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We study an instance of a general production problem called the `matching problem', which involves extremely tight mating tolerances for assembly. Situations exist in industry where the production equipment used to produce components cannot meet the tolerances required for assembly. In these situations components are often sorted into different size classes and then `meted' with other components of the same size class. As a specific instance of the general matching problem, we focus on the production control of components (needles and bodies) used in fuel injectors in an actual automobile subassembly production facility. In this setting the manufacturer sorts components into class sizes such that a needle of class i can be matched with a body of class i to satisfy the tolerance requirements. We study dynamic control rules that attempt to optimize the operation of this production facility within reasonable computational limits; we further develop a bound on optimal system performance. In the application studied, the performance of the recommended heuristic is within 0.2% of a bound on optimal performance., 1. Introduction We consider a production problem involving extremely tight mating tolerances for assembly, where components are sorted into different size classes and then mated with other components of the [...]