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Vessels face uncertain factors during a voyage, such as bad weather and harsh sea conditions along a route in container liner shipping. As such, the real vessel speed during each leg of a voyage often deviates from the planned one, which may lead to fluctuations in vessel schedule and bunker consumption. This paper investigates the problem of vessel scheduling and bunker management with speed deviations (VSBMSD) for liner shipping in the presence of collaborative agreements. By establishing the worst-case scenario of the maximum bunker consumption function with vessel sailing speed as an independent variable, we develop a mixed-integer nonlinear programming model to minimize the total liner shipping route service cost. A piecewise linear secant approximation method is designed, and then a CPLEX solver is used to solve the problem. The results of the computational experiments conducted for the AEMX route indicate that VSBMSD in the presence of collaborative agreements can enable shipping companies to design vessel schedules reasonably and reduce the total cost of liner shipping route service by at least 2.95% compared to the results from similar studies. INDEX TERMS liner shipping; vessel scheduling; bunker management; speed deviation; collaborative agreement; robust optimization.

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