Tax Preparers Inc. works 250 days per year. The company uses adding machine tape at a rate of eight rolls per day. Usage is believed to be normally distributed with a standard deviation of three rolls during lead time. The cost of ordering the tape is $10 and holding costs are $0.30 per roll per year. Lead time is two days.
(a) Calculate the economic order quantity
(Round your answer to 1 decimal place, the tolerance is +/-0.1.)
(b) What reorder point will provide an order cycle service level of 97 percent?
tapes (Round up your answer to the nearest whole number.)
(c) How much safety stock must the company hold to have a 97 percent order-cycle service level?
units (Round your answer to 2 decimal places, the tolerance is +/-0.01.)
(d) What reorder point is needed to provide an order-cycle service level of 99 percent?
tapes (Round up your answer to the nearest whole number.)
(e) How much safety stock must the company hold to have a 99 percent order-cycle service level?
units (Round your answer to 2 decimal places, the tolerance is +/-0.01.)
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To calculate the economic order quantity (EOQ), we can use the following formula:
EOQ = √((2DS)/H)
Where:
D = Demand per period (rolls/day)
S = Setup or ordering cost per order ($)
H = Holding cost per unit per period ($/roll)
In this case, the demand per period (D) is 8 rolls per day, the setup or ordering cost (S) is $10, and the holding cost per unit per period (H) is $0.30.
Substituting these values into the formula, we get:
EOQ = √((2 * 8 * 250 * $10) / ($0.30))
Simplifying:
EOQ = √(40000 / $0.30)
EOQ ≈ √133333.33
EOQ ≈ 365.12
Therefore, the economic order quantity is approximately 365.1 rolls.
To calculate the reorder point that will provide an order cycle service level of 97 percent, we can use the following formula:
Reorder Point = Demand during lead time + Safety stock
The demand during lead time is the average daily demand multiplied by the lead time, which is 2 days in this case.
Demand during lead time = D * LT
Demand during lead time = 8 * 2
Demand during lead time = 16
To determine the safety stock, we can use the following formula:
Safety stock = Z * √(LT) * σ
Where:
Z = Z-score for the desired service level (97 percent)
√(LT) = Square root of the lead time (2 days)
σ = Standard deviation of usage during lead time
The Z-score for a 97 percent service level is approximately 1.88. The standard deviation of usage during lead time is given as 3 rolls.
Substituting these values into the formula, we get:
Safety stock = 1.88 * √2 * 3
Safety stock ≈ 1.88 * √6
Safety stock ≈ 4.82
Therefore, the reorder point that will provide a 97 percent order cycle service level is approximately 16 + 4.82 = 20.82 rolls. Rounded up, it is 21 rolls.
To calculate the safety stock the company must hold to have a 97 percent order-cycle service level, we can use the formula:
Safety stock = Z * √(LT) * σ
Using the same values for Z, √(LT), and σ as before:
Safety stock = 1.88 * √2 * 3
Safety stock ≈ 1.88 * √6
Safety stock ≈ 4.82
Therefore, the safety stock the company must hold to have a 97 percent order-cycle service level is approximately 4.82 rolls.
To determine the reorder point needed to provide a 99 percent order-cycle service level, we repeat the same process as before but with a different Z-score.
The Z-score for a 99 percent service level is approximately 2.33.
Using this value, the formula for safety stock (Safety stock = Z * √(LT) * σ) remains the same.
Using the same values for √(LT) and σ as before, we get:
Safety stock = 2.33 * √2 * 3
Safety stock ≈ 2.33 * √6
Safety stock ≈ 5.99
Therefore, the reorder point needed to provide a 99 percent order-cycle service level is approximately 16 + 5.99 = 21.99 rolls. Rounded up, it is 22 rolls.
To calculate the safety stock the company must hold to have a 99 percent order-cycle service level, we again use the formula:
Safety stock = Z * √(LT) * σ
Using the same values for Z, √(LT), and σ as before:
Safety stock = 2.33 * √2 * 3
Safety stock ≈ 2.33 * √6
Safety stock ≈ 5.99
Therefore, the safety stock the company must hold to have a 99 percent order-cycle service level is approximately 5.99 rolls.