The transportation sector, is the undeniable foundation of economic and industrial development. Despite the importance of transportation to global life, it is considered dangerous for the world since it is one of the hugest consumers of petroleum products. These days, with the objective of reducing fixed and economical costs of vehicles, fuel costs, and gas emissions, most transportation systems are planning to have simultaneous pickup and delivery systems. The amount of emissions depends mainly on the amount of fuel consumed, the type of fuel, the mileage travelled, and the amount of load in that distance. Using alternative energy sources is one way to decrease greenhouse gas emissions and environmental pollution. On the other hand, the amount of fuel consumption of the vehicles is dependent on the amount of their load and it is necessary to consider their load in the planning. Hence, the work presented in this paper is focused on a medical goods distribution problem with pharmacological waste collection by plug-in hybrid vehicles considering the amount of energy consumption depends on the load of the vehicle. The problem has been modelled as a mixed integer linear programming with the aim of properly finding the route of all the vehicles with the objective of minimizing the economic costs and fuel costs of vehicles. GAMS software was used for model validation and by solving it in small size, its validity has been confirmed. Due to the complexity of this problem, the shuffled frog leaping algorithm is used for solving large-size instances. Then, the used algorithm is compared with a hybrid genetic algorithm and simulated annealing algorithm. Finally, the results obtained from the comparison of the exact solution and meta-heuristic algorithms showed that the proposed algorithm has a good performance in terms of solution quality and runtime.
