Minimum-cost ordering for selective assembly
研究了在选择性装配系统中，面对两个随机输入和有限匹配类别时，如何最小化输入成本。通过正态近似和上包络方法，给出了成本最优输入的闭式解，便于管理者理解和使用。
We consider the minimization of input cost for a selective assembly system which features two random inputs and a finite number of matching classes. This setup frequently arises in high-precision manufacturing when input tolerances are not tight enough for the required output precision. We determine optimality conditions for the cost-optimal input portfolio given an expected-output target, first using a normal approximation of the multinomial binning distribution, and second employing a simple upper envelope of the output objective. We show that the relative error tends to zero as the production scale becomes sufficiently large. The envelope optimization problem also yields a closed-form solution for the cost-minimizing inputs as well as total costs, which are easy to understand for managers. A numerical study tests the practicality of the envelope solution. The latter can be used as seed for a numerical solution of the exact problem, as well as a closed-form approximate solution which allows for an analysis of structural properties.