A bi-objective multi-population biased random key genetic algorithm for joint scheduling quay cranes and speed adjustable vehicles in container terminals

This work formulates a mixed-integer linear programming (MILP) model and proposes a bi-objective multi-population biased random key genetic algorithm (mp-BRKGA) for the joint scheduling of quay cranes and speed adjustable vehicles in container terminals considering the dual-cycling strategy. Under such a strategy, a combination of loading and unloading containers are handled by a set of cranes (moved between ships and vehicles) and transported by a set of vehicles (transported between the quayside and the storage area). The problem consists of four components: crane scheduling, vehicle assignment, vehicle scheduling, and speed assignment both for empty and loaded journey legs. The results show that an approximated true Pareto front can be found by solving the proposed MILP model and that the mp-BRKGA finds uniformly distributed Pareto fronts, close to the true ones. Additionally, the results clearly demonstrate the advantages of considering speed adjustable vehicles since both the makespan and the energy consumption can be considerably reduced.