A multi-objective fuzzy programming model for port tugboat scheduling based on the Stackelberg game

To solve the optimization problem of tugboat scheduling for assisting ships in entering and exiting ports in uncertain environments, this study investigates the impact of the decisions of tugboat operators and port dispatchers on tugboat scheduling under the scenario of dynamic task arrival and fuzzy tugboat operation time. Considering the features of the shortest distance tugboat principle, the first available tugboat principle, and the principle of fairness in the task volume of each tugboat, the tugboat company aims to minimize the total daily fuel consumption of tugboat operations, maximize the total buffer time of dynamic tasks, and minimize the total completion time as the objective functions. Due to the limitations of port vessel berthing and departure, as well as the allocation standards for piloting or relocating tugboats, the present study proposes a Stackelberg game-based fuzzy model for port tugboat scheduling with the tugboat operator and port dispatcher acting as decision makers at the upper and lower levels, respectively. A seagull optimization algorithm based on priority encoding and genetic operators is designed as a solution approach. CPLEX, genetic algorithm, standard seagull optimization algorithm, and simulated annealing algorithm are used to compare and analyze the solution results for the 45 problem cases generated from the actual data obtained from the Guangzhou Port. The results verify the efficiency of the proposed seagull optimization algorithm based on priority encoding and genetic operators. Furthermore, additional experiments are conducted to evaluate the changes in fairness coefficient, uncertain parameter correlation coefficients, and objective function correlation coefficients to demonstrate the practicality of the fuzzy programming model. This analysis involves adjusting the confidence level incrementally from 0 to 100% with respect to the model's uncertain parameters.