Confidence – based Optimization for the Single Period Inventory Control Model

In this thesis we introduce the issue of demand estimation. We study a problem of controlling the inventory of a single item over a single period with stochastic demand in which the distribution of the demand has an unknown parameter. We assume that the decision maker has a past demand sample and the demand distribution is known but some of its parameters are not known. We introduce some approaches to estimate the unknown parameter and depending on results from estimating the unknown parameter we identify a range of order quantities that-with confidence coefficient – contains the optimal order quantity, and then we construct an interval for the estimated expected cost that the manager will pay if he orders any quantity from the range of candidate quantities. We consider three cases, the demand has a Binomial distribution with unknown parameter , and the demand has a Poisson distribution with unknown parameter , also we consider the case in which the demand has an Exponential distribution with unknown parameter . We present numerical examples in order to clarify our strategy and to show how the confidence interval approach complements with the point estimation approach in order to give the best outlook to the manager to take a decision that achieve an optimal profit.