Fukuoka Institute of TechnologyAbstract This study treats a multi-item single-machine dynamic lot size scheduling problem with sequence-independent setup cost and setup time. This problem has various heterogeneous decision features, such as lot sizing and lot sequencing. Traditionally, the problem has been treated by putting artificial constraints on the other feature in order to determine one of them. The proposed model is a Lagrange decomposition and coordination method that aims at simultaneous optimization of these decision features; however, smooth convergence to a feasible near-optimal solution has been a problem. So, in this paper, we propose a model that improves the constraint equation of the existing model and showed that it satisfies the Karush–Kuhn–Tucker (KKT) condition when we obtained a feasible solution. In addition, by applying the surrogate gradient method, which has never been applied to this problem before, it was shown that smoother convergence than before can be achieved through actual example of printed circuit board.https://doi.org/10.1007/s42452-021-04669-3Lagrangian decomposition and coordination methodProduction schedulingAccelerationDummy item |
| spellingShingle | Minoru Kobayashi Application of the surrogate gradient method for a multi-item single-machine dynamic lot size scheduling problem SN Applied Sciences Lagrangian decomposition and coordination method Production scheduling Acceleration Dummy item |
| title | Application of the surrogate gradient method for a multi-item single-machine dynamic lot size scheduling problem |
| title_full | Application of the surrogate gradient method for a multi-item single-machine dynamic lot size scheduling problem |
| title_fullStr | Application of the surrogate gradient method for a multi-item single-machine dynamic lot size scheduling problem |
| title_full_unstemmed | Application of the surrogate gradient method for a multi-item single-machine dynamic lot size scheduling problem |
| title_short | Application of the surrogate gradient method for a multi-item single-machine dynamic lot size scheduling problem |
| title_sort | application of the surrogate gradient method for a multi item single machine dynamic lot size scheduling problem |
| topic | Lagrangian decomposition and coordination method Production scheduling Acceleration Dummy item |
| url | https://doi.org/10.1007/s42452-021-04669-3 |
| work_keys_str_mv | AT minorukobayashi applicationofthesurrogategradientmethodforamultiitemsinglemachinedynamiclotsizeschedulingproblem |