In the context of establishing emission control areas (ECAs) in many ports to meet the challenges posed by air pollution, the use of drone-carrying sniffers to perform emission monitoring missions has become a new monitoring mode for ECAs. The operational management problem of drones in ECAs, namely, drone scheduling problem (DSP), is eliciting the attention of researchers. To consider the influence of vessel traffic on the demand for drones, this study proposes a rental-based drone operation model. In the model, the number of drones used depends on the load of monitoring missions. Maximizing the cumulative monitoring reward and minimizing the use number of drones within the minimum monitoring rate constraint are used as optimization objectives to maximize the cost return of the rental-based operation model. The rental-based drone operation model is modeled as a multi-objective DSP (MDSP). Furthermore, we horizontally compare the characteristics of MDSP with those of many classical models in the field of operations research. Afterward, we reveal the similarities and differences between MDSP and previous models. We find that MDSP has the non-first-in-first-out property, whereas most of the advanced models have the first-in-first-out property, which leads to the failure of the developed efficient algorithms in solving MDSP. Therefore, this study innovatively designs four feasible multi-objective optimization methods for MDSP. Numerical experiments are conducted to evaluate the performance of the four methods in solving MDSP with different scales. In terms of theoretical implications, experimental results prove that the proposed methods for solving MDSP are feasible and effective In terms of practical implications, the proposed rental-based vessel monitoring operation model shows great potential for practical engineering.