Optimizing the quality control station configuration

We study unreliable serial production lines with known failure probabilities for each operation. Such a production line consists of a series of stations, existing machines, and optional quality control stations (QCSs). Our aim is to decide on the allocation of the QCSs within the assembly line, so as to maximize the expected profit of the system. In such a problem, the designer has to determine the QCS configuration and the production rate simultaneously. The profit maximization problem is approximated assuming exponentially distributed processing times, Poisson arrival process of jobs into the system, and the existing of holding costs. The novel feature of our model is the incorporation of holding costs that significantly complicated the problem. Our approximation approach uses a branch and bound strategy that employs our fast dynamic programming algorithm for minimizing the expected operational costs for a given production rate as a subroutine. Extensive numerical experiments are conducted to demonstrate the efficiency of the branch and bound procedure for solving large scale instances of the problem and for obtaining some qualitative insights.