An Approach to Multivariate Bounded Process Adjustment

Multivariate process adjustment in the presence of fixed adjustment costs is investigated in this paper. A fixed adjustment cost leads to a trade-off between adjusting a process continuously and allowing the process to drift until a bound is violated. The problem of determining the best bounded adjustment policy and the optimal bounded adjustment parameter is addressed. Although the univariate bounded adjustment problem has received interest in the past, there has been little focus on the multivariate case in the literature. It has been shown that in the univariate case, the shape of the optimal adjustment policy is a dead band. Determining the shape of the optimal dead region and the parameter that defines this region in the multivariate case is a difficult problem. A State-Space model is formulated for the multivariate bounded process adjustment problem and a Kalman Filter based controller is used. With the help of simulation, the optimal bounded adjustment parameter is computed for two dead regionsubspace shapes. A numerical illustration of a semiconductor manufacturing process demonstrates the optimal bounded adjustment policy.