A Subassembly Manufacturing Yield Problem with Multiple Production Runs

We consider the assembly of a product that needs to exceed a certain length. The subassemblies are manufactured with a planned length setting. The resulting lengths of the subassemblies are not known with certainty, and vary about the planned setting. After the subassemblies are manufactured, those that fall short are rerun. This process is repeated until all subassemblies exceed the required length. We build and solve a model, to specify the planned length at each run, that minimizes the expected cost of production.