QUESTION 22 (10 points) - Fixed-Quantity Inventory Systems (FQS) ComfyShoes is an online retailer which carries various shoe lines. For simplicity, we are only interested in the number of pairs of shoes (the unit is a pair of shoes), not in differences amongst lines and sizes. The company uses a fixed-quantity inventory system (FQS) to manage their stock. Following is key information either current or averaged over years of operations:

Average demand	1050 pairs per week
Lead time	3 weeks
Order cost	$250 per order
Unit cost	$10 for a pair of shoes
Annual inventory holding cost	21% for the whole year
Standard deviation of daily demand	12 pairs per day
Desired service level with safety stock	95%
Current on-hand inventory	3190 pairs of shoes
Current scheduled receipts	0 pairs of shoes
Current backorders	11 pairs of shoes
Weeks of operation	51 weeks
Days of operation	7 days in a week

Backorders happen because of shortages in certain sizes. A restock order would include all sizes. You would need to show equations, steps, and the final results with units for full credits. Time units should be carefully treated. Goods quantities should be rounded up to whole numbers. (a)[2] Find the Economic Order Quantity (EOQ) (rounded up to a whole number). Find the average total annual cost (TAC) for the EOQ (2 decimals). (b)[1] Given the EOQ, find the average number of orders made in a year. What is the average time between orders (in days)? (c)[1] Find the current inventory position (IP). (d)[3] Find the reorder point without safety stock R(AD). State the ordering rule. Based on the current IP, determine if the company would make an order and state the order quantity. Sketch the normal demand distribution in the lead time to illustrate the service level. Then, loosely sketch how the system would operate over time (movement of IP over time). (e)[3] Find the reorder point with safety stock R(ST). State the ordering rule. Based on the current IP, determine if the company would make an order and state the order quantity. Sketch the normal demand distribution in the lead time to illustrate the service level. Then, loosely sketch how the system would operate over time (movement of IP over time). Hint: Use the following table to find the z-value corresponding to the desired service level.

v	0.80	0.85	0.90	0.95	0.99
z = NORM.S.INV(v)	0.84162	1.03643	1.28155	1.64485	2.32635