Consider a retail store that uses the order-up-to model when ordering from its supplier. Orders are placed at the beginning of each week and received with a 4-week lead time. Weekly demand follows a Poisson distribution with mean 0.6.

[4 points] What is the average on-order inventory when the retail store uses an order-up-to level of S=7?

b. [4 points] What is the average on-hand inventory when the retailer store uses an order-up-to level of S=7?

c. [6 points] Suppose that the parent company of this retail store has six identical retail stores. Suppose also that all stores face the same demand and lead time as given above and that they order and hold their inventory separately. If each retail store wants to achieve an in-stock probability of at least 99.99%, what is the total on hand-hand inventory in the system?

d. [6 points] Now, suppose that the demand of these six retail stores is pooled together. So, instead of each store ordering and holding its own inventory, inventory is shared from a common pool of inventory. Everything else is the same including the target in-stock probability of 99.99%. What is the on-hand inventory now? Compare it to your answer in part c and explain the difference.