A climbing rope manufacturer makes ropes for climbing equipment and sells them directly to the consumer via a storefront at the side of their manufacturing facility. On an average day, they sell 20 climbing ropes. The standard deviation of this demand is 2 per day. The annual holding cost per unit is very inexpensive --- it has been calculated to be just $5 per rope per year. Assume 365 days in a year.

You manufacture ropes via production runs that are quite expensive. Each production run costs $9,000 in setup costs. However, the ropes are very fast to manufacture and the lead time per production run is 1 day no matter how many ropes you choose to manufacture. The cost of goods per rope is $52.

Suppose the manufacturer uses a continuous review policy to manage their production and inventory, and they endeavor to have a service level of 90%.

You may use the following table of z-values for reference.

a. What is the optimal reorder point? Answer: ROP = 22.56

b. What is the reorder quantity? Answer: Q = 5,126.40

c. What is the average inventory of ropes on hand? Avg inv level = 2565.76 d. A layperson comes in and sees thousands of ropes in storage at this rope manufacturing facility. Theyre puzzled surely it cant be efficient to have that much inventory! The owner of the shop responds. (Pick the response that best explains why they have so much inventory.)

a. Sure, there are a lot of ropes, but thats because we aim for a 90% service level! We need plenty on hand to make sure the customer is happy!

b. Sure, there are a lot of ropes, but thats because theyre cheap to store and its expensive to set up a production run! We need to be efficient when we make these!

c. Sure, there are a lot of ropes, but thats because theyre inexpensive! We need plenty of inventory on hand to meet our sales quotas!

d. Sure, there are a lot of ropes, but thats because demand is so variable! We need plenty of inventory on hand to handle spikes in demand!

Answer: B.

e. The rope company gets an opportunity to create climbing ropes for competitive courses. These ropes must be stored in very precise coils and humidity-controlled rooms to preserve their quality. This increases the annual rope holding cost to $100 per rope. Everything else is the same. What is the difference between the old order quantity and the new order quantity using these ropes costs? Answer: Difference is 3980.10 (+/- rounding error)

\begin{tabular}{|l|l|l|l|l|l|l|} \hline Z value: & 0.0 & 0.433 & 0.675 & 1.04 & 1.28 & 1.65 \\ \hline Probability: & 50% & 66.7% & 75% & 85% & 90% & 95% \\ \hline \end{tabular}