inventory planning & uncertainity
TRANSCRIPT
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Opposing Views of Inventories
Nature of Inventories
Fixed Order Quantity Systems Fixed Order Period Systems
Other Inventory Models
Some Realities of Inventory Planning
Wrap-Up: What World-Class Companies Do
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Why We Want to Hold Inventories?
Why We Do Not Want to Hold Inventories?
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Finished Goods
o Essential in produce-to-stock positioning strategieso Necessary in level aggregate capacity planso Products can be displayed to customers
Work-in-Process
o Necessary in process-focused productiono May reduce material-handling & production costs
Raw Material
o Suppliers may produce/ship materials in batcheso Quantity discounts and freight/handling $$ savings
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Certain costs increase such as
o carrying costso cost of customer responsivenesso cost of coordinating productiono cost of diluted return on investmento reduced-capacity costso large-lot quality costo cost of production problems
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Current trends in inventory management
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Two Fundamental Inventory Decisions
Terminology of Inventories
Independent Demand Inventory Systems Dependent Demand Inventory Systems
Inventory Costs
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Demand for an item carried in inventory isindependent of the demand for any other item ininventory
Finished goods inventory is an example
Demands are estimated from forecasts and/orcustomer orders
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Items whose demand depends on the demands forother items
For example, the demand for raw materials andcomponents can be calculated from the demand forfinished goods
The systems used to manage these inventories aredifferent from those used to manage independentdemand items
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B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand(components)
A
Independent Demand(finished goods and spare parts)
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Costs associated with ordering too much(represented by carrying costs)
Costs associated with ordering too little(represented by ordering costs)
These costs are opposing costs, i.e., as oneincreases the other decreases
. . . more
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Annual Cost ($)Annual Cost ($)
Order QuantityOrder Quantity
MinimumMinimum
Total AnnualTotal Annual
Stocking CostsStocking Costs
MinimumMinimum
Total AnnualTotal Annual
Stocking CostsStocking Costs
AnnualAnnualCarrying CostsCarrying Costs
AnnualAnnualOrdering CostsOrdering Costs
Total AnnualTotal AnnualStocking CostsStocking Costs
SmallerSmaller LargerLarger
Lowe
r
Lowe
r
High
er
High
er
EOQEOQ
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Inventory Costs
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Behavior of Economic Order Quantity (EOQ)Systems
Determining Order Quantities
Determining Order Points
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As demand for the inventoried item occurs, theinventory level drops
When the inventory level drops to a critical point, theorder point, the ordering process is triggered
The amount ordered each time an order is placed isfixed or constant
When the ordered quantity is received, the inventorylevel increases
An application of this type system is the two-bin system
A perpetual inventory accounting system is usuallyassociated with this type of system
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Basic EOQ
EOQ for Production Lots
EOQ with Quantity Discounts
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Typical assumptions made
o annual demand (D), carrying cost (C) andordering cost (S) can be estimated
o
average inventory level is the fixed orderquantity (Q) divided by 2 which implies
no safety stock
orders are received all at once
demand occurs at a uniform rate
no inventory when an order arrives
o . . . more
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Assumptions (continued)
o Stockout, customer responsiveness, and other costs areinconsequential
o acquisition cost is fixed, i.e., no quantity discounts
Annual carrying cost = (average inventory level) x(carrying cost) = (Q/2)C
Annual ordering cost = (average number of ordersper year) x (ordering cost) = (D/Q)S
. . . more
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CDS/2=EOQ
Total annual stocking cost (TSC) = annualcarrying cost + annual ordering cost = (Q/2)C +(D/Q)S
The order quantity where the TSC is at aminimum (EOQ) can be found using calculus (takethe first derivative, set it equal to zero and solvefor Q)
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Used to determine the order size, production lot, ifan item is produced at one stage of production,stored in inventory, and then sent to the next stage
or the customer
Differs from Model I because orders are assumed tobe supplied or produced at a uniform rate (p) raterather than the order being received all at once
. . . more
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It is also assumed that the supply rate, p, isgreater than the demand rate, d
The change in maximum inventory level
requires modification of the TSC equation TSC = (Q/2)[(p-d)/p]C + (D/Q)S
The optimization results in
dpp
CDS2=EOQ
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Under this condition, acquisition cost becomes anincremental cost and must be considered in thedetermination of the EOQ
The total annual material costs (TMC) = Totalannual stocking costs (TSC) + annual acquisitioncost
TSC = (Q/2)C + (D/Q)S + (D)ac
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Basis for Setting the Order Point
DDLT Distributions
Setting Order Points
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In the fixed order quantity system, the orderingprocess is triggered when the inventory level drops toa critical point, the order point
This starts the lead time for the item.
Lead time is the time to complete all activitiesassociated with placing, filling and receiving theorder.
. . . more
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During the lead time, customers continue to drawdown the inventory
It is during this period that the inventory is
vulnerable to stockout (run out of inventory)
Customer service level is the probability that astockout will not occur during the lead time
. . . more
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The order point is set based on
o the demand during lead time (DDLT) and
o the desired customer service level
Order point (OP) = Expected demand during leadtime (EDDLT) + Safety stock (SS)
The amount of safety stock needed is based on
the degree of uncertainty in the DDLT and thecustomer service level desired
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If there is variability in the DDLT, the DDLT isexpressed as a distribution
o discrete
o Continuous
In a discrete DDLT distribution, values (demands)can only be integers
A continuous DDLT distribution is appropriatewhen the demand is very high
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Assume a probability distribution of actual DDLTs isgiven or can be developed from a frequencydistribution
Starting with the lowest DDLT, accumulate theprobabilities. These are the service levels for DDLTs
Select the DDLT that will provide the desiredcustomer level as the order point
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Assume that the lead time (LT) is constant
Assume that the demand per day is normally distributed
with the mean (d ) and the standard deviation ( d )
The DDLT distribution is developed by adding togetherthe daily demand distributions across the lead time
. . . more
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The resulting DDLT distribution is a normaldistribution with the following parameters:
EDDLT =LT(d)
DDLT
=
2)( dLT
2)( dLT
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The customer service level is converted into a Zvalue using the normal distribution table
The safety stock is computed by multiplying the Zvalue by DDLT .
The order point is set using OP = EDDLT + SS, orby substitution
2
dOP = LT(d) + z LT( )
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Set safety stock level at a percentage of EDDLT
OP = EDDLT + j(EDDLT)
where j is a factor between 0 and 3. Set safety stock level at square root of EDDLT
OP = EDDLT+EDDLT
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Behavior of Economic Order Period (EOP) Systems
Economic Order Period Model
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As demand for the inventoried item occurs, the inventorylevel drops
When a prescribed period of time (EOP) has elapsed, theordering process is triggered, i.e., the time between ordersis fixed or constant
At that time the order quantity is determined using orderquantity = upper inventory target - inventory level +EDDLT
. . . more
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After the lead time elapses, the ordered quantityis received , and the inventory level increases
The upper inventory level may be determined by
the amount of space allocated to an item
This system is used where it is desirable tophysically count inventory each time an order is
placed
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EOP = 2S / DC
Using an approach similar to that used to deriveEOQ, the optimal value of the fixed time betweenorders is derived to be
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Optional replenishment model
o Similar to the fixed order period model
o Unless inventory has dropped below a prescribedlevel when the order period has elapsed, no order isplaced
o Protects against placing very small orders
o Attractive when review and ordering costs are large
. . . more
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Base stock model
o Start with a certain inventory level
o
Whenever a withdrawal is made, an order ofequal size is placed
o Ensures that inventory maintained at anapproximately constant level
o
Appropriate for very expensive items withsmall ordering costs
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ABC Classification
EOQ and Uncertainty
Dynamics of Inventory Planning
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Start with the inventoried items ranked by dollarvalue in inventory in descending order
Plot the cumulative dollar value in inventoryversus the cumulative items in inventory
. . . more
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Typical observations
o A small percentage of the items (Class A) makeup a large percentage of the inventory value
o
A large percentage of the items (Class C) makeup a small percentage of the inventory value
These classifications determine how muchattention should be given to controlling the
inventory of different items
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Items kept in inventory are not of equalimportance in terms of:
o dollars invested
o
profit potential
o sales or usage volume
o stock-out penalties 0
30
60
30
60
AB
C
% of$ Value
% of
Use
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The TSC and TMC curves are relatively flat, thereforemoving left or right of the optimal order quantity on theorder quantity axis has little effect on the costs
Estimation errors of the values of parameter used tocompute an EOQ usually do not have a significantimpact on total costs
Many costs are not directly incorporated in the EOQand EOP formulas, but could be important factors
Emergency procedures to replenish inventories quicklyshould be established
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Continually review ordering practices and decisions
Modify to fit the firms demand and supply patterns
Constraints, such as storage capacity and availablefunds, can impact inventory planning
Computers and information technology are usedextensively in inventory planning
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Maximum Inventory Level, M
MActual Inventory Level, I
q = M - I
I
Q = minimum acceptable order quantityDecision rule: If q > Q, order q, otherwisedo not order any
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Two-Bin System
Full Empty
Order One Bin of
Inventory when
one is emptied
One-Bin System
Periodic
Check
Order Enough toRefill Bin
(e.g. check book)
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Inventory cycle is the central focus ofindependent demand inventory systems
Production planning and control systems arechanging to support lean inventory strategies
Information systems electronically link supply
chain
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