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Differential Evolution Algorithm for Multilevel Assignment Problem: A Case Study in Chicken Transportation

1
Faculty of Informatics, Mahasarakham University, Maha Sarakham 44150, Thailand
2
Department of Economics, Rajamangala University of Technology Thanyaburi, Patumthani 12110, Thailand
3
Faculty of Engineering, Nakhon Phanom University, Nakhon Phanom 48000, Thailand
4
Faculty of Liberal Arts and Sciences, Sisaket Rajabhat University, Sisaket 33000, Thailand
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2018, 23(4), 55; https://doi.org/10.3390/mca23040055
Received: 12 September 2018 / Revised: 30 September 2018 / Accepted: 30 September 2018 / Published: 2 October 2018
(This article belongs to the Special Issue Optimization in Control Applications)
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Abstract

This study aims to solve the real-world multistage assignment problem. The proposed problem is composed of two stages of assignment: (1) different types of trucks are assigned to chicken farms to transport young chickens to egg farms, and (2) chicken farms are assigned to egg farms. Assigning different trucks to the egg farms and different egg farms to the chicken farms generates different costs and consumes different resources. The distance and the idle space in the truck have to be minimized, while constraints such as the minimum number of chickens needed for all egg farms and the longest time that chickens can be in the truck remain. This makes the problem a special case of the multistage assignment (S-MSA) problem. A mathematical model representing the problem was developed and solved to optimality using Lingo v.11 optimization software. Lingo v.11 can solve to optimality only small- and medium-sized test instances. To solve large-sized test instances, the differential evolution (DE) algorithm was designed. An excellent decoding method was developed to increase the search performance of DE. The proposed algorithm was tested with three randomly generated datasets (small, medium, and large test instances) and one real case study. Each dataset is composed of 12 problems, therefore we tested with 37 instances, including the case study. The results show that for small- and medium-sized test instances, DE has 0.03% and 0.05% higher cost than Lingo v.11. For large test instances, DE has 3.52% lower cost than Lingo v.11. Lingo v.11 uses an average computation time of 5.8, 103, and 4320 s for small, medium and large test instances, while DE uses 0.86, 1.68, and 8.79 s, which is, at most, 491 times less than Lingo v.11. Therefore, the proposed heuristics are an effective algorithm that can find a good solution while using less computation time. View Full-Text
Keywords: assignment problem; chicken transportation; differential evolution algorithm; mathematical model assignment problem; chicken transportation; differential evolution algorithm; mathematical model
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Kaewman, S.; Srivarapongse, T.; Theeraviriya, C.; Jirasirilerd, G. Differential Evolution Algorithm for Multilevel Assignment Problem: A Case Study in Chicken Transportation. Math. Comput. Appl. 2018, 23, 55.

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