Shipping is recognised as the most important mode of transportation of goods world-wide. Safety of a ship voyage is a vital factor. Adequate manning and robust crew schedules are crucial for safety on board. In the last decades, port frequencies and container ship sizes have drastically increased, but manning levels have not been adapted. Additionally, crew sizes and work schedules on board are devised manually and based on experience. This thesis proposes a structured mathematical approach to face this challenge in an efficient manner. The problem of Ship Crew Scheduling with Rest Hours Constraints (SCSP-RHC) is specified in detail based on direct input from industry partners. An adequate and realistic integer programme is presented for the SCSP-RHC which is subject to complex legal regulations for hours of rest. Calculation runs for scenarios of interest are performed by using state-of-the-art solvers. A hybrid approach, that uses a heuristic as start solution generator for exact methods, have been developed and solves challenging instances fast. This thesis presents further performance improvement strategies to enable the calculation of real-world scenarios.