This paper considers a two-location production and inventory model for a single product which can be produced and demanded at each of two locations. Demands during a finite number of discrete time periods are known and must be satisfied by production, inventory or transshipment. We consider the change of production capacity. The costs to be incurred are restricted to production, inventory and transshipment costs, and all cost functions we assumed to be concave. The objective is to minimize the total cost of production, inventory and transshipment. The model is formulated as a shortest path problem for an acyclic network from which properties associated with optimal solutions are derived. Using these properties. we develop a dynamic programming algorithm that finds optimal solutions for problems.