Consider the Reorder Point inventory control for the following setting: annual demand = 15,000; order cost = $50; carrying cost = 20% per year; item value = $20; Average lead time = 2 weeks; stockout cost = $5/unit short; probability of being in stock = 80%; standard deviation of demand = 40/week; and standard deviation of lead time = 0.8 weeks. The optimal order size for this setting is 1174.13 units.

If the product is only sold in multiple of 800 units, how many should be ordered and what is the total cost? And, using the optimal order sizes, by what percentage does the total cost change if the Probability of being in-stock during the lead time is 90%, instead of 80%?

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