Abstract ABSTRACT: Control over cost processes can be exercised either via Markovian control, i.e., in the traditional manner by investigating the process whenever the reported cost exceeds a fixed critical cost, or via Bayesian control, i.e., by using the reported cost to update the probability of the process being out of control at the time of the next cost signal, and investigating the process whenever such posterior probability exceeds a fixed critical value. This paper compares the long-run expected cost per period of the best Markovian control (Dittman-Prakash policy) vis-a-vis the optimal control (the best Bayesian policy) for a wide range of cost situations. It is observed that Markovian control performs almost as well as the optimal control unless the in-control cost has at least a moderately large coefficient of intrusion (or relative uncertainty) and a substantially greater dispersion than the out-of-control cost. Sensitivity analysis shows that this observation is reasonably robust with respect to changes in the values of other parameters.
Dittman et al. (Sun,) studied this question.