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12-2
Learning ObjectivesLearning Objectives
Define the term inventory, list the major reasons for holding inventories, and list the main requirements for effective inventory management.
Discuss the nature and importance of service inventories
Discuss periodic and perpetual review systems. Discuss the objectives of inventory management. Describe the A-B-C approach and explain how it
is useful.
12-3
Learning ObjectivesLearning Objectives
Describe the basic EOQ model and its assumptions and solve typical problems.
Describe the economic production quantity model and solve typical problems.
Describe the quantity discount model and solve typical problems.
Describe reorder point models and solve typical problems.
Describe situations in which the single-period model would be appropriate, and solve typical problems.
12-4
Independent Demand
A
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand
Independent demand is uncertain. Dependent demand is certain.
Inventory: a stock or store of goods
InventoryInventory
12-5
Inventory ModelsInventory Models
Independent demand: finished goods, items that are ready to be sold E.g. a computer
Dependent demand: components of finished products E.g. parts that make up the computer
12-6
Types of InventoriesTypes of Inventories
Raw materials and purchased parts Partially completed goods called
work-in-process (WIP)
Finished-goods inventories (manufacturing firms)
or merchandise (retail stores)
12-7
Types of InventoriesTypes of Inventories
Replacement parts, tools, and supplies
Goods-in-transit to warehouses or customers
12-8
Functions of InventoryFunctions of Inventory
To meet anticipated demand
To smooth production requirements
To decouple operations
To protect against stockouts
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Functions of InventoryFunctions of Inventory
To take advantage of order cycles
To help hedge against price increases
To permit operations
To take advantage of quantity discounts
12-10
Objectives of Inventory ControlObjectives of Inventory Control
To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds
Level of customer service
Costs of ordering and carrying inventory
Inventory turnover is the ratio ofthe annual cost of goods sold tothe average inventory investment.
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A system to keep track of inventory
A reliable forecast of demand
Knowledge of lead times
Reasonable estimates of Holding costs
Ordering costs
Shortage costs
A classification system
Effective Inventory ManagementEffective Inventory Management
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Inventory Counting SystemsInventory Counting Systems
Periodic System Physical count of items made at periodic
intervals
Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoringcurrent levels of each item
12-13
Inventory Counting SystemsInventory Counting Systems
Two-bin system: Two containers of inventory; reorder when the first is empty
Universal Product Code (UPC): Bar code printed on a label that hasinformation about the item to which it is attached
Radio Frequency Identification
(RFID) Tags
0
214800 232087768
12-14
Lead time: time interval between ordering and receiving the order
Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year
Ordering costs: costs of ordering and receiving inventory
Shortage costs: costs when demand exceeds supply of inventory
Key Inventory TermsKey Inventory Terms
12-15
ABC Classification SystemABC Classification System
Classifying inventory according to some measure of importance and allocating control efforts accordingly.
AA - very important
BB - moderately important
CC - least important
Figure 12.1
Annual $ valueof items
AA
BB
CC
High
Low
Low HighPercentage of Items
12-16
Cycle CountingCycle Counting
A physical count of items in inventory
Cycle counting management
How much accuracy is needed?
When should cycle counting be performed?
Who should do it?
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Economic order quantity (EOQ) model
The order size that minimizes total annual cost
Economic production model
Quantity discount model
Economic Order Quantity ModelsEconomic Order Quantity Models
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Only one product is involved
Annual demand requirements known
Demand is even throughout the year
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts
Assumptions of EOQ ModelAssumptions of EOQ Model
12-19
The Inventory CycleThe Inventory CycleFigure 12.2
Profile of Inventory Level Over Time
Quantityon hand
Q
Receive order
Placeorder
Receive order
Placeorder
Receive order
Lead time
Reorderpoint
Usage rate
Time
12-20
Total CostTotal Cost
Annualcarryingcost
Annualorderingcost
Total cost = +
TC = Q2
H DQ
S+
Q = Order quantity in unitsH = Holding (carrying) cost per unitD = Demand, usually in units per yearS = Ordering cost
12-21
Cost Minimization GoalCost Minimization Goal
Order Quantity (Q)
The Total-Cost Curve is U-Shaped
Ordering Costs
QO
An
nu
al C
os
t
(optimal order quantity)
TCQH
D
QS
2
Figure 12.4C
12-22
Deriving the EOQDeriving the EOQ
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.
Q = 2DS
H =
2(Annual Demand)(Order or Setup Cost)
Annual Holding CostOPT
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Minimum Total CostMinimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal.
Q2
H DQ
S=
12-24
Production done in batches or lots Capacity to produce a part exceeds the
part’s usage or demand rate Assumptions of EPQ are similar to EOQ
except orders are received incrementally during production
Economic Production Quantity (EPQ)Economic Production Quantity (EPQ)
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Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production rate is constant Lead time does not vary No quantity discounts
Economic Production Quantity AssumptionsEconomic Production Quantity Assumptions
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Economic Run SizeEconomic Run Size
QDS
H
p
p u0
2
Q0 = Order quantity in unitsH = Holding (carrying) cost per unitD = Demand, usually in units per yearS = Ordering cost p = Production or delivery rateu = Usage rate
12-27
Total Costs with Purchasing CostTotal Costs with Purchasing Cost
Annualcarryingcost
PurchasingcostTC = +
Q2
H DQ
STC = +
+Annualorderingcost
PD +
12-28
Total Costs with PDTotal Costs with PDC
ost
EOQ
TC with PD
TC without PD
PD
0 Quantity
Adding purchasing costdoesn’t change EOQ
Figure 12.7
12-30
When to Reorder with EOQ OrderingWhen to Reorder with EOQ Ordering
Reorder Point: When the quantity on hand of an item drops to this amount, the item is reordered
Safety Stock: Stock that is held in excess of expected demand due to variable demand rate and/or lead time
Service Level: Probability that demand will not exceed supply during lead time
12-31
Determinants of the Reorder PointDeterminants of the Reorder Point
The rate of demand The lead time Demand and/or lead time variability Stockout risk (safety stock)
Reorder PointReorder Point
If demand and lead time are both constant, the reorder point is simply
ROP = d X LT
Where
d = Demand rate (units per day or week)
LT = Lead times in days or weeks
12-32
12-33
Safety StockSafety StockFigure 12.12
LT Time
Expected demandduring lead time
Maximum probable demandduring lead time
ROP
Qu
an
tity
Safety stockSafety stock reduces risk ofstockout during lead time
12-34
Reorder PointReorder PointFigure 12.13
ROP
Risk ofa stockout
Service level
Probability ofno stockout
Expecteddemand Safety
stock
0 z
Quantity
z-scale
The ROP based on a normaldistribution of lead time demand
12-35
Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed
intervals May require only periodic checks of
inventory levels Risk of stockout Fill rate: the percentage of demand
filled by the stock on hand
Fixed-Order-Interval ModelFixed-Order-Interval Model
12-36
Tight control of inventory items Items from same supplier may yield
savings in: Ordering Packing Shipping costs
May be practical when inventories cannot be closely monitored
Fixed-Interval BenefitsFixed-Interval Benefits
12-37
Requires a larger safety stock for given risk of stockout
Increases carrying cost Costs of periodic reviews
Fixed-Interval DisadvantagesFixed-Interval Disadvantages
12-38
Single period model: model for ordering of perishables and other items with limited useful lives
Shortage cost: unrealized profits per unit (generally)
Excess cost: difference between purchase cost and salvage value of items left over at the end of a period
Single Period ModelSingle Period Model
12-39
Continuous stocking levels
Identifies optimal stocking levels
Optimal stocking level balances unit shortage and excess cost
Discrete stocking levels
Service levels are discrete rather than continuous
Desired service level is matched or exceeded
Single Period ModelSingle Period Model
12-40
Optimal Stocking LevelOptimal Stocking Level
Service Level
So
Quantity
Ce Cs
Balance point
Service level =Cs
Cs + CeCs = Shortage cost per unitCe = Excess cost per unit
Figure 12.16
12-41
Example 15Example 15
Ce = $0.20 per unit Cs = $0.60 per unit Service level = Cs/(Cs+Ce) = .6/(.6+.2) Service level = .75
Service Level = 75%
Quantity
Ce Cs
Stockout risk = 1.00 – 0.75 = 0.25