This paper considers a single-product problem for inbound lot-sizing and outbound dispatching at a third-party warehouse, where the demand is dynamic over the discrete time horizon. Each demand must be delivered into the corresponding delivery time window which is the time interval characterized by the earliest and latest delivery dates of the demand. Ordered products are shipped by heterogeneous container types. Each container type has type-dependent carrying capacity and the unit freight cost depends on each container type. Total freight cost is proportional to the number of each container type used. Also it is assumed that related cost functions are concave and backlogging is not allowed. The objective of the paper is to simultaneously determine the optimal inbound lot-sizing and outbound dispatching plans that minimize total costs which include ordering, shipping, and inventory holding costs. The optimal solution properties are characterized for the problem and then a dynamic programming algorithm is presented to find the optimal solution.