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© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-1
Operations Operations ManagementManagement
Inventory ManagementInventory ManagementChapter 12Chapter 12
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-2
Stock of materials Stored capacity
© 1995 Corel Corp.© 1984-1994 T/Maker Co. © 1984-1994 T/Maker Co.
© 1995 Corel Corp.
What is Inventory?What is Inventory?
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-3
Types of InventoryTypes of Inventory
Raw material Work-in-progress Maintenance / repair / operating supplies Finished goods
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-4
The Material Flow CycleThe Material Flow Cycle
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-5
The Functions of InventoryThe Functions of Inventory
To ”decouple” or separate various parts of the production process
To provide a stock of goods that will provide a selection for customers
To take advantage of quantity discounts To hedge against inflation and upward price
changes
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-6
Higher costs Interest or opportunity costs Holding (or carrying) costs – storage, handling, taxes,
insurance, shrinkage Ordering (or setup) costs
Risk of deterioration or obsolescence Hides production problems
Yield / scrap variations Unscheduled downtime
Disadvantages of InventoryDisadvantages of Inventory
Total cost = 20% - 40% of inventory value / yearTotal cost = 20% - 40% of inventory value / year
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-7
Pressures on inventoryPressures on inventory
Pressure for lower inventory
•Inventory investment
•Inventory holding cost
Pressure for higher inventory
•Customer service
•Other costs related to inventory
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-8
Different Views of InventoryDifferent Views of Inventory
Demand TypeDemand TypeIndependentIndependentDependentDependent
Process stageProcess stageRaw MaterialRaw MaterialWork in ProcessWork in ProcessFinished GoodsFinished Goods
OtherOtherMaintenance / RepairMaintenance / RepairOperating SuppliesOperating Supplies
Types of InventoryTypes of InventoryCycleCyclePipelinePipelineSafety StockSafety StockAnticipationAnticipation
Annual $ VolumeAnnual $ VolumeAABBCC
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-9
How Is Inventory Created?How Is Inventory Created?
Cycle Inventory – result of lot size
Pipeline Inventory – in transit
Safety Stock Anticipation Inventory
Pipeline inventory = DL = dL
Average cycle inventory = Q + 0
2
Types of InventoryTypes of InventoryCycleCyclePipelinePipelineSafety StockSafety StockAnticipationAnticipation
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-10
Inventory CalculationsInventory Calculations
We use 70 hypodermic needles a week. We buy them in lots of 280. It takes three weeks for order handling and shipment.
Cycle inventory = Q/2= 280/2= 140 needles
Pipeline inventory = DL = dL= (70 needles/week)(3 weeks)= 210 drills
Inventory WorksheetsInventory Worksheets
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-11
Inventory Reduction TacticsInventory Reduction Tactics
Cycle inventory
Pipeline inventory
Safety Stock
Anticipation inventory
Reduce lot size
Reduce lead time
Various
Reduce uncertainties
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-12
Divides on-hand inventory into three classes on the basis of annual dollar volume – A, B, and C $ volume = Annual demand x Unit cost
Policies based on ABC analysis Develop class A suppliers more Maintain tighter physical control of A items Forecast A items more carefully
ABC AnalysisABC Analysis
Annual $ VolumeAnnual $ VolumeAABBCC
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-13
ABC AnalysisABC Analysis
Class % $ Vol % ItemsA 80 20B 15 30C 5 50
% of Inventory Items
0
20
40
60
80
100
0 50 100
% Annual $ Usage
AABB
CC
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-14
Fixed order-quantity models Economic order quantity Production order quantity Quantity discount
Probabilistic models
Fixed order-period models
Help answer the inventory planning questions!
Help answer the inventory planning questions!
© 1984-1994 T/Maker Co.
Inventory Models forInventory Models forIndependent DemandIndependent Demand
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-15
Objective: minimize (ordering cost + holding cost)
Assumptions: Known and constant demand Known and constant lead time Instantaneous receipt of material No quantity discounts Only ordering / setup cost and holding cost No stockouts
EOQ – Economic Order QuantityEOQ – Economic Order Quantity
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-16
Inventory Usage Over TimeInventory Usage Over Time
Time
Inve
ntor
y Le
vel
Average Cycle
Inventory
0
Q
Usage Rate
Q2
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-17
EOQ ModelEOQ ModelHow Much to Order?How Much to Order?
Order quantity (Q)
Annual Cost
Holding CostTotal Cost
Ordering (Setup) Cost
Optimal Order Quantity (Q*)
Minimum total cost
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-18
More units must be stored if more are ordered
Purchase OrderDescription Qty.Microwave 1
Order quantity
Purchase OrderDescription Qty.Microwave 1000
Why Holding Costs IncreaseWhy Holding Costs Increase
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-19
Cost is spread over more unitsExample: You need 1000 microwave ovens
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
Purchase Order
Description Qty.Microwave 1
1 Order (Postage $ 0.33) 1000 Orders (Postage $330)
Order quantity
Purchase OrderDescription Qty.Microwave 1000
Why Ordering Costs DecreaseWhy Ordering Costs Decrease
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-20
EOQ Model – When to OrderEOQ Model – When to Order
Time
Inventory Level
Average Cycle
Inventory
Q*
Reorder Point (ROP)
Lead Time
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-21
Optimal Order Quantity
Expected Number of Orders
Expected Time Between Orders
Working Days / Year=
= ×
= N = DQ*
Working Days / Year= =TN
dD
ROP d L
= =× ×
Q*D SH
2
D = Demand per year
S = Setup (order) cost per order
H = Holding (carrying) cost
d = Demand per day
L = Lead time in days
EOQ Model EquationsEOQ Model Equations
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-22
Fixed order-quantity models Economic order quantity Production order quantity Quantity discount
Probabilistic models
Fixed order-period models
Help answer the inventory planning questions!
Help answer the inventory planning questions!
© 1984-1994 T/Maker Co.
Inventory Models forInventory Models forIndependent DemandIndependent Demand
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-23
Answers how much to order and when to order Allows partial receipt of material
Other EOQ assumptions apply
Suited for production environment Material produced, used immediately Provides production lot size
Lower holding cost than EOQ model
POQ – Production Order QuantityPOQ – Production Order Quantity
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-24
EOQ EOQ POQ ModelPOQ Model
Time
Inve
ntor
y Le
vel
Both production and usage take
place Usage only takes placeMaximum
inventory level
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-25
Fixed order-quantity models Economic order quantity Production order quantity Quantity discount
Probabilistic models
Fixed order-period models
Help answer the inventory planning questions!
Help answer the inventory planning questions!
© 1984-1994 T/Maker Co.
Inventory Models forInventory Models forIndependent DemandIndependent Demand
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-26
Quantity Discount ModelQuantity Discount Model
Answers how much to order & when to order Allows quantity discounts
Other EOQ assumptions apply Trade-off is between lower price & increased holding cost
Discount Number
Discount Quantity
Discount (%)
Discount Price (P)
1 0 to 999 No discount $ 5.00
2 1,000 to 1,999 4 $ 4.80
3 2,000 and over 5 $ 4.75
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-27
Quantity Discount – How Much to OrderQuantity Discount – How Much to Order
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-28
Fixed order-quantity models Economic order quantity Production order quantity Quantity discount
Probabilistic models
Fixed order-period models
Help answer the inventory planning questions!
Help answer the inventory planning questions!
© 1984-1994 T/Maker Co.
Inventory Models forInventory Models forIndependent DemandIndependent Demand
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-29
Answer how much & when to order
Allow demand to vary Other EOQ assumptions apply
Consider service level & safety stock Service level = 1 – Probability of stockout Higher service level means more safety stock More safety stock means higher ROP
Probabilistic ModelsProbabilistic Models
X
Service Level P(Stockout)
Freq
uenc
y
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-30
Probabilistic Models - When to Order?Probabilistic Models - When to Order?
Reorder Point
(ROP)
X
Safety Stock (SS)
Time
Inve
ntor
y Le
vel
Lead Time
SS
ROP
Service Level P(Stockout)
Place order
Receive order
Freq
uenc
y
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-31
Fixed order-quantity models Economic order quantity Production order quantity Quantity discount
Probabilistic models
Fixed order-period models
Help answer the inventory planning questions!
Help answer the inventory planning questions!
© 1984-1994 T/Maker Co.
Inventory Models forInventory Models forIndependent DemandIndependent Demand
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-32
Answers how much to order Orders placed at fixed intervals
Inventory brought up to target amount Amount ordered varies
No continuous inventory count Possibility of stockout between intervals
Useful when vendors visit routinely Example: Office Max representative calls every week
Fixed Period (P) SystemsFixed Period (P) Systems
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-33
Inventory in a Fixed Period SystemInventory in a Fixed Period System
Various amounts (Qi) are ordered at regular time intervals (p) based on the quantity necessary to bring inventory up to target maximum
pp pp pp
QQ11 QQ22
QQ33
QQ44
Target maximum
Time
On-
Han
d In
vent
ory
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-34
Comparison of Comparison of QQ and and PP Systems Systems
Continuous Review System (Q)A system designed to track the remaining inventory of an item each time a withdrawal is made, to determine whether it is time to replenish
Periodic Review System (P) A system in which an item’s inventory position is reviewed periodically rather than continuously
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-35
Continuous Review System (Q) Individual review frequencies Possible quantity discounts Lower, less-expensive safety stocks
Periodic Review System (P) Convenient to administer Orders may be combined Inventory position only required at review
Comparison of Comparison of QQ and and PP Systems Systems
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-36
Inventory MeasuresInventory MeasuresAverage inventory = $2 millionCost of goods sold = $10 million52 business weeks per year
= = 5 turns/year$10 million
$2 million
Inventory turns =
= = 10.4 weeks$2 million
($10 million)/(52 weeks)
Weeks of supply =Average inventory value
Weekly sales (at cost)
Annual sales (at cost)
Average inventory value
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 0745812-37
SummarySummary Functions of inventory –
Inventory enables value creation for many processes Costs of inventory Different views of inventory Inventory reduction tactics ABC and EOQ are traditional tools used to manage
inventory – still used in many circumstances Continuous review system (Q) for high-value parts;
Periodic review system (P) for some low value parts Weeks of Supply and inventory turns are widely-used
measures of inventory