Running Bears Workout Gear, an online athletic apparel retailer, sells a fitness accessory called "the Protector" $-$ so named because it protects the user to from a wide variety of weather conditions. This versatile product is a tubular piece of stretchy fabric which can be worn many ways $($around the neck, as a head scarf, as a face shield, etc.$)$ and protects its user from sun, wind, dust, cold, and heat. The product is just one of many varieties of this type accessory currently on the market. The Protector comes in several different colors and patterns, but it is a one$-$size$-$fits$-$all design, so the group of SKUs is managed as a single item.

The Protector is a steady seller throughout the year. Weekly orders average $10,000$ and vary with a standard deviation of $3,200$ units. The cost to place an order with Running Bears$$ supplier is $$380$ and the holding cost is estimated to be $13\%$ per dollar of inventory per year. The time it takes to receive a replenishment order from when the order is placed is $1\mathrm{.}1$ weeks. Although the supplier and shipping service are reliable, the international supply chain is not perfect, therefore, lead time varies with a standard deviation of $0\mathrm{.}25$ weeks. One unit of The Protector costs Running Bears $$4\mathrm{.}00$ to purchase.

The Company$$s CFO has noticed inventory costs are very high and wonders if anything can be done to reduce cost in this area. The COO, however, argues that the inventory is needed to meet the quick response time customers want. The marketing department is worried that if inventory is reduced and The Protector is out of stock when customers want to place an order, they$$ll just go to a competitor$$s website.

To quell these stockout fears, the previous supply managers set up a continuous review, fixed order quantity replenishment system to maintain enough inventory to meet customer demand. The policy is set to place an order of $10,000$ units when the inventory level drops to $30,000$ units.

Although the CEO dislikes the high inventory costs, the rest of the C$-$team has persuaded her to maintain the current replenishment policy because $$the customer comes first.$$ You may be able to find a way to lower cost and provide the customer what they need. Your job is to present a detailed inventory analysis to the C$-$level team and suggest ways to reduce inventory cost while maintaining a high level of product availability and customer satisfaction. The marketing team has analyzed online customer activity and found that if stockouts occur in $15\%$ or less of all replenishment cycles, customers will remain loyal, and that if at least $93\%$ of orders are filled from product in inventory, no sales will be lost, so you decide to set CSL and product fill rate targets accordingly.

Use the Canvas version of the above narrative to fill in the blanks with numbers you get when you open the exam and then answer the following questions in blue or black ink $($you may type answers into this document if you do not have a printer$).$ Do not round calculations until you have reached the final answer. All answers except Cycle Service Level and fill rate should be rounded to the nearest whole number. CSL and fr should be rounded to $2$ decimal places. Submit a legible $($check to make you$$re your scan is easily readable$)$ scanned pdf copy of your finished handout on Canvas, or upload this document with the numbers typed in blanks.

$$

Questions $1-21(4$ points each$)$

$1.$ D $($weekly$)10,000$ units

$2.\backslash$sigma D $3,200$ units

$3.$ coefficient of variation for demand $0\mathrm{.}32$

$4.$ S $$380$

$5.$ h $13\%$

$6.$ L $1\mathrm{.}1$ weeks

$7.$ sL $0\mathrm{.}25$

$8.$ C $$4\mathrm{.}00$

$9.$ Current Q $10,000$

$10.$ Current ROP $30,000$ units

$11.$ DL $11,000$ units

$12.\backslash$sigma L $\_\_\_\_\_\_\_\_\_\_$

$13.$ Current safety stock $19,000$ units

$14.$ Current CSL $0\mathrm{.}98$

$15.$ Current ESC $24,000$ units

$16.$ Current product fill rate $0\mathrm{.}99$

$17.$ Current Average Inventory Level $\_\_\_\_\_\_\_\_\_\_$

$($remember$,$ average inventory includes cycle inventory and safety stock$)$

$18.$ Current annual inventory holding cost $($using average inventory$)\_\_\_\_\_\_\_\_\_\_$

$19.$ Current annual ordering cost $\_\_\_\_\_\_\_\_\_\_$

$$

Based on marketing$$s customer activity analysis, answer questions $20$ & $21$:

$20.$ What is the target CSL$?85\%$

$21.$ What is the target product fill rate? $93\%$

Question $22(6$ points$)$

$22.$ EOQ $($use annual demand to calculate, $52$ weeks$/$year$)\_\_\_\_\_\_\_\_\_\_$

Using the EOQ you calculated in question $22$ as the new fixed order quantity, answer the following $($applies to questions $23-25$ when Q is needed$)$:

Question $23(4$ points$)$

$23.$ What is the minimum safety stock level needed to meet the target CSL$?\_\_\_\_\_\_\_\_\_\_$

Questions $24-25(3$ points each$)$

$24.$ What is the minimum ROP needed to meet the target fill rate? $\_\_\_\_\_\_\_\_\_\_$

$($Hint: Use goal seek$)$

$25.$ What is the ROP needed to ensure both the target fill rate and cycle service level measures are met? $\_\_\_\_\_\_\_\_\_\_$

$$Bonus$$ question $(4$ points$)$

What is the cost savings, if any, when you use the EOQ as the fixed order quantity and set the ROP at t