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Answer :
a. The total costs will be $2,406 higher owing to the error in EOQ caused by the forecast error. b. The total costs will be $45.01 higher owing to the error in EOQ caused by not adjusting it to reflect the reduction in ordering costs.
a. To determine the increase in total costs due to the distorted Economic Order Quantity (EOQ) caused by the forecast error, we need to compare the total costs with the incorrect EOQ to the total costs with the correct EOQ. The incorrect EOQ is calculated using the forecasted demand of 70 bags per week.
Using the formula for EOQ:
EOQ = sqrt((2 * demand * order cost) / holding cost)
Incorrect EOQ = sqrt((2 * 70 * $58) / (0.3 * $12.50)) = 105.91 bags
With the incorrect EOQ, the order quantity would be rounded up to the nearest whole number, resulting in ordering 106 bags per order. However, since the actual demand is only 45 bags per week, there would be excess inventory and higher holding costs.
The increase in total costs can be calculated by comparing the holding costs for the incorrect EOQ with the holding costs for the correct EOQ. Since the current on-hand inventory is 320 bags and there are no open orders or backorders, the holding costs for the incorrect EOQ would be:
Holding costs for incorrect EOQ = (320 + 106) / 2 * $12.50 * 0.3 = $2,406
To find the increase in total costs, we need to subtract the holding costs for the correct EOQ from the holding costs for the incorrect EOQ:
Increase in total costs = Holding costs for incorrect EOQ - Holding costs for correct EOQ
Increase in total costs = $2,406 - Holding costs for correct EOQ
b. To calculate the increase in total costs compared to what they could be if the EOQ were adjusted, we need to determine the correct EOQ based on the reduced ordering cost.
Using the formula for EOQ:
EOQ = sqrt((2 * demand * order cost) / holding cost)
Correct EOQ = sqrt((2 * 45 * $9) / (0.3 * $12.50)) = 30 bags
With the correct EOQ, the order quantity would be 30 bags per order. However, if the EOQ is not adjusted and remains at the previous value, there would be more frequent orders and higher ordering costs.
The increase in total costs can be calculated by comparing the ordering costs for the incorrect EOQ with the ordering costs for the correct EOQ. The ordering costs for the incorrect EOQ would be:
Ordering costs for incorrect EOQ = (48 weeks * 6 days/week * $58) / 365 = $54.01 per week
To find the increase in total costs, we need to subtract the ordering costs for the correct EOQ from the ordering costs for the incorrect EOQ:
Increase in total costs = Ordering costs for incorrect EOQ - Ordering costs for correct EOQ
Increase in total costs = $54.01 - $9
By not adjusting the EOQ to reflect the reduced ordering cost, the increase in total costs would be $45.01 per week.
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