This thesis focuses on the problem of designing a material flow network for a given block layout. For an efficient design of a network, locations of input and output points, flow paths, and the smoothness of material flows are considered simultaneously. The problem is formulated as a mixed integer program by representing a block layout as a directed graph. For the problem with the objective of minimizing the sum of transportation cost, flow path construction cost and penalty cost for non-smooth material flows, we suggest two heuristic algorithms based on the LP-relaxation and the Lagrangian relaxation techniques. To evaluate performance of the suggested algorithms, a series of computational experiments is performed on well-known problem instances as well as randomly generated test problems. Results show that the suggested algorithms give good solutions in a reasonable amount of computation time.