Ocean shipment plays an important role in international trade and internationallogistics. How to improve revenue, reduce cost and improve utilization of ships hasa significant impact to the liner shipping industry. For the liner shipping industry,slot allocation problems of loaded container and empty container usually are notconsidered at the same time. If a container department wants to ship emptycontainers, they need to find unused slots. Sometimes the container department hasto ship empty containers by using an empty container ship. This situation is usuallyincreases cost for liner shipping industry. This research discusses slot allocationtransportation problems by considering container loading, container emptying,container renting, container returning and container holding by constructing amathematic model. Two examples are developed to illustrate the mathematic model.The first only considers the program with six ports and one liner. The secondexample elaborates the details of a liner which operates routes between Far East andthe west coast of the U.S. Several scenarios are discussed and the correspondingcomputational results are presented.