Assignment:
QUESTION- 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 52 weeks per year and 7 days per week. Following is key information either current or averaged over years of operations:
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Average demand
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1280 pairs per week
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Lead time
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6 weeks
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Order cost
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$480 per order
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Unit cost
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$18 for a pair of shoes
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Annual inventory holding cost
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30% for the whole year
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Standard deviation of daily demand
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32 pairs per day
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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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7823 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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58 pairs of shoes
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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) 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.
(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.
(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.
Hint: Use the following table to find the z-value corresponding to the desired service level.
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a*
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0.80
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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 = NORM.S.INV(a*)
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0.84162
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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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