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

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.