A priority based genetic algorithm for nonlinear transportation costs problems

• A nonlinear mathematical program is proposed.
• The mathematical program is converted to a linear MI mathematical program.
• A priority based genetic algorithm is developed.
• The efficacy of the proposed algorithm verses CPLEX is evaluated.
• The robustness and computational efficiency of the proposed approach is confirmed.

In this manuscript, a vehicle allocation problem involving a heterogeneous fleet of vehicles for delivering products from a manufacturing firm to a set of depots is considered. Each depot has a specific order quantity and transportation costs consist of fixed and variable transportation cost. The objective is to assign the proper type and number of vehicle to each depot route to minimize the total transportation costs. It is assumed that the number of chartering vehicle types is limited. It is also assumed that a discount mechanism is applied to the vehicles renting cost. The discount mechanism is applied to the fixed cost, based on the number of vehicles to be rented. A mathematical programming model is proposed which is then converted to a mixed 0–1 integer programming model. Due to the computational complexity of the proposed mathematical model, a priority based genetic algorithm capable of solving the real world size problems was proposed. A computational experiment is conducted through which, the performance of the proposed algorithm is evaluated. The results reveal that the proposed algorithm is capable of providing the astonishing solutions with minimal computational effort, comparing with the CPLEX solutions.