Question

In: Operations Management

Set up the Economic Order Quantity model given the information below. Annual Demand 50,000 units Order...

Set up the Economic Order Quantity model given the information below.


Annual Demand	50,000 units
Order Cost	$150 per order
Unit Cost	$100 per unit
Inventory Holding	15% of unit cost

What is the Economic Order Quantity of the product?

What is the total annual cost when EOQ is ordered each time?

Expert Solution

Given are following details :

Annual demand of bath towels = D = 175 /month x 12 months =2100

Order placement cost = Co =$12

Annual unit inventory carrying cost = Ch = 27% of $2.50 = $0.675

Optimal order quantity

= Square root ( 2 x Co x D/ Ch )

= Square root ( 2 x 12 x 2100 / 0.675 )

= 273.25 ( 273 rounded to nearest whole number )

Order frequency = Optimal order quantity / Annual demand x 365 = 274/2100 x 365 = 47.62 days

Annual set up ( order placement) cost

= Ordering cost x Number of orders

= Co x annual demand / Optimal order quantity

= $12 x 2100 / 273

= $92.30

Annual inventory carrying cost

= annual unit inventory carrying cost x Average inventory

= Ch x Optimal order quantity / 2

= $0.675 x 273/2

= $92.13

Annual holding and set up cost = $92.30 + $92.13 = $184.43

Given are following data :

Annual demand = D = 50,000 units

Order cost = Co = $150

Annual unit inventory holding cost = Ch = 15% of $100 per unit =$15

Economic order quantity = Square root ( 2 x Co x D / Ch ) = Square root ( 2 x 150 x 50000/15) =1000

Annual Ordering cost

= Ordering cost x Number of orders

= Ordering cost x annual demand / EOQ

= Co x D/EOQ

= $ 150x 50,000/1000

= $7500

Annual inventory holding cost

= Annual unit inventory holding cost x Average inventory

= Ch x EOQ/2

= $15 x 1000/2

= $7500

Annual procurement cost = $100/ unit x 50,000 units = $5,000000

Total annual cost when EOQ is ordered

= Annual ordering cost + annual inventory holding cost + annual procurement cost

= $7500 + $7500 + $5000000

= $5015000

keosha answered 1 year ago

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