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A manufacturer produces a product in batches of Q units to be delivered to a customer. The customer has an annual requirement of D units. The manufacturer's production rate is P units/year, its holding cost rate is h dollars/dollar/year. The unit variable production cost is C dollars and the fixed cost to setup a manufacturing batch is S dollars per batch.
For each batch produced, half of the batch (i.e. Q/2 units) is shipped to the customer as soon as these are completed.
The remaining units are shipped when the whole lot is completed. In other words, each production batch is delivered to customer in two equal sized sub-batches.
What is the manufacturer's average inventory level? What is the customer's average inventory level?
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