In the manufacture of mechanical heart valves, very high precision man
ufacturing and quality control is an absolute necessity. Since a mecha
nical heart valve consists of a number of components, it is imperative
that the components match precisely. Motivated by this need in heart
valve manufacturing, we study a new production control model for a pro
duct comprised of matching components. The model is also applicable to
other production systems for manufacturing high precision products re
quiring careful matching of components. For a two-component case, we p
rove that a ''greedy'' production sequencing rule is optimal. Based on
this result, we then develop an effective greedy heuristic sequencing
rule for more general cases. An extensive empirical study is used to
evaluate the performance of this and one other heuristic rule.