EOQ Model Cost Curves

1. Average inventory = Q/2 D = = Expected Number of Orders N Q* Q* Expected Time Between Orders = D 2 D Co EOQ, Q* = Ch EOQ Model Cost Curves Annual cost ($) Total Cost curve D = Demand/year Co= cost per order Ch = Holding (carrying) cost Slope = 0 Minimum total cost Carrying Cost = ChQ/2 Ordering Cost = CoD/Q Optimal order Q* (EOQ) Order Quantity, Q Total Costs = Carrying Cost + Ordering Cost Ct = ChQ/2 + CoD/Q

2. Example: Basic EOQ QUESTION The annual demand for a product is 8,000 units. The ordering cost is € 30 per order. The cost of the item is € 10 and the carrying cost has been calculated at € 3 to carry out one item in stock for one year. Calculate: • What is the EOQ? • The numbers of orders to be placed annually, and • The overall costs.

3. 2 C D o = Q * C h 2 (8,000) (30) = 3 = 400 units D 8,000 = = Number of orders per year = 20 orders Total Costs = Carrying Cost + Ordering Cost 400 Q * Holding Costs = Average quantity in stock x Cost of holding item for 1 year = 400/2 x 3 = € 600 Ordering Costs = Cost of ordering x Number of orders = 30 x 20 = € 600 therefore Total Costs = € 600 + € 600 = € 1,200. Example: Basic EOQ D = 8,000 units CO = € 30 Ch = €3 ANSWER

4. Example: Basic EOQ QUESTION A local distributor for a national tire company expects to sell approximately 9,600 steelbelted radial tires of a certain size and tread design next year. Annual carrying cost is $16per tire, and ordering cost is $75. The distributor operates 288 days a year. a. What is the EOQ? b. How many times per year does the store reorder? c. What is the length of an order cycle? d. What is the total annual cost if the EOQ quantity is ordered?

5. Example: Basic EOQ

6. Example: Basic EOQ Zartex Co. produces fertilizer to sell to wholesalers. One raw material – calcium nitrate – is purchased from a nearby supplier at $22.50 per ton. Zartex estimates it will need 5,750,000 tons of calcium nitrate next year. The annual carrying cost for this material is 40% of the acquisition cost, and the ordering cost is $595. a) What is the most economical order quantity? b) How many orders will be placed per year? c) How much time will elapse between orders?

7. EOQ = 2(5,750,000)(595)/9.00 Example: Basic EOQ • Economical Order Quantity (EOQ) D = 5,750,000 tons/year Ch = .40(22.50) = $9.00/ton/year Co = $595/order = 27,573.135 tons per order

8. Example: Basic EOQ • Total Annual Stocking Cost (TSC) TSC = (27,573.135/2)(9.00) + (5,750,000/27,573.135)(595) = 124,079.11 + 124,079.11 = $248,158.22

9. Example: Basic EOQ • Number of Orders Per Year = D/Q = 5,750,000/27,573.135 = 208.5 orders/year • Time Between Orders = Q/D = 1/208.5 = .004796 years/order = .004796(365 days/year) = 1.75 days/order Note: This is the inverse of the formula above.

10. Example: Basic EOQ A large bakery buys flour in 25-kg bags. The bakery uses an average of 4860 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $4 per order. Annual carrying costs are $30/bag. • Determine the economic order quantity • What is the average number of bags on hand? • How many orders per year will there be? • Compute the total cost of ordering and carrying flour • If annual ordering cost were to increase by $1 per order. How much would that affect the minimum total annual cost?

11. Example: Basic EOQ • EOQ = √(2(4860)(4)/30 = 36 bags/order • Average number of bags on hand = 36/2 = 18 bags/order • No = 4 860/36 = 135 orders/year • TC = √(2(4860)(4)(30) = $1080/year • TC = √(2(4 860)(5)(30) = $1207.48/year Increase = 1207.48 – 1 080 = $127.48/year It will affect the total inventory cost to increase by $127.48/year.