We examine the component procurement problem in a single-item, make-to-stock assembly system. The suppliers are uncapacitated and have independent but non-identically distributed stochastic delivery lead times. Assembly is instantaneous, product demand follows a Poisson process and unsatisfied demand is backordered. The objective is to minimize the sum of steady-state holding and backorder costs over a pre-specified class of replenishment policies. To keep the analysis tractable, we impose a synchronization assumption that no mixing occurs between sets of component orders. Combining existing results from queueing theory with original results concerning distributions that are closed under maximization and translation, we derive a simple approximate solution to the problem when lead time variances are identical. In simulations, our derived policy is within 2% of optimal and significantly outperforms policies that ignore either component dependence or lead time stochasticity. It is also quite robust with respect to various model assumptions, except the synchronization one.
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