QUESTION 28 (10 points) FixedQuantity Inventory Systems (FQS) AllShoes is an onl
ID: 457775 • Letter: Q
Question
QUESTION 28 (10 points) FixedQuantity Inventory Systems (FQS)
AllShoes 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. Following is key information either current or averaged over years of operations:
Average demand
1200 pairs per week
Lead time
5 weeks
Order cost
$400 per order
Unit cost
$20 for a pair of shoes
Annual inventory holding cost
20% for the whole year
Number of weeks
52 weeks per year
Standard deviation of weekly demand
90 pairs
Desired service level with safety stock
95%
Current onhand inventory
6150 pairs of shoes
Current scheduled receipts
0 pairs of shoes
Current backorders
50 pairs of shoes
In the following, you need to show equations, steps, and final results with units. Giving only the final results yields half of the credits. All quantities should be rounded up to a whole number.
Backorders happen because of shortages in certain sizes. A new order will include all sizes.
(a)[2] Find the Economic Order Quantity (EOQ). (Rounded up to a whole number)
(b)[2] Find the total annual ordering and inventoryholding cost (TAC) for the EOQ. (c)[2] Find the current inventory position (IP).
(d)[2] 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. (e)[2] 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. Hint: Use the following table to find the zvalue corresponding to the desired service level.
Service level = *
0.85
0.90
0.95
0.99
zvalue = NORM.S.INV(*)
1.03643
1.28155
1.64485
2.32635
QUESTION 29 (10 points) FixedPeriod Inventory Systems (FPS)
A corner store carries milk jugs with the following current and average information.
Average demand
20 jugs per week
Lead time
4 days
Order cost
$10 per order
Unit cost
$2 per jug
Annual inventory holding cost
600% for a year
Number of weeks
52
Standard deviation of weekly demand
3 jugs per week
Desired service level with safety stock
85%
Current onhand inventory
16
Current scheduled receipts
0
Current backorders
0
The store follows a fixedperiod inventory system (FPS) to manage its carriage of milk jugs. The corner store is open for 52 weeks per year and 7 days per week. Because milk is perishable, a jug held for a month costs half of its cost, which is 50% per month or 600% per year.
In the following, you need to show equations, steps, and final results with units. Giving only the final results yields half of the credits. Intervals and quantities are rounded up to whole numbers. You should work with a time unit of days, find average daily demand and standard deviation of daily demand, and scale those daily measures to find necessary values. (a)[2] Find the Economic Order Quantity (EOQ). (Rounded up to a whole number)
(b)[1] Based on part (a), find the time interval between reviews T in days. (Rounded up) (c)[1] Find the current inventory position (IP).
(d)[3] Given that no safety stock is considered, find the replenishment level M(AD). Explain how this inventory system would operate. If today is the review day, what is the order quantity? (e)[3] Given that the corner store carries safety stock and aims for the desired service level, find the replenishment level M(ST). Explain how this inventory system would operate. If today is the review day, what is the order quantity?
Hint: Use the following table to find the zvalue corresponding to the desired service level.
Service level = *
0.85
0.90
0.95
0.99
zvalue = NORM.S.INV(*)
1.03643
1.28155
1.64485
2.32635
QUESTION 30 (10 points) SinglePeriod Inventory Model
A pharmacy considers selling graduation congratulation cards with 2016 printed on the cards. These cards are typically released in April and need to be sold before end of June for full value.
After June, the remaining cards would be marked down to get sold. For each card, the item cost is $1.49, the selling price from April to June is $4.99, and marked down price after June is $0.98. In the following, you need to show equations, steps, and final results with units. Giving only the final results yields half of the credits. Answers are in millions using 5 decimals (example: 1.76384 million cards). For simplicity, all taxes and other costs are not considered.
(a)[5] Given that the pharmacy's historical demand is uniformly distributed from 1.2 million to
1.8 million cards, determine how many cards the pharmacy should carry this year.
(b)[5] Given that the pharmacy's historical demand is normally distributed with mean 2.1 million and standard deviation to 0.18 million cards, determine how many cards the pharmacy should carry this year.
Hint: Use the following table to find the zvalue.
*
0.06359
0.12718
0.50000
0.87282
0.93641
z = NORM.S.INV(*)
1.52531
1.13981
0.00000
1.13981
1.52531
Average demand
1200 pairs per week
Lead time
5 weeks
Order cost
$400 per order
Unit cost
$20 for a pair of shoes
Annual inventory holding cost
20% for the whole year
Number of weeks
52 weeks per year
Standard deviation of weekly demand
90 pairs
Desired service level with safety stock
95%
Current onhand inventory
6150 pairs of shoes
Current scheduled receipts
0 pairs of shoes
Current backorders
50 pairs of shoes
Explanation / Answer
We have most of the information given in tabular format so putting the value in formulae,
Average Annual Demand Quantity = 1200 per week x 52 weeks = 62400 shoes
Carrying Cost Per Unit = 20% of $20 = $4
1)
EOQ = SQRT(2 × Average Annual Demand Quantity × Cost Per Order / Carrying Cost Per Unit)
EOQ = SQRT (2 × 62400 x 400 / 4)
EOQ = 3532.70
Economic Order Quantity will be 3532 Units
2)
Total Annual Ordering cost for EOQ
Average Annual Demand Quantity = 1200 per week x 52 weeks = 62400 shoes
Number of Orders of EOQ required to meet the demand = 62400 / 3532 = 18 Orders (approx)
Total Ordering cost = 18*400 = $7200
Total inventory holding cost for EOQ
Inventory holding cost for EOQ = 3532 * $4 = $14128
Inventory holding cost for the Annual Deman Qty = 62400 * $4 = $249600
3)
Current inventory position (IP) = Current onhand inventory + Current scheduled receipts - Current backorders
IP = 6150 + 0 - 50 = 6100
4)
Reorder point without safety stock
Re-order point = Lead time demand + Safety Stock
Lead time Demand = Lead time * Average demand during that period
LT Demand = 5 weeks * 1200 per week
LT Demand = 6000 pairs per week
Safety Stock = 0 (in case of without ss)
Re-order point = 6000 pairs
5)
Reorder point with safety stock
Service level = 95% so, z = 1.64485
Standard deviation of weekly demand = 90 pairs
Re-order point = Average Lead Time*Average Demand + Service Level*(Avg. Lead Time*Standard Deviation of Demand2 + Avg. Demand2*Standard Deviation of Lead Time2)
= 5 weeks * 1200 pairs + 1.64485*(5 weeks * 902 + 12002 * 0)
= 6000 + 331
= 6331 pairs of shoes
6)
Current inventory position = 6100
Re-order point = 6331
IP < ROP so Company needs to place an order for EOQ i.e. 3532 pairs
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