1 Chapter 10- Order Quantities IM417 Manufacturing Resources Analysis Southeast Missouri State University Compiled by Bart Weihl Spring 2001

2 Order Quantities Inventory Management How much should be ordered at one time? When should an order be placed? Stock-Keeping Unit (SKU)

3 Order Quantities Decision Rules Lot-size Decision Rules Lot-for-lot Order what is needed - no more - no less Fixed order quantity Specifies the number to order each time Easily understood, but does not minimize costs Order “n” periods supply Order enough to satisfy future demand for a given period of time.

4 Order Quantities Economic Order Quantity (EOQ) The EOQ is based on assumptions: Demand is relatively constant and known The item is produced or purchased in lots or batches Order preparation costs and inventory carrying costs are constant and known Replacement occurs at once Assumptions usually valid for finished goods whose demand is independent and uniform.

5 Order Quantities A Model of Inventory Q = Lot Size Time (weeks) Units in Stock

6 Example: Average Inventory and Number of Orders Q: The annual demand for an SKU is 6,750 units, and it is ordered in quantities of 450 units. Calculate the average inventory and the number of orders placed per year. A: Average inventory = order quantity / 2 = 450 / 2 = 225 units Number of orders per year = annual demand / order quantity = 6,750 / 450 = 15

7 Order Quantities EOQ Costs Annual cost of placing orders Annual cost of carrying orders Carrying Cost Lot Size Ordering Costs Total Cost Cost in Dollars

8 Order Quantities EOQ Formula Carrying costs = Ordering costs Qic / 2 = AS / Q

9 Order Quantities EOQ Formula Q 2 = 2AS ic or Q = 2AS ic where Q = Economic Order Quantity

10 Example: EOQ Q: An item has a annual demand of $10,000, carrying costs of 15% per order, and ordering costs of $50. What is the EOQ in dollars? A: A = Annual usage in dollars = $10,000 S = ordering cost in dollars = $50 i = carrying cost rate as a decimal of a percent = 15% = 0.15 Therefore -EOQ = 2AS / i = (2 x x 50) / 0.15 = $2,582

11 Order Quantities Costs and Lot Size EOQ will increase as annual demand and ordering costs increase. EOQ will decrease as carrying costs and unit costs increase. The cost of ordering is either the cost of placing a purchase order or the cost of placing a manufacturing order. The cost of a manufacturing order includes production control costs and setup costs.

12 Order Quantities Quantity Discounts A discount given by a supplier on orders over a certain size. When deciding whether to accept a discount the total cost must be considered including: Purchase costs Ordering costs Carrying costs

13 Order Quantities EOQ When Costs Are Not Known Many times the costs are not known or easy to determine The ordering and carrying costs are generally the same for each item in a family Use an approach to arrive at an average of “K” to reduce the total cost of inventory Where K = SQRT(Ad)/N

14 Order Quantities Period Order Quantity When demand is not uniform the EOQ may not produce the lowest total cost The POQ uses the EOQ to calculate an economic time between orders Orders are placed to satisfy requirements for the calculated time period POQ = EOQ/Avg. weekly usage

15 Order Quantities Miscellaneous Considerations Lumpy Demand The EOQ assumes that demand is fairly uniform Determining Costs The EOQ model is relatively robust with respect to cost estimates Minimum Orders Some suppliers require a minimum order quantity Often “C” items where plenty is ordered not EOQ

16 Example # 10.4, pg Q. A company wishes to establish an EOQ for an item for which the annual demand is $800,000, the ordering cost is $32, and the cost of carrying inventory is 20%. Calculate the following: a. The EOQ in dollars. A = $800,000 S = $32 i = 20% EOQ = 2AS/i = (2 x 800,000 x 32)/.2 EOQ = $16,000

17 Example # 10.4, pg b. Number of orders per year Number of Orders = A / Q = 800,000 / 16,000 = 50 c. Cost of ordering, cost of carrying inventory, and total cost. Cost of Ordering = AS / Q = (800,000 X 32) / 16,000 = $1600 Cost of Carrying = QiC / 2 = (16,000 X 0.2) / 2 = $1600 Total Cost = $3200

18 Next Week... n Work the following: –10.1 –10.2 –10.3 –10.10