Continuous review (S,s) policies for multiechelon distribution systems

The purpose of this research is to develop improved analytical methods for predicting performance of inventory control policies in multiechelon distribution systems. Specifically the difficult problem of computing service levels, as measured by average number of units short per unit time, is addressed. The research covers a one-warehouse/N-retailer system that is operating under continuous review (S,s) policies. The external demands in this study are assumed to follow either a stationary Poisson or stuttering Poisson process. For the external demand with Poisson process, both identical and non-identical retailer cases are investigated. For the external demand with stuttering Poisson process, only the identical retailer case is considered. The non-identical retailer case and the identical retailers with external demand following a stuttering Poisson process have likely never been addressed.;The basic frameworks for constructing methodologies to predict service levels are similiar. Two important features in the methodologies are addressed: the number of orders placed at the warehouse during the warehouse reordering lead time, and the delay time of retailers. For the former, the exact probability mass function of the number of orders placed at the warehouse by individual retailers is derived. These probability mass functions are numerically convoluted to determine the probability mass function of total orders placed at the warehouse. It is shown that this probability mass function converges to a discrete normal as the number of orders placed at the warehouse increases. For the determination of the mean and variance of the delay time, an approximate probability density function is derived based on the distribution of the number of orders placed at the warehouse during the warehouse reordering lead time.;The performance of the new methodologies is tested by comparison with simulation results. It is shown that overall, the new methodologies provide sufficient accuracy in estimating the service levels for a reasonable range of parameter values. In addition, optimization algorithms based on one-dimensional search are developed to determine the economic inventory policies. It is shown that the algorithms can be implemented practically.