This paper considers an inbound ordering and outbound dispatching problem for multi-products and multi-vehicles in a third-party distribution center. The demands are dynamic over a discrete and finite time horizon, and replenishing orders are shipped in various transportation modes and the freight cost is proportional to the number of vehicles used. Any mixture of products is loaded onto any type of vehicles. The objective of the study is to simultaneously determine the inbound lot-sizes, the outbound dispatching sizes, and the types and numbers of vehicles used to minimize total costs, which consist of inventory holding cost and freight cost. Delivery time window is one of the general dispatching policies between a third-party distribution center and customers in practice. In the policy, each demand of product for a customer must be delivered within the time window without penalty cost. We derive mixed integer programming models for the dispatching policy with delivery time windows and on-time delivery dispatching policy, respectively and analyze the effect on a dispatching policy with delivery time windows by comparing with on-time delivery dispatching policy using various computational experiments.