True Football Helmet Company uses the fixed-period system to manage the inventory of the Riddell SpeedFlex model of football helmets. The following information has been collected:

Demand = 200 units/week

Number of weeks per year = 52

Order lead time = two weeks

Order costs = $60/order

Carrying costs per year = $1.50 per year for each helmet

Desired service level = 95%

Standard deviation of weekly demand = 22

What would be your calculated order review interval (i.e., T)? What would be your calculated order up to level (i.e., M)? If the company still has an on-hand inventory of 450 helmets at the inventory review date on October 11, how many additional should be ordered?

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To calculate the order review interval (T) using the fixed-period system, we need to determine the time between inventory reviews. T is calculated by adding the order lead time to the safety stock. The safety stock is the extra inventory held to account for variations in demand.

First, we need to calculate the safety stock. To do this, we need to know the service level and the standard deviation of weekly demand. The service level is the probability that demand will not exceed supply during lead time. We can use a z-table to determine the corresponding z-score for a service level of 95%.

The formula for safety stock is: safety stock = z-score * standard deviation of weekly demand * square root of lead time

Using the given values:

z-score = 1.645 (from the z-table) standard deviation of weekly demand = 22 lead time = 2 weeks

safety stock = 1.645 * 22 * sqrt(2) = 52.13 ≈ 53 helmets

Now, we can calculate T:

T = order lead time + safety stock = 2 + 53 = 55 weeks

Next, we need to calculate the order-up-to level (M). M is the level of inventory at which we place an order to bring the inventory level back up to a certain level. To calculate M, we need to know the average demand during lead time (d) and the carrying cost per year.

The formula for M is: M = (d * T) + safety stock

Using the given values:

d = demand * lead time = 200 * 2 = 400 helmets carrying cost per year = $1.50 per helmet per year

M = (400 * 55) + 53 = 22,053 helmets

Finally, if the company still has an on-hand inventory of 450 helmets at the inventory review date on October 11, we need to determine how many additional helmets should be ordered.

The formula for order quantity (Q) is: Q = M - on-hand inventory

Using the given values:

M = 22,053 helmets on-hand inventory = 450 helmets

Q = 22,053 - 450 = 21,603 helmets

Therefore, the company should order an additional 21,603 helmets.

To calculate the order review interval (T) using the fixed-period system, we need to determine the time between inventory reviews. T is calculated by adding the order lead time to the safety stock. The safety stock is the extra inventory held to account for variations in demand.

First, we need to calculate the safety stock. To do this, we need to know the service level and the standard deviation of weekly demand. The service level is the probability that demand will not exceed supply during lead time. We can use a z-table to determine the corresponding z-score for a service level of 95%.

The formula for safety stock is: safety stock = z-score * standard deviation of weekly demand * square root of lead time

Using the given values:

z-score = 1.645 (from the z-table) standard deviation of weekly demand = 22 lead time = 2 weeks

safety stock = 1.645 * 22 * sqrt(2) = 52.13 ≈ 53 helmets

Now, we can calculate T:

T = order lead time + safety stock = 2 + 53 = 55 weeks

Next, we need to calculate the order-up-to level (M). M is the level of inventory at which we place an order to bring the inventory level back up to a certain level. To calculate M, we need to know the average demand during lead time (d) and the carrying cost per year.

The formula for M is: M = (d * T) + safety stock

Using the given values:

d = demand * lead time = 200 * 2 = 400 helmets carrying cost per year = $1.50 per helmet per year

M = (400 * 55) + 53 = 22,053 helmets

Finally, if the company still has an on-hand inventory of 450 helmets at the inventory review date on October 11, we need to determine how many additional helmets should be ordered.

The formula for order quantity (Q) is: Q = M - on-hand inventory

Using the given values:

M = 22,053 helmets on-hand inventory = 450 helmets

Q = 22,053 - 450 = 21,603 helmets

Therefore, the company should order an additional 21,603 helmets.