| This dissertation focuses on issues associated with the value of information in models of sequential decision making under uncertainty. All of these issues are motivated by inventory management problems. First, we study the effect of the accuracy of inventory counts on system performance when using a zero-memory controller in an inventory system that is modeled as a partially observed Markov decision process (POMDP). We derive conditions for which improving the accuracy of inventory counts will either (i) improve system performance, (ii) degrade system performance or (iii) will not affect system performance. With a computational study, we determine the range of profitability impacts that result from inaccurate inventory counts when using reasonable zero-memory control policies.; Second, we assess the value of demand observation quality in an inventory system with Markovian demand and lost sales. Again, the POMDP serves as a problem model, and we develop computationally tractable suboptimal algorithms to enable the computation of effective lower bounds on system profitability when demand observations are noise-corrupted. We then extend our results to consider the effects that product substitution has on system performance. We show that systems with low demand variability, high holding cost levels, and high levels of substitution benefit more from demand observability than systems with high demand variability, low holding cost levels, and low levels of substitution.; Third, to enhance our understanding of sequential inventory control with substitutable products, we analyze a two-item inventory problem with known deterministic primary demand, but stochastic one-way substitution. We model this problem as a MDP and show that a decision rule that minimizes the single period cost function, when applied at every decision epoch over the infinite horizon, is an optimal policy for the infinite horizon problem. A definition of increased substitutability is presented, and it is shown that increased substitutability never increases optimal expected total discounted cost. |
