An optimization model for fleet sizing and empty pallet allocation considering CO(2) emissions

Pallets are the most common equipment for transporting and storing goods. More and more companies are willing to rent pallets. Pallet rental companies need to transport pallets from their pallet rental service stations to customers and take these pallets back when they are unloaded. Hence, managers should scientifically configure vehicles for their pallet rental service stations. The fleet size, which indicates the amount and types of vehicles, can significantly affect the efficiency and costs of empty pallet allocation. Therefore, an optimization model for fleet sizing and empty pallet allocation is proposed using the methods of mixed-integer programming and stochastic programming. The objectives of this model are to maximize the profits of pallet rental companies and minimize carbon dioxide (CO(2)) emissions from vehicles. A particle swarm optimization algorithm with inertia weight (IPSO) is developed to solve the proposed model because IPSO can avoid becoming trapped in local optima and is able to find a globally optimal solution within a reasonable number of iterations. A numerical example proves the effectiveness of the proposed model and IPSO. The results of numerical tests show that the amount of CO(2) emissions from vehicles can affect the decision on fleet sizing and empty pallet allocation. However, if the price, rental fees, or idle costs of the vehicles with low CO(2) emissions are too high, managers would not choose them.