14 Variability

8/3/2019 14 Variability

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Variability

The Bull Whip EffectA Vicious Cycle

Build-to-Order, Lean, JIT,

Managing Variability: A different view ofinventory

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ExampleProcter & Gamble: Pampers

Smooth consumer demandFluctuating sales at retail stores

Highly variable demand on distributorsWild swings in demand on

manufacturingGreatest swings in demand on suppliers



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Illustration

Consumer Sales at Retailer

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900

RetailerOrder

Consumerdem

and

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1000

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Retailer's Orders to Distributor

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Illustration

Retailer's Orders to Distributor

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Distributor's Orders to P&G

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DistributorOr

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Illustration

Distributors Orders to P&G

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P&G

Order

DistributorO

rder900

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P&G's Orders with 3M

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Illustration

Consumer Sales at Retailer

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900

Consumerdem

and

P&G

Order

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01

1

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P&G's Orders with 3M

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What Are the Effects?

What problems, costs, challenges doesthis create for the players in thesupply chain?

What problems does this create for theproduct in the market place?



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Forecasting

Poorer forecasts

More variability

Less reliable supply



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Causes of Bullwhip TodayProduct Proliferation/Mass

CustomizationMore varieties of products

Build-to-OrderProhibits pooling orders to smoothrequirements

LeanPrevents pooling releases to smoothdemand on the supply chain



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Why Lean (Just-In-Time)?

Reduces inventoryCapital requirementsEtc

Reduces handlingDirect-to-Line

Improves QualitySee problems quickly

Increases launch speed15.057 Spring 03 Vande Vate 10


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Why Not Lean?Capacity

Changes in requirements create upstreaminventory

Changes in requirements raise transportcosts

Reliability

Distant suppliers subject to disruption



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Release Variability

Daily Receipt

1400

1200

1000

800

600

400

200

0

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Managing Variability

Capacity Buffer

Inventory Buffer

Time Buffer



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Freight Cost

Capacity

Utilized Capacity

R

equired

rateofconveyances

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Expediting Expedited Service

R

equiredrateofconveyances

Lower Capacity

Utilized Capacity

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Ideal Supply Chain

Same requirements every dayNo excess capacityNo inventory No service failuresMinimum Cost



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Buffer Inventory with Constant Supply


Volum

e

Time

Variation in Demand

Variation in Buffer


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A Financial ModelFrom Revenues

Cash Expenses

Cash Acct15.057 Spring 03 Vande Vate 18


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A Financial ModelFrom Revenues

Cash Expenses

Sell Assets

Invest

Cash Acct15.057 Spring 03 Vande Vate 19


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ControlsWhen Cash

Invest

balance reachesenoughto bring it

to here

here



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Controls

When Cashbalance

falls to here

Sell assetsto bring it

to here



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Controls

T

bt



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Trade-offs

Opportunity cost of Cash BalanceTransaction costs of investing andselling assets

Set the controls, T, t and b tobalance these costs



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Inventory Analogy

Cash Expenses Daily Production reqs.From Revenue Constant suppliesSell Assets Expedited orderInvest Excess Curtailed order



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Trade-offs

Opportunitycost of Cash BalanceTransactioncosts ofinvesting andselling assets

Cost ofholding

InventorySupply chain

costs ofexpeditingand curtailingorders

Set the controls, T, t and b

to balance these costs15.057 Spring 03 Vande Vate 25


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Challenges

Data intensive:pi

s and qi

s

Computationally intensive

Alternative

Brownian motionInventory behaves like

a random walk

Model of a particle in spaceTwo parameters: mean and variance

Advanced calculus methods make it easy to work with



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Release Variability

Daily Receipt

1400

1200

1000

800

600

400

200

= 367

= 412

68% of time usage is

between 0 and 800

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The EOQ as a Special Case

Average usage rate Variance in usage 2

Nominal release rate < Since we order less than we consume,

inventory drifts downward

How much should we expedite when it

reaches 0?



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Trade offs

Expediting disrupts the supply chain

Fixed cost F for each time we expedite

Variable cost f for each item in the order

holding cost h for inventory

Larger orders mean less frequent but larger disruptions and more inventory



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EOQ as Special Case

Order Q

Time between orders is Q/()

Order frequency is ()/Q

Average Inventory is Q/2 + 2/2()

Average Cost is

Expediting Cost: (F+fQ)()/QInventory Cost: h(Q/2 + 2/2())



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The Total Cost Formula

hQ/2 + F( )/Q + h2/2( ) + f( )EOQ: Transaction Constant that doesnt depend on Q

EOQ: Inventory

The best Q balances inventory and orderingcosts:

hQ/2 = F( )/QQ2 = 2F( )/hQ = 2F( )/h



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Fixed Expediting Quantity

Find the best nominal release rate to get the right frequency of expediting



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The Total Cost Formula

hQ/2 + h2/2r + fr + Fr/Q

EOQ: Transaction EOQ: Inventory

Constant that doesnt depend on r

The best drift rate r = balancesinventory and ordering costs:

h2/2r = fr + Fr/Q

r2 = h2Q/2(F+fQ)

r = h2Q/2(F+fQ)15.057 Spring 03 Vande Vate 34


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Two-sided Version

If inventory grows too large, curtailshipments

Whats too large?

How much should we curtail?If expediting is expensive

create a positive driftorder more than you need

curtail shipments when inventory is too high



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Differences

Constant Stream of Releases punctuatedby Expediting and Curtailing

If supplier can see inventory,

can anticipate expedited and curtailed orders

Have to set a lower bound > 0 to protect

against disruptions safety stock



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Example: Shipments300

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Example: Inventory

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0

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14 Variability

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