Optimal Cycle Times in a Two-Stage Serial System With Set-Up and Inventory Costs

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Abstract
Two 2-stage serial production systems under constant average demand rate and infinite horizon are considered. The first and the simpler system assumes zero final product inventory; while the second assumes it nonzero but with a continuous demand. The stages have finite production rates greater than or equal to the demand rate and operate with periodic start-ups and shutdowns. No stock-outs are allowed in the inventories. Analytical results for determining a cyclic schedule with the minimum sum of set-up and inventory costs are presented. The optimal lot sizing policy for the first system involves integer splitting/merging of lots; however noninteger split/merge policy may be optimal in some instances of the second.