Optimal Location of Inspection Stations in a Multistage Production Process

Abstract

A method for determining where to locate the inspection stations in a multistage production process with imperfect inspection is presented. Dynamic programming is used to establish that the optimal expected total cost function at every stage is piecewise linear and concave. While the optimal policy at every stage usually consists of one “inspect” region and one “do not inspect” region, this policy structure is found not to hold in general. A computation scheme based directly on the dynamic programming formulation is proposed, a time-sharing computer program is discussed, and the results of an example problem are presented.