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# Methodology to Solve the Combination of the Generalized Assignment Problem and the Vehicle Routing Problem: A Case Study in Drug and Medical Instrument Sales and Service

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Department of Marketing, Mahasarakarm Business School, Mahasarakham University, Maha Sarakham 44000, Thailand
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Department of Computer Science, Faculty of informatics, Mahasarakham University, Maha Sarakham 44000, Thailand
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Author to whom correspondence should be addressed.
Received: 30 September 2018 / Revised: 8 December 2018 / Accepted: 20 December 2018 / Published: 26 December 2018
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# Abstract

This article presents algorithms for solving a special case of the vehicle routing problem (VRP). We define our proposed problem of a special VRP case as a combination of two hard problems: the generalized assignment and the vehicle routing problem. The different evolution (DE) algorithm is used to solve the problem. The recombination process of the original DE is modified by adding two more sets of vectors—best vector and random vector—and using two other sets—target vector and trial vector. The linear probability formula is proposed to potentially use one out of the four sets of vectors. This is called the modified DE (MDE) algorithm. Two local searches are integrated into the MDE algorithm: exchange and insert. These procedures create a DE and MDE that use (1) no local search techniques, (2) two local search techniques, (3) only the exchange procedure, and (4) only the insert procedure. This generates four DE algorithms and four MDE algorithms. The proposed methods are tested with 15 tested instances and one case study. The current procedure is compared with all proposed heuristics. The computational result shows that, in the case study, the best DE algorithm (DE-4) has a 1.6% better solution than that of the current practice, whereas the MDE algorithm is 8.2% better. The MDE algorithm that uses the same local search as the DE algorithms generates a maximum 5.814% better solution than that of the DE algorithms. View Full-Text
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

MDPI and ACS Style

Thongkham, M.; Kaewman, S. Methodology to Solve the Combination of the Generalized Assignment Problem and the Vehicle Routing Problem: A Case Study in Drug and Medical Instrument Sales and Service. Adm. Sci. 2019, 9, 3.

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

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