a. Average Time Between Orders = 510 bags / 4,680 bags/week ≈ 0.109 weeks
b. The reorder point should be approximately 289 bags.
c. Current Inventory Level = 320 bags + 0 bags - 10 bags = 310 bags
d. Annual Ordering Cost = (4,680 / 500) * $54/order ≈ $504.48
To solve these inventory To solve these inventory management questions, we can use the following formulas and calculations:
a. EOQ
Given:
Annual Demand = 90 bags/week * 52 weeks = 4,680 bags
Order Cost = $54/order
Annual Holding Cost = 27% of $11.70 = $3.16/bag
Plugging in the values:
EOQ = sqrt((2 * 4,680 * 54) / 3.16) ≈ 509.52 (rounded to the nearest whole number)
The EOQ is approximately 510 bags.
Average Time Between Orders = EOQ / Annual Demand
Average Time Between Orders = 510 bags / 4,680 bags/week ≈ 0.109 weeks
b. R (Reorder Point) can be calculated using the formula:
R = Lead Time Demand + Safety Stock
The desired cycle-service level is 80%, so the Z-score corresponding to that level can be found using a standard normal distribution table. Let's assume it is 1.28.
Standard Deviation of Weekly Demand = 15 bags
Lead Time Demand = Weekly Demand * Lead Time = 90 bags/week * 3 weeks = 270 bags
Plugging in the values:
Safety Stock = 1.28 * 15 bags ≈ 19.2 bags (rounded to the nearest whole number)
R = 270 bags + 19 bags ≈ 289 bags (rounded to the nearest whole number)
The reorder point should be approximately 289 bags.
c. After an inventory withdrawal of 10 bags, we need to check if it is time to reorder.
Current Inventory Level = On-Hand Inventory + Open Orders - Backorders
Current Inventory Level = 320 bags + 0 bags - 10 bags = 310 bags
d. we can use the following formulas:
Annual Holding Cost = (Q / 2) * Holding Cost per bag
Annual Ordering Cost = (Annual Demand / Q) * Order Cost
Plugging in the values:
Annual Holding Cost = (500 / 2) * $3.16/bag = $790
Annual Ordering Cost = (4,680 / 500) * $54/order ≈ $504.48
e. The annual cost saved by shifting from the 500-bag lot size to the EOQ can be calculated by finding the difference in annual holding and ordering costs.
Annual Cost Savings = Annual Holding Cost (500-bag lot size) - Annual Holding Cost (EOQ) + Annual Ordering Cost (500-bag lot size) - Annual Ordering Cost (EOQ)
a. EOQ (Economic Order Quantity) can be calculated using the formula:
EOQ = sqrt((2 * Annual Demand * Order Cost) / Annual Holding Cost)
Given:
Annual Demand = 90 bags/week * 52 weeks = 4,680 bags
Order Cost = $54/order
Annual Holding Cost = 27% of $11.70 = $3.16/bag
Plugging in the values:
EOQ = sqrt((2 * 4,680 * 54) / 3.16) ≈ 509.52
The EOQ is approximately 510 bags.
Average Time Between Orders = EOQ / Annual Demand
Average Time Between Orders = 510 bags / 4,680 bags/week ≈ 0.109 weeks
b. R (Reorder Point) can be calculated using the formula:
R = Lead Time Demand + Safety Stock
The desired cycle-service level is 80%, so the Z-score corresponding to that level can be found using a standard normal distribution table. Let's assume it is 1.28.
Standard Deviation of Weekly Demand = 15 bags
Lead Time Demand = Weekly Demand * Lead Time = 90 bags/week * 3 weeks = 270 bags
Plugging in the values:
Safety Stock = 1.28 * 15 bags ≈ 19.2 bags
R = 270 bags + 19 bags ≈ 289 bags
c.
Current Inventory Level = On-Hand Inventory + Open Orders - Backorders
Current Inventory Level = 320 bags + 0 bags - 10 bags = 310 bags
If the current inventory level falls below the reorder point (R), it is time to reorder. In this case, 310 bags < 289 bags, so it is not yet time to reorder.
d. we can use the following formulas:
Annual Holding Cost = (Q / 2) * Holding Cost per bag
Annual Ordering Cost = (Annual Demand / Q) * Order Cost
Plugging in the values:
Annual Holding Cost = (500 / 2) * $3.16/bag = $790
Annual Ordering Cost = (4,680 / 500) * $54/order ≈ $504.48
calculated by finding the difference in annual holding and ordering costs.
Annual Cost Savings = Annual Holding Cost (500-bag lot size) - Annual Holding Cost (EOQ) + Annual Ordering Cost (500-bag lot size) - Annual Ordering Cost (EOQ)
Substituting the values:
Annual Cost Savings = $
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