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. The online retailer operates 51 weeks per year and 7 days per week. Following is key information either current or averaged over years of operations: Average demand 1037 pairs per week Lead time 6 weeks Order cost $425 per order Unit cost $16 for a pair of shoes Annual inventory holding cost 32% for the whole year Standard deviation of daily demand 14 pairs per day Desired service level with safety stock 90% Current on-hand inventory 6315 pairs of shoes Current scheduled receipts 0 pairs of shoes Current backorders 27 pairs of shoes Backorders happen because of shortages in certain sizes. A restock order would include all sizes. Goods quantities should be rounded up to whole numbers.
Average demand 1037 pairs per week
Lead time 6 weeks
Order cost $425 per order
Unit cost $16 for a pair of shoes
Annual inventory holding cost 32% for the whole year
Standard deviation of daily demand 14 pairs per day
Desired service level with safety stock 90%
Current on-hand inventory 6315 pairs of shoes
Current scheduled receipts 0 pairs of shoes
Current backorders 27 pairs of shoes
(a) Find the Economic Order Quantity (EOQ). (Rounded up to a whole number)
(b) Find the total annual ordering and inventory-holding cost (TAC) for the EOQ. (2 decimals)
(c) Find the current inventory position (IP).
(d) 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.
(e) 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.
Hint: Use the following table to find the z-value corresponding to the desired service level. αv 0.80 0.85 0.90 0.95 0.99 z = NORM.S.INV(αv) 0.84162 1.03643 1.28155 1.64485 2.32635.