Port Call Optimization at a Ferry Terminal with Stochastic Servicing Time and Additional Visits

Ferry shipping is an indispensable method of public transportation, especially in areas with well-developed river systems or coastal areas. The increasing demand for transport requires additional visits and introduces the problem of ship visit schedule engineering at ferry terminals with stochastic servicing time. In this paper, we propose a ferry visit planning problem to maximize the total profit, in which the berthing time, berthing location, and servicing time for each ferry visit are optimized. Then, a mixed-integer nonlinear programming model is proposed to formulate the focal problem. We propose a tailored solution method to convert the mixed-integer nonlinear programming model to a mixed-integer linear programming model. We further devise an inserting algorithm to test the performance of our model. A comparison between the results of the basic instance yielded by our model and those of the inserting algorithm validates our model and solution method. We then conduct sensitivity analyses of the impacts of different numbers of existing ferry visits and added ferry visits, different expectations of the real time taken by all the ferry visits, and different distribution patterns of existing ferry visits, to further validate the performance of our model.