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Inventory Management
Inventory Management Inventory: A quantity of goods/materials in
the control of a firm and hold for a time in a relatively idle state awaiting its intend use or sale
Inventory Management: To determine an optimal level of holding such idle resources through certain procedures/rules on the decisions of when/how much to order for procurement or production
How How Much?Much? When!When!
Conflicting Pressures on Inventory Levels
Pressures for Small Inventories Pressures for Large Inventories
Interest or opportunity cost Customer service
Storage and handling cost Ordering or setup cost
Property taxes Labor and facility utilization
Insurance premiums Transportation cost
Shrinkage costs: pilferage, obsolescence, and deterioration
Cost of purchased items
Inventory Management (II) Major objectives of inventory
management:
1. Minimizing total inventory management cost under given constraints
2. Satisfying desired customer service level
Functions of Inventory 1. To prevent fluctuation in demand 2. To meet seasonal demand change 3. To protect variation in supply 4. To obtain economy of scale in
procurement/production 5. To maintain independence of operations 6. To smooth production process 7. To provide flexibility for production planning
and scheduling
Type of InventoryInventory types: 1. RM/purchased parts/subassemblies 2. Work-in-process 3. Finished goods
Inventory: Purpose and TypesPurpose: Buffering against any uncertainty in the work flow process from material
purchasing to finished goods shipping through providing a buffer between successive work flow stages.
Types:
Operation Type Inventory Type Buffered Flows
Manufacturing Purchased RMs and Parts
Between Purchasing and manufacturing operations
Work-In-Process Between Successive Production Operations
Finished Goods Between production and Sales
Services Delivery: Supplies Between Purchasing and Services delivery
Wholesale/ Retail Finished goods Stock Between Distribution and Final Sales
Costs Constraints and Customer Service
Relevant costs in inventory management: 1. Fixed costs: purchase ordering
cost/production setup cost 2. Variable costs: holding cost/shortage
cost/purchase costMajor constraint in inventory management: 1. Supply constraint 2. Internal constraint 3. Marketing constraint
Inventory ManagementCosts affected by inventory decisions
Ordering (or setup costs)Clerical costsTransportation and receiving costsCost incurred in setting up
productionOrder follow-up cost
Inventory holding costSpace costsStorage costsCost of capital investedInsurance costsTaxes on investment valuesCosts of spoilage
Stockout or shortage costsExpediting costsRush shipment costsPossible lossLoss of profitPotential loss of customer
Costs of purchased items on which price discounts are offered based on
Total dollar values of purchase order for items
Inventory CostsInventory Costs Interest or opportunity CostInterest or opportunity Cost
Storage and Handling CostsStorage and Handling Costs
Taxes, Insurance, and ShrinkageTaxes, Insurance, and Shrinkage
Customer Service CostCustomer Service Cost
Ordering Cost/Setup CostOrdering Cost/Setup Cost
Labor and Equipment Cost Labor and Equipment Cost
Transportation CostsTransportation Costs
Payments to SuppliersPayments to Suppliers
Customer Service in Inventory Management
Customer Service: measured by the availability of items when needed a performance measure of inventory management
Customer may be: purchaser of FG/distribution/another plant or shop where next operation is performed
Customer Service Level: a target level for keeping initial delivery schedules and backorders
Service Level and Safety Stock Service level: an inventory management
performance criterion measured by
---the percentage of stock-out occurrence defined as service level=1-P(percentage of stock-out)
Safety stock: a quantity of inventory which have been set aside to reduce the probability of stock-out or to improve the service level.
Service Level and Safety StockSafety Stock is: A Quantity of Inventory which have
been set aside to reduce the Probability of Stock-Out, or to improve the Service Level.
The General Relationship Between Safety Stock and Services Level is:
The ABC Classification Method A small percentage of the items that would account for a large percent of the
total values of annual usage- these are called “A” items A large percentage of the item that would account for a small percentage of
the total value of annual usage- these are called “C” items Items in between “A” and “C” items- these are called “B” itemsA typical relationship among A, B and C items is:
ABC AnalysisABC Analysis
1010 2020 3030 4040 5050 6060 7070 8080 9090 100100
Percentage of itemsPercentage of items
Per
cen
tag
e o
f d
oll
ar v
alu
eP
erce
nta
ge
of
do
llar
val
ue
100 100 —
90 90 —
80 80 —
70 70 —
60 60 —
50 50 —
40 40 —
30 30 —
20 20 —
10 10 —
0 0 —
Figure 15.2Figure 15.2
Class C
Class A
Class B
See ABC Classification Example on your
Supplement (p.15-8)
Reading Article about 80/20 Rule on p. 15-11.
ABC Classification ExamplesA wholesaler has ten items in a product line. The item number, selling price, and estimated annual volume in units are:
item Selling price Annual usage in units
Annual Usage in Values
1001 $3.00 10,000 30,0003080 15.00 350 5,2500053 4.60 4,000 18,4004197 2.56 5,000 12,8003683 21.00 200 4,2004421 0.65 10,500 6,8252222 4.49 12,500 56,1255376 6.38 4,400 28,0722121 4.21 750 3,157.50070 5.44 2,000 10,880
Total= 175,709.50
The first step in categorizing the item is to estimate the dollar value of annual usage for each item (multiply the selling price by the estimated annual usage). Then, they should be arranged in descending order. The result of these two steps are:
Item Value of annual usage
Cumulative value of annual usage
Cumulative percent of value of annual usage
2222 $56,125.00 $ 56,125.00 31.9 %
1001 30,000.00 86,125.00 49.0 A5376 28,072.00 114,197.00 65.0
0053 18,400.00 132,597.00 75.5
4197 12,800.00 145,397.00 82.7
0070 10,880.00 156,277.00 88.9 B
4421 6,825.00 163,352.00 92.8
3080 5,250.00 168,352.00 95.8 C3683 4,200.00 172,552.00 98.2
2121 3,157.50 175,709.50 100.0
Assume the wholesaler wants to construct the ABC classification Assume the wholesaler wants to construct the ABC classification with “A” items representing 75% of the sales, “B” using the table with “A” items representing 75% of the sales, “B” using the table above the classification would be:above the classification would be:
Item A Item B Item C
2222 4197 4421
1001 0070 3080
5376 3683
0053 2121
Classification of Inventory Control Models
Demand Characteristics:1. Independent Demand Item (finished goods):
demand of an item is independent to others usually with high uncertainty uncontrollable and external determined
2. Dependent Demand Item (RM/part/ subassembly): demand of an item is dependent on other items’ requirements usually with certainty controllable and internal determined
Types of Demand Independent Demand
When item’s demand is influenced by market conditions and is not related to (i.e. “independent” of) production decisions for any other item
Only end items can qualify in manufacturing Demand must be forecast (uncontrollable)
Dependent Demand When item’s demand derives from (i.e. “depends” on) the production
decisions for its parent All intermediate and purchased items in manufacturing Demand should be derived (can be controlled)
Some items can be viewed as both “independent” and “dependent” demand items!
Classification of Inventory Control Models
Single item inventory vs. multiple-item inventory
Single stage inventory vs. multi-stage Static demand vs. dynamic demand Stochastic demand vs. determined demand
Five Types of Inventory Control System for Independent Demand Items
1. Fixed Order Quantity (Q)- Reorder Point (R) System: (Q,R) Continue review on inventory status (It),
2. Fixed Order Interval (T)- Maximum Level (M) System: (T,M) Periodical review at fixed time interval (T) Place an order at end of each period with a quantity that build On- Hand Inventory
up to M
3. Hybrid System: Combination of Fixed Order Interval (T) and Reorder Point System (R) (Several Possible Combinations).
4. Time-Phased Order Point System: (MRP Application on Independent Demand Items)
5. Single-Period Model: for Perishable Items (Newspaper/ Flower)
Basic Fixed-Order Quantity Model
Economic Order QuantityEconomic Order Quantity
Figure 15.3Figure 15.3
Inventory depletion Inventory depletion (demand rate)(demand rate)
Receive Receive orderorder
1 cycle1 cycle
On
-han
d i
nve
nto
ry (
un
its)
On
-han
d i
nve
nto
ry (
un
its)
TimeTime
AverageAveragecyclecycleinventoryinventory
QQ——22
Fixed-Interval Inventory System(T,M) System
Continuous ReviewContinuous Review So
up Sou
pS
ou
p
Figure 15.7Figure 15.7
TimeTime
On
-han
d i
nve
nto
ryO
n-h
and
in
ven
tory
RR
TBOTBO
LL
TBOTBO
LL
TBOTBO
LL
OrderOrderreceivedreceived
OrderOrderreceivedreceived
OHOH
OrderOrderplacedplaced
IPIP
OrderOrderreceivedreceived
OHOH
OrderOrderplacedplaced
IPIP
OrderOrderreceivedreceived
OrderOrderplacedplaced
IPIP
OHOH
Periodic Review SystemsPeriodic Review Systems
Figure 15.12Figure 15.12
PP PPTimeTime
On
-han
d i
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nto
ryO
n-h
and
in
ven
tory
TT
QQ11
OrderOrderplacedplaced
LL
OrderOrderplacedplaced
OrderOrderreceivedreceived
OrderOrderreceivedreceived
OrderOrderplacedplaced
QQ22
QQ33
OrderOrderreceivedreceived
OHOH
LL LL
Protection intervalProtection interval
IPIP11
IPIP33
IPIP22
IPIP IPIPIPIP
OHOH
Fixed Order Quantity SystemA perceptual system (sometimes called a fixed
quantity or Q/R system) is one that used a fixed reorder point (R) and a fixed order quantity (Q). The time between orders varies depending on when the inventory reaches the reorder point.
Fixed Order Quantity System The inventory behavior is:
LT LT LT
Q QR
(d)
SS= 0
Fixed Order Quantity SystemWhere:
R= reorder point = (d*L) + SS
Q= economic order quantity = EOQ = √D= annual demand (expressed in units/ year)L= reorder lead time (expressed as a fraction of a year)S= ordering cost (expressed as $ per order)C= item cost (expressed in $ per unit)F= inventory holding cost fraction (expressed as a fraction of item cost per year)H= holding cost = (C*F)
The total annual cost (TC) for a purchased item managed with a perpetual inventory system can be calculated as follows:TC= (cost of the item) + (ordering cost) + (inventory holding cost)D*C + ( Q/2)*H + (D/Q)*S
2* DS
H
Example 15.2Example 15.2
3000 3000 —
2000 2000 —
1000 1000 —
0 0 —| | | | | | | |
5050 100100 150150 200200 250250 300300 350350 400400
Lot Size (Lot Size (QQ))
An
nu
al c
ost
(d
oll
ars)
An
nu
al c
ost
(d
oll
ars) Total cost = (Total cost = (HH) + () + (SS))
DDQQ
QQ22
Holding cost = (Holding cost = (HH))QQ22
Ordering cost = (Ordering cost = (SS))DDQQ
Economic Order QuantityEconomic Order Quantity
Economic Order QuantityEconomic Order QuantityA
nn
ual
co
st
(do
llars
)A
nn
ual
co
st
(do
llars
)
Lot Size (Lot Size (QQ))Figure 15.4Figure 15.4
Holding cost (Holding cost (HCHC))
Ordering cost (Ordering cost (OCOC))
Total cost = Total cost = HCHC + + OCOC
See Example on Your Supplement
P. 15-15.
Example of Determining Economic Order Quantity
An importer/distributor or toys uses a standard, corrugated cardboard box for shipping orders to customers. These boxes are used at the rate of 120,000 per year. Each box costs $0.30, and the estimated annual holding cost is 60% of the purchase price.
It requires 20 minutes (or 0.33 hours) to prepare an order for this item. The wage rate of the inventory and purchasing clerks is $5.00 per hour.
D=120,000; C=0.30; F=0.60; H=0.3x0.6=0.18
Problem: Determine how many boxes should be ordered from the supplier each time.
Solution: S= (1/3) x $5= $1.65
EOQ= √2.D.S/H = √2x120,000x1.65/0.18
= 1,483
≈1,500
Problem: If lead time is one day and there are 250 working days during the year, what is the reorder point?
Solution: d= 120,000/250= 480, L=1, SS=0
R= d.L + SS= (480X1) + 0 = 480
Problem: What is the total annual cost of this reordering system?
Solution:
TC = D.C + (D/Q).S + (Q/2).H
= (120,000)(0.3) + (120,000/1,483)1.65+(1483/2)X0.18
= $36,267
Economic Order QuantityEconomic Order Quantity
1.1. Demand rate is constantDemand rate is constant2.2. No constraints on lot sizeNo constraints on lot size3.3. Only relevant costs are holding and Only relevant costs are holding and
ordering/setupordering/setup4.4. Decisions for items are independent Decisions for items are independent
from other itemsfrom other items5.5. No uncertainty in lead time or supplyNo uncertainty in lead time or supply6.6. One Time delivery.One Time delivery.
AssumptionsAssumptions
Fixed Order Quantity System with Gradual Replenishment
The inventory behavior is:
Fixed Order Quantity System with Gradual Replenishment
EPQ= economic production quantity = √
WhereD= annual demand (expressed in units/ year)S= ordering cost (expressed as $ per order)C= item cost (expressed in $ per unit)F= inventory holding cost fraction (expressed as a fraction of item cost per year)P= production rate (expressed in units per period)d= usage rate (expressed in units per period)
TC = [D*C] + ( )*S + ( )*H*( )
2*D*S
H
P
P-d
DQ
Q
2
P-d
P
Special Inventory ModelsSpecial Inventory Models
Production Production and demandand demand
Demand Demand onlyonly
TBOTBO
Production quantityProduction quantity
Demand during Demand during production intervalproduction interval
Maximum inventoryMaximum inventory
On
-han
d i
nve
nto
ryO
n-h
and
in
ven
tory QQ
TimeTime
IImaxmax
p – d
Figure E.1Figure E.1
Imax = (p – d) = Q( )Qp
p – dp
See Example on Your Supplement
P. 15-17.
Example of Determining Economic Production Quantity
A manufacturer of steel products uses a large, special bolt as a fastener in all products in a particular product line. The usage rate of this item is 2000 per day. There are 250 working days in the year. It takes 30 minutes to prepare a manufacturing order for this bolt. The clerks make $5.00 per hour. It takes one hour to change the tooling to begin a production run for the bolt. The setup personnel make $9.00 per hour. The production run is 5000 units per day.C=1.30; F=25%; H=(1.3x25%)=0.325; d= 2,000; D=2,000x250=500,000Problem: What is the economic production quantity for this item assuming a manufacturing cost of $1.30 and an annual holding cost of 25% of the manufacturing cost? S: (0.5x5) + (1x9)= $11.50, P=5,000
EPQ= √(2.D.S)x P/H.(P-d) = √(2x500,000x11.50)x5,000/0.325X(5,000-2,000) ≈7,680
Problem: If lead time is 1.5 days, what is the reorder point?
Solution:
L= 1.5; SS=0
R = d.L +SS
= 2,000X1.5+0
= 3,000
Periodic Systems
Periodic SystemsT= economic order interval = L= reorder lead time (expressed as a fraction of a year)S= ordering cost (expressed as a fraction of a year)D= annual demand (expressed in units/year)C= item cost (expressed in $ per unit)F= inventory holding cost fraction (expressed as a fraction of item
cost per year)Order quantity =
Q= d(L+T) + SS – It
= M- It
(M= (Base-Level) = d(L+T) + SSIt = [On-Hand] + [On-Order] – [Back Order])
See Example on Your Supplement
P. 15-19.
Example of Determining Economic Order Interval
An auto parts store carrier a universal gasoline filter. The store sells 4000 units of this item annually. The cost of this filter from the supply house is $0.50 and the annual holding cost is 20% of the unit value. The cost of preparing a purchase order is $8.00.
D=4,000; C=0.5; F=20%; H=0.5X0.2=0.1
Problem: If the store is open 51 weeks per year, how many weeks should there be between orders?
S=$8.00
T= √2.S/H.D = √2x8/0.1x4,000
=0.2 (Years) x 51
=10.2 (Weeks)
Problems: If the lead time is one week, what is the quantity to be ordered if 110 units are currently on hand at the end of a reorder interval?
D=4,000/51=78, L=1; It=110, SS=0
Q=d(T+L)+SS-It
=78(10.2+1)+0-110≈770Problem: How many orders should be placed each
year?N= 51/10.2 =5 (Orders)
Hybrid SystemA hybrid inventory system has a combination of a
fixed order interval and a fixed reorder point. Examples of hybrid systems are:
Place an order every 4 weeks unless the inventory drops below 100 units. Then, place the order immediately
Place a order every 4 weeks unless the inventory on hand is more than 250 units. Then, wait another week to place the order
Summary Of Basic Inventory Models
Decision Perpetual System (Q,R)
Periodic System (T,M)
When to order
R= d*L + SST= √
How much to order EOQ = √ Q = d* (L+T)+SS - It2*D*S
H
2*S
H*D
√
EPQ= 2DS H
PP-d( )
Inventory Control System Continuous Review (Q,R) System – fixed-order quantity
system for independent demand item: When a withdrawal brings Inventory down to the reorder point
(R), place an order for Q (fixed) units R= average demand during the lead time + safety stock (safety
stock = z* σL)
Periodic Review (P) System – periodic reorder system. Review the inventory every P time periods- place an order (Q)
equal to (T-IP), where T is the target inventory. Here Q varies, and time between orders (TBO) is fixed. Same
four assumptions, but again allow for uncertain demand.
Inventory Control Models ComparisonFixed Order Quantity [Q,R] vs. Fixed Order Periods [T,M]
Fixed Order Quantity Fixed Order Period
Order Quantity Q is fixed (order same) Q is variable (order different)
Order Time Variable, anytime when on-hand reaching R
Fixed at T (period)
Initiated By Event triggered (when I→R)
Time triggered (when t→T)
Control Point Continuous review on inventory
Periodical review only
Operating Cost Very high Low
Implementation Difficult Easy
Data Managing Difficult and time consuming
Easy and simple
Factors to Consider When Determining which System to Use
Factors favoring a Fix-Order Quantity system:
1. high cost items2. items that have high stockout costs3. items that have discount price based on
order quantity4. items that have relatively more irregular
demand patterns
Factors to Consider When Determining which System to Use
Factors favoring a fix Order-Period system:
1. low cost items
2. items that have low stockout costs
3. items that have discount price based on dollar value
4. items that have relatively regular demand patterns
5. items that can be purchased from the same supplier
6. items that their values will change period-by-period
Comparison of Q and P SystemsComparison of Q and P Systems
P SystemsP Systems
Q SystemsQ Systems
Convenient to administerConvenient to administer Orders may be combinedOrders may be combined IP only required at reviewIP only required at review
Individual review frequenciesIndividual review frequencies Possible quantity discountsPossible quantity discounts Lower, less-expensive safety stocksLower, less-expensive safety stocks
Inventory Control System (II) Comparative Advantage of Two Systems
Periodic review system Administration is convenient Standardized routes for transportation systems Easier to combine orders to same supplier May help with price break or paperwork May reduce supplier’s shipping costs
Continuous review system Tailoring Q to costs for each item Easier for quantity discounts or capacity limitations Less safety stock
Hybrid systems Optional replenishment system Base stock system Special case of Q and P system Single- bin system Two- bin system
Basis for Setting the Order Point In the fixed order quantity system, the ordering process is
trigged when the inventory level drops to a critical point the order point
This starts the lead time the item--lead time is the time to complete all activities associated with placing filling and receiving the order.
During the lead time customers continue to draw down the inventory so during this period that the inventory is vulnerable to stock-out ( run out of inventory)
Customer service level is the probability that a stock out will not occur during the lead time (DDLT).
The order point is set based on: the demand during lead time and the desired customer service level
Basis for Setting the Order Point (II) Order point = expected demand + safety stock The amount of safety stock needed is based on
the degree of uncertainty in the DDLT and the customer service level desired
If there is variability in the DDLT the DDLT is expressed as a distribution discrete /continuous DDLT distribution is appropriate when the demand is very high.
Determine R and Safety StockR= Average Demand during Lead-time + Safety Stock
= d*L + SSSS = determined by desired Service Level (%) and Standard
deviation of (d*L)= z* σL
Example: Service Level = 95%, α = 5%, z=1.96; α = 1%, z= 2.33)Given: (d*L)=250, σL=22, α= 1%, z= 2.33
SS= z* σL = 2.33*22 = 51R = (d*L) + SS = 250 + 51 = 301 ≈ 300
Determine R and Safety Stock
R = Average Demand during Lead Time + Safety Stock= d*L + SS
SS = determined by desired Service Level (%) and Standard deviation of (d*L)= z*σL
Example: Service Level = 95%α = 5% z = 1.96α = 1% z = 2.33
Given:(d*L) = 250 σL = 22 α = 1% z = 2.33
SS = z* σL = 2.33*22 = 51
R = (d*L) + SS = 250 +51 = 301 ~300
Reorder Point / Safety StockReorder Point / Safety Stock
Example 15.5Example 15.5
Average Average demand demand
during during lead timelead time
Average demand
during lead time
Cycle-service level = 85%Cycle-service level = 85%
Probability of stockoutProbability of stockout(1.0 – 0.85 = 0.15)(1.0 – 0.85 = 0.15)
zzLL
RR
Safety Stock/R
Safety stock = zL
= 2.33(22) = 51.3= 51 boxes
Reorder point = ADDLT + SS= 250 + 51= 301 boxes
A Quantity Discount ScheduleOrder Quantity Price per Unit
1-99 $ 4.00
100-199 $ 3.50
200 and over $ 3.00
Example: EOQ with Discount Price Given:
D=1000, S=2000, F=20%
Supplier offered a price discount:If the order quantity: Q < 2000; pay $ 100/unit
If the order quantity: Q > 2000; pay $ 80/unit
What is the most economic order quantity that minimizes the total cost?
Example: EOQ with Discount Price (II) 1. assume you normally order less than
2000, then
H=? Q*= ? TC=? 2. if you order Q=2000 to obtain the
discount price then:
H=? Q*=? TC=?
Savings=
Example: EOQ with Discount Price
Given: D= 10,000 S= $2,000 F= 20%Supplier offered a price discount:
If order quantity: Q≤ 2000 You pay $100/unitIf order quantity: Q> 2000 You pay $80/unit
What is the most economic order quantity that minimize the total cost? Assume you normally order less than 2000,
Then H= C1*F = $100 * 0.20 = $20,
So, Q*= √ = 1,414 (<2,000)
TC= (10,000 *100) + (1414/2)*20 + (10,000/1414)* 2000 = $1,028,284 If you order (just) Q= 2000 to obtain the discount price ($80), Then H= C2*F= $80*0.20 = $16, with Q* = 2,000
TC= (10,000*80)+2000/2*16 + 10,000/2000*2000= 826,000 Savings: 1,028,284-826,000=$202.284
2*10,000*200020
unattainable
unrational
1,414 2,000
TC
Q
P1=100
P2=80
CC for for PP = $4.00 = $4.00CC for for PP = $3.50 = $3.50CC for for PP = $3.00 = $3.00
PDPD for forPP = $4.00 = $4.00 PDPD for for
PP = $3.50 = $3.50 PDPD for forPP = $3.00 = $3.00
Special Inventory ModelsSpecial Inventory ModelsQuantity DiscountsQuantity Discounts
EOQ EOQ 4.004.00
EOQ EOQ 3.503.50
EOQ EOQ 3.003.00
First First price price breakbreak
Second Second price price breakbreak
To
tal c
ost
(d
olla
rs)
To
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ost
(d
olla
rs)
To
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(d
olla
rs)
To
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ost
(d
olla
rs)
Purchase quantity (Purchase quantity (QQ))00 100100 200200 300300
Purchase quantity (Purchase quantity (QQ))00 100100 200200 300300
First price break
Second price break
(a) Total cost curves with purchased materials added(a) Total cost curves with purchased materials added (b) EOQs and price break quantities(b) EOQs and price break quantities
Figure E.3Figure E.3
Sensitivity of EOQ Model to Changes Sensitivity of EOQ Model ( Effect of changes)
Due to “Square-Root” effect, the EOQ model is relatively “insensitive” to small changes from model parameter.
For change in the demand rate (D) or Order Cost (S):
-D (or S) is the numerator, EOQ varies directly as the square root of D (or S)
For Change in the holding cost (h):
-H is in the denominator, so if H decreases, EOQ increases Errors in estimating D, H and S
Errors such as overestimating ordering cost may be offset by other errors such as overestimating holding cost.
The square root also reduces the effect of errors. If one misses a cost or demand estimate by 10%, the effect on total cost is often undetectable
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