Book Description

This dissertation presents optimal and suboptimal procedures to solve inventory control problems that have non-stationary demand and partial information. In each period, the underlying demand distribution may change according to a known Markov process. The problem is characterized as partial information because some parameter of the demand probability distribution is not known with certainty; however, there is a known prior distribution for the unknown parameter. In one case, there is a probability density function for the demand that has at least one unknown parameter, but this parameter has a known probability distribution. In another case, there is a set of candidate demand probability distributions. The parameter which indicates which demand is in effect at any given time is unknown, but has a known probability mass function. The control strategies are adaptive because the controllers learn information about these unknown parameters over time and adapt accordingly. Because of the complexity of these problems, managers often estimate the unknown parameters and make decisions assuming the estimate is correct. The computational results presented in this dissertation demonstrate that there exist efficient and effective optimal and sub optimal procedures to solve these problems that potentially provide large cost savings compared with this current practice. The control strategies include open loop feedback and limited look ahead control for a finite horizon problem, which are compared to optimal and certainty equivalence control policies. A grid approximation and upper and lower bounds for an infinite horizon problem are also developed.