A dynamic production and transportation model with heterogeneous vehicle types

This paper considers the single-product production and transportation problem with dynamic demand and a discrete, finite time horizon, which is an extension of the classical dynamic lot-sizing problem. The model allows heterogeneous vehicle types to immediately transport the finished product in the same period it is produced. Moreover, each vehicle has type-dependent carrying capacity and the unit freight cost for each vehicle type depends on its capacity. The total freight cost is proportional to the number of each vehicle type employed. Also, the model assumes that the production and inventory cost functions may differ among time periods, and backlogging is not allowed. The objective of this study is to simultaneously determine the optimal production and transportation policy that minimizes the total system cost (production cost, inventory ding cost, and freight cost) to satisfy the dynamic demands over the finite time horizon. The paper characterizes the rules of the optimal policy, and then uses these to construct a dynamic programming algorithm to compute an optimal policy. A numerical example is then presented to demonstrate the procedure.