Planning order release dates for multilevel linear supply chain with random lead times

A multilevel linear supply chain is considered in this paper. The lead times at each level are random discrete variables, and the finished product demand is fixed and known. The objective is to minimize the sum of holding and backlogging costs for the finished product. We propose a novel mathematical model which gives the optimal order release dates for the components. From a theoretical point of view, this formulation is equivalent to the discrete Newsboy model. Numerical tests are reported.