Multistage inventory management with expediting

After reformulating Clark and Scarf's classical serial multi-echelon model so that the lead time between adjacent echelons is one week (period), the option to expedite between each resulting echelon is added. Thus, each week requires a decision to be made at each echelon on how many units to expedite in from the next upstream echelon (to be received immediately) and how many to regular order (to be received in one week), with the remainder detained (left as is). The model can be interpreted as addressing dynamic lead time management, in which the (remaining) effective lead time for each ordered unit can be dynamically reduced by expediting and/or extended. Use of Clark and Scarf's idea of echelon stocks reduces a complex, multidimensional stocking problem to the analysis of a series of one-dimensional subproblems. What are called top-down base stock policies, which are readily amenable to managerial interpretation, are shown to be optimal. Myopic policies are shown to be optimal in the stationary, infinite horizon case. The results are illustrated numerically.