Performance analysis and optimization of assemble-to-order systems with random lead times

We study a single product assembly system in which the final product is assembled to order whereas the components (subassemblies) are built to stock Customer demand follows a Poisson process and replenishment lead times for each component are independent and identically distributed random variables For any given base-stock policy the exact performance analysis reduces to the evaluation of a set of M/G/infinity queues with a common arrival stream We show that unlike the standard M/G/infinity queueing system, lead time (service time) variability degrades performance in this assembly system We also show that it is desirable to keep higher base stock levels for components with longer mean lead times (and lower unit costs) We derive easy to compute performance bounds and use them as surrogates for the performance measures in several optimization problems that seek the best trade off between inventory and customer service Greedy type algorithms are developed to solve the surrogate problems Numerical examples indicate that these algorithms provide efficient solutions and valuable insights to the optimal inventory/service trade-off in the original problems.