QUESTION 23 (10 points) - Fixed-Quantity Inventory Systems (FQS) ComfyShoes is a
ID: 372157 • Letter: Q
Question
QUESTION 23 (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. The online retailer operates 51 weeks per year and 7 days per week. Following is key information either current or averaged over years of operationss Average demand Lead time Order cost Unit cost 1037 pairs per week 6 weeks S425 per order 16 for a pair of shoes 32% for the whole year 14 pairs per day Annua inventory holding cost Standard deviation of daily demand Desired service level sith safety stock Current on-hand inventory Current scheduled receipts Current backorders | 9096 6315 pairs of shoes O pairs of shoes 27 pairs of shoes 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) (b)[1] Find the total annual ordering and inventory-holding cost (TAC) for the EOQ. (2 decimals) (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 (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. Hint: Use the following table to find the z-value corresponding to the desired service level atv 0.80 0.85 0.90 0.95 0.99 NORM.S.INV(av) 0.841621.036431.28155 1.64485 2.32635Explanation / Answer
Economic Order Quantity ( EOQ )
= Square root ( 2 x F X D/C)
F = Order cost = $480 /order
D = Annual demand = 1280 x 52 = 66560
C= Annual inventory holding cost = 30% of unit cost = 0.3 x $18 = $5.4 per unit per year
EOQ
= Square root ( 2 x 480 X 66560 / 5.4)
= square root ( 11832888.88)
= 3440 ( rounded off to nearest whle number)
ECONOMIC ORDER QUANTITY = 3440
Inventory holding cost, $ = EOQ/ 2 x C = 3440/2 X 5.4 = $9288
Total annual ordering cost, $ = D/EOQ x F = 66560/3440 x 480 = $ 9287.44
Current inventory position :
Inventory on hand = 7823 pairs
Current backorders = 58 pairs
Available to promise = 7823 – 58 pairs = 7765 pairs
Reorder point without safety stock
= Average demand/ week x Lead time ( in weeks)
= 1280 x 6
= 7680 units
Available to promise quantity 7765 pairs
= 7765/ 1280 = 6.066 weeks of inventory
Since lead time is of 6 weeks, it is right time to order
Order quantity = EOQ = 3440
Safety stock
= Z ( Z value for 0.85) x standard deviation of daily demand
= 1.03643x 32
= 33.16 ( say 33 if rounded off to nearest whole number)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.