Fixed‐Quantity Inventory Systems (FQS) All Shoes 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
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1200 pairs per week
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Lead time
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5 weeks
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Order cost
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$400 per order
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Unit cost
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$20 for a pair of shoes
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Annual inventory holding cost
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20% for the whole year
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Number of weeks
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52 weeks per year
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Standard deviation of weekly demand
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90 pairs
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Desired service level with safety stock
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95%
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Current on‐hand inventory
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6150 pairs of shoes
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Current scheduled receipts
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0 pairs of shoes
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Current backorders
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50 pairs of shoes
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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 inventory‐holding 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 z‐value corresponding to the desired service level.
Service level = α*
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0.85
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0.90
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0.95
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0.99
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z‐value = NORM.S.INV(α*)
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1.03643
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1.28155
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1.64485
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2.32635
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QUESTION 29 (10 points) ‐ Fixed‐Period Inventory Systems (FPS)
A corner store carries milk jugs with the following current and average information.
Average demand
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20 jugs per week
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Lead time
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4 days
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Order cost
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$10 per order
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Unit cost
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$2 per jug
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Annual inventory holding cost
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600% for a year
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Number of weeks
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52
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Standard deviation of weekly demand
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3 jugs per week
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Desired service level with safety stock
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85%
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Current on‐hand inventory
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16
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Current scheduled receipts
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0
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Current backorders
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0
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The store follows a fixed‐period 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 z‐value corresponding to the desired service level.
Service level = α*
|
0.85
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0.90
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0.95
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0.99
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z‐value = NORM.S.INV(α*)
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1.03643
|
1.28155
|
1.64485
|
2.32635
|
QUESTION 30 (10 points) ‐ Single‐Period 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 z‐value.
α*
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0.06359
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0.12718
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0.50000
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0.87282
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0.93641
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z = NORM.S.INV(α*)
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‐1.52531
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‐1.13981
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0.00000
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1.13981
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1.52531
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