$($a$)$ Do you agree with the following statement: "According to the EOQ model, when the setup cost

increases, the optimal order cycle has to increase." Explain. $($Hint: The optimal batches per

year are given by D$/$EOQ and so the "optimal order cycle," defined as the time from the two

adjacent orderings, is equal to $EO\frac{Q}{D}.)$

$($b$)$ Suppose you operate a store. The weekly average demand for an item sold in your store is $20$

units. Your upstream supplier charges $$100$ for each item sold to you. The annual holding cost

is $20\%$ of the item cost. It costs $$160$ to place an order. The lead time is $1$ week and your store

operates $50$ weeks per year.

i$)$ What is the optimal order quantity?

ii$)$ Suppose you want to achieve a $95\%$ service level during the lead time, and the weekly demand

is normally distributed with a mean of $20$ and standard deviation of $10$ units. What will be your

reorder point? What will be the safety stock level? $(z=1\mathrm{.}645)$

$|$

iii$)$ Suppose you want to achieve a $95\%$ service level during the lead time, and the distribution of

weekly demand is listed in the following table. What will be your reorder point? What will be

the safety stock level?