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This study addresses a real-life multiship routing and scheduling application with inventory constraints that arises in pickup and delivery operations of different types of crude oil from various offshore oil rigs (platforms) to coastal terminals. Oil transportation largely results from the need to maintain inventories at each supply point (platform) between minimum and maximum levels, considering production rates in these operational points, and to meet demands of different oils in the terminals within the planning time horizon. Routing and scheduling of the available fleet aims to obtain solutions of minimum total costs, subject to various constraints such as the maximum volume of cargo carried on each ship, simultaneous cargo unloading in some terminals, conditions that rule ship docking in offshore platforms and terminal berths, among others. In this research, we modify and extend inventory constrained maritime routing and scheduling models to appropriately represent the problem of a case study at a Brazilian company and to solve small-to-moderate instances based on real data. We also present a matheuristic to deal with larger problem instances. Solution evaluation by company experts indicates that the model and this hybrid heuristic properly represent the problem and highlights the potential of their application in practice.