The aim of this paper is to solve a multi-period supplier selection and inventory lot-sizing problem with multiple products in a serial supply chain. Compared to previous models proposed in the literature, our research incorporates a richer cost structure involving joint replenishment costs for raw material replenishment and production, and a more realistic description of the transportation costs represented as a vector of full-truck load costs for different size trucks. This problem can be displayed graphically as a time-expanded transshipment network defined by nodes and arcs that can be reached by feasible material flows. First, we propose an integrated mixed integer linear programming model that minimizes the cost over the entire supply chain for a given planning horizon. The model determines the optimal dynamic supplier selection, inventory lot-sizing, and production schedule simultaneously. Second, a sequential approach is proposed to solve the same problem. That is, a production schedule is determined first, and then a supplier selection and replenishment strategy is obtained according to that predetermined schedule. Sensitivity analysis comparing the two approaches is performed. Results show that, even though the integrated approach achieves the minimum cost, the sequential approach may be suitable for solving large-scale instances of the problem as it requires less information sharing and generates a near-optimal solution with shorter implementation time and computational effort.