Question: Risk pooling in a supply chain. Example 4.19 (page 254) shows that the standard deviation of demand on the centralized warehouse is less than the

Risk pooling in a supply chain. Example 4.19 (page 254) shows that the standard deviation of demand on the centralized warehouse is less than the sum of standard deviations of the demands on each of the decentralized warehouses. The smaller the standard deviation of demand on the centralized warehouse, the less safety stock needs to be held. For given standard deviations of demand on two decentralized warehouses, what is the ideal value of ρ that will result in the least safety stock needed at a centralized warehouse? (Hint: Refer to Rule 3 of the rules for variances.)

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