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Performance analysis and optimization of assemble-to-order systems with random lead times. (English) Zbl 1163.90473
Summary: 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 $$M/G/\infty$$ queues with a common arrival stream. We show that unlike the standard $$M/G/\infty$$ 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.

##### MSC:
 90B30 Production models 90B22 Queues and service in operations research
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