can someone help me with this thanks in advance Suppose your

can someone help me with this, thanks in advance

Suppose your firm purchases a $4 per unit part from a supplier. Your firm uses the part to assemble red widgets. On average, you use 50,000 units of this part each year. Every time you order this particular part, you incur a sizable ordering cost of $800 regardless of the number of parts you order. Your cost of capital is 20% per year and your unit holding cost per year is 10%.

1. How many parts should you purchase each time you place an order (i.e., what is the optimal order quantity)?

2. To satisfy annual demand, how many times per year will you place orders for this part if you order the optimal order quantity ?

3. What is the total annual cost if you order the optimal order quantity ?

4. What is the total annual cost if you order 1,000 units instead of the optimal order quantity ?

Solution

Unit Cost (C) = $4

Demand (D) = 50,000 units per year

Ordering Cost (C₀₎ = $ 800

Inventory Carrying Cost (C_h) = ((( Holding Cost + Capital Cost) / 100) * Unit Cost )

= (((10 + 20) / 100 ) * $4 )= $ 1.2

1. Number of parts you should purchase each time you place an order is given by

EOQ = ((2DC₀ ) / C_h)^1/2

   ⁼ ((2 * 50,000* 800) / 1.2) ^1/2

   = 8164.9 = 8165 units

2. Number of order = Demand / EOQ

= 50,000 / 8165

= 6.12 = 6 order per year

3. Total Annual cost = Purchasing cost + Ordering Cost + Carrying Cost

= (Demand * Unit Price) + ( (Demand / EOQ) * Ordering Cost) + ((EOQ / 2) * Holding Cost )

= 50, 000 * $4 + ((50,000 / 8165) * $800) + ((8165 / 2) * $ 1.2)

= $2,00,000 + $4899 + $4899

= $2,09,798

4. Total Cost if the order quantity is of 1000 units instead of EOQ

Total Annual cost = Purchasing cost + Ordering Cost + Carrying Cost

= 50, 000 * $4 + ((50,000 / 1000) * $800) + ((1000 / 2) * $ 1.2)

= $2,00,000 + $40,000 + $600

= $2,40,600

Note : EOQ is Economic Order Quantity also known as Optimal Order Quantity