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Carrying no spare parts would be the best strategy for what range of shortage cost?

To determine the range of shortage cost \( Cs \) where carrying no spare parts would be the best strategy, we need to consider the relationship between the carrying cost and the shortage cost.

### Given dataTo determine the range of shortage cost \( Cs \) where carrying no spare parts would be the best strategy, we need to consider the relationship between the carrying cost and the shortage cost.

### Given 
- Purchase cost per part \( C_p = 170 \) dollars
- Carrying cost \( C_c = 190\% \) of the purchase price, which means \( C_c = 1.90 \times 170 = 323 \) dollars per part
- Stockout cost \( C_s \approx 110,000 \) dollars
- Poisson distribution mean \( \lambda = 4.4 \) parts for the life of the turbine
- The optimal number of spares calculated is \( n = 11 \) parts.

### Solution approach:
The cost-benefit analysis is typically based on balancing the carrying cost and the shortage cost. For no spares to be the best strategy, the carrying cost should exceed the shortage cost. Thus, we want to find the range for \( Cs \) where the shortage cost is less than or equal to the carrying cost, meaning \( Cs \leq C_c \).

Therefore:
\[
 Cs \leq C_c = 323
\]

### Answer:
The best strategy of carrying no spare parts would apply if the shortage cost \( Cs \) is less than or equal to **323 dollars**.

Do you need any more details or explanations?

Here are some follow-up questions related to this:

1. How does the Poisson distribution influence the decision on spare parts?
2. What would happen if the mean demand for parts increased?
3. Why is the carrying cost proportional to the purchase price of parts?
4. What factors might affect the estimated shortage cost in practice?
5. How does the optimal number of spares minimize both carrying and shortage costs?

**Tip**: Understanding the balance between carrying costs and shortage costs is key in inventory management for high-value parts.

Learn how to determine the best strategy for carrying no spare parts based on cost-benefit analysis for turbine maintenance. This problem involves understanding the Poisson distribution, inventory costs, and cost estimation techniques. Suitable for Grades 11-12 students.

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