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Here we consider the problem of maximum throughput routing and scheduling for flexible manufacturing systems/cells (FMS/FMC) and processing networks. Such a system consists of a set of machines which process materials and a transport network for moving materials among the machines. The goal in this problem is to find a policy for introducing jobs into the network and routing jobs through the network that maximizes the average number of jobs entering the system per unit time. We present an 0-1 linear program formulation of the maximum throughput routing and scheduling problem. This formulation is based on an extension of the linear programming formulation of the multistage network flow problem. For small problem instances, existing 0-1 solvers can be used to find an optimal schedule. For larger problem instances, we discuss the use of linear programming relaxations to find performance guarantees and rounding techniques for extracting feasible 0-1 solutions from the linear program solution. Finally, we demonstrate the general techniques described in the paper on a large-scale example. For this example, solving the linear programming relaxation and extracting a feasible schedule produces an optimal solution.