ComfyShoes is an online retailer which carries various shoe lines. For simplicit
ID: 372076 • Letter: C
Question
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 fixedquantity 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 onhand 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 onhand 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 inventoryholding 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 zvalue 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
Explanation / Answer
Solution:
a) Formula for EOQ
= square root of {(2*Annual demand*cost per order) / (holding cost per unit per year)}
Annual Demand = 1280*52 = 66,560
Ordering cost = $480 per order
Holding cost =$18*30% = 5.4
Therefore, EOQ = square root of {(2*66,560*480) / (5.4)}
= square root of {(63,897,600) / (5.4)}
= square root of 11,832,890 = 3,440
b) Total annual ordering cost = Number of orders * cost to place a single order
= (Annual demand / EOQ) * Ordering cost
=(66,560 / 3,440) * $480 per order = $9,287.44
Inventory holding cost = (EOQ / 2) * holding cost per unit per year
= (3,440 / 2) * 5.4 = $9,288
Total annual ordering cost and Inventory holding cost for EOQ = $9,287.44 + $9,288 = $18,575.44
c) Computation of current inventory position:
Formula for Inventory position (IP) = on-hand quantity (OH) + any orders placed but which have not arrived (called scheduled receipts, SR) - any backorders (BO)
=> IP = OH + SR – BO = 7,823 + 0 – 58 = 7,765
d) Computation of re-order point without safety stock:
First we need to find the demand per day
d = 1280/7
d = 183 demand per day
m = lead time = 6weeks
r = dm
r = 183 *(6)
r = 1098 units is the reorder point
e) Computation of re-order point with safety stock:
= (demand per day * lead time) + (Z at 85% * standard deviation 32 per day)
= 1098 + (1.03643 * 32)
= 1098 + 33.17 = 1131 units