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

Malichan Thongkham and Sasitorn Kaewman
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Malichan Thongkham: Department of Marketing, Mahasarakarm Business School, Mahasarakham University, Maha Sarakham 44000, Thailand
Sasitorn Kaewman: Department of Computer Science, Faculty of informatics, Mahasarakham University, Maha Sarakham 44000, Thailand

Administrative Sciences, 2018, vol. 9, issue 1, 1-21

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.

Keywords: vehicle routing problem; assignment problem; differential evolution algorithm; local search; insertion; drug and medical instrument sales and service (search for similar items in EconPapers)
JEL-codes: L M M0 M1 M10 M11 M12 M14 M15 M16 (search for similar items in EconPapers)
Date: 2018
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