Chapter 10-Order QuantitiesIM417 Manufacturing Resources AnalysisSoutheast Missouri State UniversityCompiled by Bart WeihlSpring 2001

Order QuantitiesInventory ManagementHow much should be ordered at one time?

When should an order be placed?

Stock-Keeping Unit (SKU)http://www.inventoryops.com

Order QuantitiesDecision RulesLot-size Decision RulesLot-for-lotOrder what is needed - no more - no less

Fixed order quantitySpecifies the number to order each timeEasily understood, but does not minimize costs

Order n periods supplyOrder enough to satisfy future demand for a given period of time.

Order QuantitiesEconomic Order Quantity (EOQ)The EOQ is based on assumptions:Demand is relatively constant and knownThe item is produced or purchased in lots or batchesOrder preparation costs and inventory carrying costs are constant and knownReplacement occurs at once

Assumptions usually valid for finished goods whose demand is independent and uniform.

Order QuantitiesA Model of Inventory

Example: Average Inventory and Number of OrdersQ: 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 unitsNumber of orders per year = annual demand / order quantity = 6,750 / 450 = 15

Order QuantitiesEOQ CostsAnnual cost of placing ordersAnnual cost of carrying orders

Carrying Cost Lot SizeOrdering CostsTotal CostCost in Dollars

Order QuantitiesEOQ Formula

Carrying costs = Ordering costs

Qic / 2 = AS / Q

Order QuantitiesEOQ Formula

Q 2 = 2AS icor

Q = 2AS ic

where Q = Economic Order Quantity

Example: EOQQ: 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 = $10,000S = ordering cost in dollars = $50i = carrying cost rate as a decimal of a percent = 15% = 0.15

Therefore -EOQ = 2AS / i = (2 x 10000 x 50) / 0.15 = $2,582

Order QuantitiesCosts and Lot SizeEOQ 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.

Order QuantitiesQuantity DiscountsA 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 costsOrdering costsCarrying costs

Order QuantitiesEOQ When Costs Are Not KnownMany 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 inventoryWhere K = SQRT(Ad)/N

Order QuantitiesPeriod Order QuantityWhen 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

Order QuantitiesMiscellaneous ConsiderationsLumpy DemandThe EOQ assumes that demand is fairly uniform

Determining CostsThe EOQ model is relatively robust with respect to cost estimates

Minimum OrdersSome suppliers require a minimum order quantityOften C items where plenty is ordered not EOQ

Example # 10.4, pg. 271. . .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 = $800,000S = $32i = 20%EOQ = 2AS/i

= (2 x 800,000 x 32)/.2

EOQ = $16,000

Example # 10.4, pg. 271. . .b. Number of orders per yearNumber of Orders = A / Q = 800,000 / 16,000 = 50c. Cost of ordering, cost of carrying inventory, and total cost.Cost of Ordering = AS / Q = (800,000 X 32) / 16,000 = $1600Cost of Carrying = QiC / 2 = (16,000 X 0.2) / 2 = $1600Total Cost = $3200

Next Week. . .Work the following:10.110.210.310.10