inventory planning & uncertainity

8/8/2019 Inventory Planning & Uncertainity

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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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inventory planning & uncertainity

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