Question

A table factory requires 500 logs per year. Each time an order for logs is placed, an ordering cost of $20 is incurred. Each log costs $12 and the holding cost is $2/log/year. Assume that demand occurs at a constant rate and shortages are not allowed and the lead time is zero.

(a) If the quantity ordered is 150 units, calculate the total cost incurred (including ordering costs, purchasing costs and holding costs).

(b) What is EOQ?

(c) What is the minimum total cost?

(d) What is the number of cycles in a year, when EOQ is used as the order quantity?

(e) What is the duration of each cycle (in months)? (f) If the lead time (L) is 2 months, what will be the new reorder point? (g) If the lead time (L) is 3 months, what will be the new reorder point?

Answer 1

Solution:

Part a ---

Quantity Ordered = 150 Units

Number of orders to be placed in a year = Total Annual Demand / Ordered Quantity

= 500 / 150

= 3.33 orders

	Total Cost Per Annual
Ordering Cost (Number of Orders 3.33 * Ordering cost per order $20)	$66.67
Purchasing Cost (500 Units x 12)	$6,000
Carrying or Holding Costs (1/2x Order Quantity 150 x Holding cost per unit per annum $2)	$150
Total Costs	$6,216.67

Total Cost if we assumed that number of orders placed in a year = 3.33 4 Orders

	Total Cost Per Annual
Ordering Cost (Number of Orders 4 * Ordering cost per order $20)	$80
Purchasing Cost (500 Units x 12)	$6,000
Carrying or Holding Costs (1/2x Order Quantity 150 x Holding cost per unit per annum $2)	$150
Total Costs	$6,230

Part b – EOQ

EOQ = ((2 x Annual Demand x Ordering Cost per order) / Carrying Cost per unit per annum)^1/2

= ((2 x 500 x 20) / 2)^1/2

= 100 Units

Part c – Minimum Total Costs

Number of Orders in a year = 500 / EOQ 100 = 5 orders

	Total Cost Per Annual
Ordering Cost (Number of Orders 5 * Ordering cost per order $20)	$100
Purchasing Cost (500 Units x 12)	$6,000
Carrying or Holding Costs (1/2 x EOQ 100 x Holding cost per unit per annum $2)	$100
Minimum Total Costs	$6,200

Part d –

Assuming number of days in a year is 365 days

Number of cycles in a year, when EOQ is used as the order quantity = Number of Days in a year / Number of Orders to be placed in a year

= 365 / 5

= 73

Assuming number of days in a year is 360 days

Number of cycles in a year, when EOQ is used as the order quantity = Number of Days in a year / Number of Orders to be placed in a year

= 360 / 5

= 72

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