Mathematical modeling and hybridized evolutionary LP local search method for lot-sizing with supplier selection, inventory shortage, and quantity discounts
•A multi-period lot-sizing problem with supplier selection and shortage is tackled.•A mixed integer non-linear programming (MINLP) model is developed.•A hybridized search Evolutionary LP-driven local search method is developed.•Overall results show superiority of developed hybridized search method.•...
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| Published in: | Computers & industrial engineering Vol. 109; pp. 96 - 112 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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01.07.2017
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| ISSN: | 0360-8352 |
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| Abstract | •A multi-period lot-sizing problem with supplier selection and shortage is tackled.•A mixed integer non-linear programming (MINLP) model is developed.•A hybridized search Evolutionary LP-driven local search method is developed.•Overall results show superiority of developed hybridized search method.•Results obtained from industrial case demonstrate applicability of approach.
This paper addresses the multi-period inventory lot-sizing problem with supplier selection and inventory shortage, and it considers both all-units and incremental quantity discounts. A unique preprocessing approach is introduced that transforms discount quantity intervals into newer ones, revealing the supplier that has the minimum total ordering, purchasing, and transportation costs. This transformation changes the lot-sizing problem with multiple quantity discount models into a problem of a single quantity discount schedule. The problem is formulated as a Mixed Integer Non-Linear Programming (MINLP) model. Since the problem is intractable, a hybridized search method is developed, where both an Evolutionary Algorithm (EA) and a Linear Programming (LP) driven local search are combined. For initialization, Wagner-Whitin (WW), back-shifting and relaxed LP approaches are used. Finally, for validation and justification purposes, test cases from the industry and literature are used. |
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| AbstractList | •A multi-period lot-sizing problem with supplier selection and shortage is tackled.•A mixed integer non-linear programming (MINLP) model is developed.•A hybridized search Evolutionary LP-driven local search method is developed.•Overall results show superiority of developed hybridized search method.•Results obtained from industrial case demonstrate applicability of approach.
This paper addresses the multi-period inventory lot-sizing problem with supplier selection and inventory shortage, and it considers both all-units and incremental quantity discounts. A unique preprocessing approach is introduced that transforms discount quantity intervals into newer ones, revealing the supplier that has the minimum total ordering, purchasing, and transportation costs. This transformation changes the lot-sizing problem with multiple quantity discount models into a problem of a single quantity discount schedule. The problem is formulated as a Mixed Integer Non-Linear Programming (MINLP) model. Since the problem is intractable, a hybridized search method is developed, where both an Evolutionary Algorithm (EA) and a Linear Programming (LP) driven local search are combined. For initialization, Wagner-Whitin (WW), back-shifting and relaxed LP approaches are used. Finally, for validation and justification purposes, test cases from the industry and literature are used. |
| Author | Vital Soto, Alejandro Baki, Mohammed F. Azab, Ahmed Chowdhury, Nusrat T. Allahyari, Maral Z. |
| Author_xml | – sequence: 1 givenname: Alejandro surname: Vital Soto fullname: Vital Soto, Alejandro email: vitalsoa@uwindsor.ca organization: Product and Lifecycle Management Research Lab, Faculty of Engineering, University of Windsor, Windsor, Ontario N9B 3P4, Canada – sequence: 2 givenname: Nusrat T. surname: Chowdhury fullname: Chowdhury, Nusrat T. email: chowd117@uwindsor.ca organization: Product and Lifecycle Management Research Lab, Faculty of Engineering, University of Windsor, Windsor, Ontario N9B 3P4, Canada – sequence: 3 givenname: Maral Z. surname: Allahyari fullname: Allahyari, Maral Z. email: zafaram@uwindsor.ca organization: Product and Lifecycle Management Research Lab, Faculty of Engineering, University of Windsor, Windsor, Ontario N9B 3P4, Canada – sequence: 4 givenname: Ahmed surname: Azab fullname: Azab, Ahmed email: azab@uwindsor.ca organization: Product and Lifecycle Management Research Lab, Faculty of Engineering, University of Windsor, Windsor, Ontario N9B 3P4, Canada – sequence: 5 givenname: Mohammed F. surname: Baki fullname: Baki, Mohammed F. email: fbaki@uwindsor.ca organization: Odette School of Business, University of Windsor, Windsor, Ontario N9B 3P4, Canada |
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| Title | Mathematical modeling and hybridized evolutionary LP local search method for lot-sizing with supplier selection, inventory shortage, and quantity discounts |
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