A Prufer-based genetic algorithm for allocation of the vehicles in a discounted transportation cost system

ABSTRACT

In this document, allocation of different types of vehicles for transporting products from a manufacturing firm to its depots is considered. The problem involves a limited number of vehicles of various capacities, with the fixed and variable costs as well as a discount mechanism. The objective is defined as the minimisation of the total transportation costs. A mathematical model in the form of nonlinear integer programming is developed and converted to the linear zero-one programme. Due to the NP hard complexity of the proposed mathematical model, a Prufer-based genetic algorithm capable of solving large instances is developed. The efficiency of the proposed algorithm is compared with the solution obtained by CPLEX and the results are reported. The results reveal that the proposed algorithm is capable of providing astonishing solutions with the minimum computational effort.

KEYWORDS:

• Fixed-cost transportation model
• Prufer-based genetic algorithm
• nonlinear combinatorial optimisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Zahrasadat Hashemi

Zahrasadat Hashemi obtained her bachelor degree from the department of Mathematics, Alzahra University and her master degree from the department of Industrial Engineering, Sharif University of Technology. Her primary fields of research interest are optimization, operations research, and logistics.

Farhad Ghassemi Tari

Farhad Ghassemi obtained his bachelor degree from the department of Industrial Engineering, Sharif University of Technology, and his master and Ph.D. degrees from the department of Industrial Engineering Texas A & M University. Right after his graduation, he joined Sharif University of Technology as an assistant professor in the Department of Industrial Engineering. Farhad's teaching interests include the facility layout, scheduling, operations research and optimization subjects. His primary fields of research interest are optimization, operations research, facility panning, logistics, scheduling, and sequencing.