Joe Henry's machine shop uses 2,500 brackets during the course of a year. These brackets are purchased from a supplier 90 miles away.
the following information is known about the brackets.
annual demand 2,500
holding cost per bracket per year $1.50
order cost per order $18.75
Lead time 2 days
working days per year 250
a. Given the above information, what would be the economic order quanity (EOQ)?
b. Given the EOQ, what would be the average inventory? What would be the annual inventory holding cost?
c. Given the EOQ, how many orders would be made each year? What would be the annual order cost?
d. Given the EOQ, what is the total annual cost of managing the inventory?
e. What is the time between orders?
f. What is the reorder point (ROP)?
Annual demand : 2,500 pieces
Holding cost per bracket per year: $1.50
Order cost per order : $18.75
Lead time : 2 days
Working days per year : 250
a) Given the above information, what would be the economic order quantity (EOQ)?
Q* = Square root {(2* Order Cost * Demand) / Holding Cost}
Q* = Square root {(2* 2500 * 18.75) / 1.50} = 250
b) Given the EOQ, what would be the average inventory?
Average inventory = 250/2 = 125
c) Given the EOQ, how many orders would be made each year?
10 orders per year
d) Given the EOQ, what is the total annual inventory cost?
Total annual inventory cost = Square root {(2* annual demand * Order cost per order * holding cost)}
= Square root {(2*2500*18.75*1.50)} = 375
e) What is the time between orders?
25 days
f) What is the reorder point (ROP)?
ROP = dL
= Daily demand * Lead Time
= (2500/250)(2) = 10*2= 20
a. The economic order quantity (EOQ) can be calculated using the formula:
EOQ = √(2DS/H)
Where:
D = annual demand = 2,500 brackets
S = order cost per order = $18.75
H = holding cost per bracket per year = $1.50
Plugging in the values:
EOQ = √(2 * 2,500 * 18.75 / 1.50) = √(93750) ≈ 306
Therefore, the economic order quantity (EOQ) would be approximately 306.
b. The average inventory can be calculated as half of the EOQ:
Average Inventory = EOQ / 2 = 306 / 2 = 153 brackets
The annual inventory holding cost can be calculated by multiplying the average inventory by the holding cost per bracket per year:
Annual Inventory Holding Cost = Average Inventory * Holding Cost per bracket per year = 153 * $1.50 = $229.50
c. The number of orders made each year can be calculated by dividing the annual demand by the economic order quantity:
Number of Orders = Annual Demand / EOQ = 2,500 / 306 ≈ 8.17
However, since we cannot have a fraction of an order, the number of orders would be rounded up to the next whole number. Therefore, there would be approximately 9 orders made each year.
The annual order cost can be calculated by multiplying the number of orders by the order cost per order:
Annual Order Cost = Number of Orders * Order Cost per order = 9 * $18.75 = $168.75
d. The total annual cost of managing the inventory can be calculated by summing the annual inventory holding cost and the annual order cost:
Total Annual Cost = Annual Inventory Holding Cost + Annual Order Cost = $229.50 + $168.75 = $398.25
Therefore, the total annual cost of managing the inventory would be approximately $398.25.
e. The time between orders can be calculated by dividing the working days per year by the number of orders:
Time between Orders = Working Days per Year / Number of Orders = 250 / 9 ≈ 27.78 days
Therefore, the time between orders would be approximately 27.78 days.
f. The reorder point (ROP) can be calculated by multiplying the lead time by the average daily demand:
ROP = Lead Time * Average Daily Demand
To calculate the average daily demand, we divide the annual demand by the number of working days per year:
Average Daily Demand = Annual Demand / Working Days per Year = 2,500 / 250 = 10 brackets per day
Plugging in the values:
ROP = 2 * 10 = 20 brackets
Therefore, the reorder point (ROP) would be 20 brackets.
To find the answers to these questions, we can use the Economic Order Quantity (EOQ) model. The EOQ formula is:
EOQ = √((2 * D * S) / H)
Where:
D = Annual demand = 2,500 brackets
S = Order cost per order = $18.75
H = Holding cost per bracket per year = $1.50
Using these values, let's calculate the answers step-by-step:
a. Calculation of EOQ:
EOQ = √((2 * 2500 * 18.75) / 1.50)
EOQ = √75000 / 1.50
EOQ = √50000
EOQ ≈ 223.61
Therefore, the economic order quantity (EOQ) for Joe Henry's machine shop is approximately 223.61 brackets.
b. Calculation of Average Inventory and Annual Holding Cost:
Average Inventory = EOQ / 2
Average Inventory = 223.61 / 2
Average Inventory = 111.81 (rounded to two decimal places)
Annual Holding Cost = Average Inventory * Holding cost per bracket per year
Annual Holding Cost = 111.81 * $1.50
Annual Holding Cost ≈ $167.72
Therefore, the average inventory would be approximately 111.81 brackets, and the annual inventory holding cost would be approximately $167.72.
c. Calculation of Number of Orders and Annual Order Cost:
Number of Orders = Annual Demand / EOQ
Number of Orders = 2500 / 223.61
Number of Orders ≈ 11.18 (rounded to two decimal places)
Annual Order Cost = Number of Orders * Order cost per order
Annual Order Cost = 11.18 * $18.75
Annual Order Cost ≈ $209.63
Therefore, approximately 11.18 orders would be made each year, and the annual order cost would be approximately $209.63.
d. Calculation of Total Annual Cost of Managing Inventory:
Total Annual Cost = Annual Holding Cost + Annual Order Cost
Total Annual Cost = $167.72 + $209.63
Total Annual Cost ≈ $377.35
Therefore, the total annual cost of managing the inventory would be approximately $377.35.
e. Calculation of Time Between Orders:
Time Between Orders = Working days per year / Number of Orders
Time Between Orders = 250 / 11.18
Time Between Orders ≈ 22.39 (rounded to two decimal places)
Therefore, the time between orders would be approximately 22.39 days.
f. Calculation of Reorder Point (ROP):
ROP = Lead Time * Demand per day
Demand per day = Annual Demand / Working days per year
Demand per day = 2500 / 250 = 10 brackets per day
ROP = 2 * 10
ROP = 20 brackets
Therefore, the reorder point (ROP) would be 20 brackets.
To find the answers to these questions, we will use the Economic Order Quantity (EOQ) model. The EOQ is a formula that calculates the optimal order quantity to minimize inventory costs. Let's go step by step:
a. Economic Order Quantity (EOQ): The formula to calculate the EOQ is as follows:
EOQ = sqrt((2 * D * S) / H)
Where:
D = Annual demand (2,500 brackets)
S = Order cost per order ($18.75)
H = Holding cost per bracket per year ($1.50)
Substituting the values into the formula:
EOQ = sqrt((2 * 2,500 * $18.75) / $1.50)
EOQ ≈ sqrt(75,000 / $1.50)
EOQ ≈ sqrt(50,000)
EOQ ≈ 223.61
So, the Economic Order Quantity (EOQ) would be approximately 224 brackets.
b. Average Inventory & Annual Holding Cost:
To calculate the average inventory, use the formula:
Average Inventory = EOQ / 2
Average Inventory = 224 / 2
Average Inventory = 112 brackets
The annual inventory holding cost can be calculated using the formula:
Annual Holding Cost = Average Inventory * Holding cost per bracket per year
Annual Holding Cost = 112 * $1.50 = $168
So, the average inventory would be 112 brackets, and the annual inventory holding cost would be $168.
c. Number of Orders & Annual Order Cost:
To find the number of orders made each year, use the formula:
Number of Orders = Annual demand / EOQ
Number of Orders = 2,500 / 224 ≈ 11.16
Since we can't have a fraction of an order, we round it up to 12.
The annual order cost can be calculated using the formula:
Annual Order Cost = Number of Orders * Order cost per order
Annual Order Cost = 12 * $18.75 = $225
So, there would be 12 orders made each year, and the annual order cost would be $225.
d. Total Annual Cost of Managing Inventory:
The total annual cost of managing inventory is the sum of the annual holding cost and the annual order cost:
Total Annual Cost = Annual Holding Cost + Annual Order Cost
Total Annual Cost = $168 + $225 = $393
So, the total annual cost of managing inventory would be $393.
e. Time Between Orders:
The time between orders can be calculated using the formula:
Time Between Orders = Working days per year / Number of Orders
Time Between Orders = 250 / 12 ≈ 20.83
So, the time between orders would be approximately 20.83 days.
f. Reorder Point (ROP):
The reorder point is the inventory level at which a new order should be placed. It is calculated using the formula:
ROP = Lead time * Average demand per day
Average demand per day = Annual demand / Working days per year
Average demand per day = 2,500 / 250 = 10
ROP = 2 * 10 = 20 brackets
So, the reorder point (ROP) would be 20 brackets.