Variability

The Bull Whip Effect A Vicious Cycle Build-to-Order, Lean, JIT, … Managing Variability: A different view of inventory

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Example Procter & Gamble: Pampers

Smooth consumer demand Fluctuating sales at retail stores Highly variable demand on distributors

Wild swings in demand on manufacturing Greatest swings in demand on suppliers

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IllustrationRetailer's Orders to Distributor

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Distributor's Orders to P&G 1000

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IllustrationDistributor’s Orders to P&G

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What Are the Effects?

What problems, costs, challenges does this create for the players in the supply chain?

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

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Forecasting

Poorer forecasts

More variability

Less reliable supply

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Causes of Bullwhip Today

Product Proliferation/Mass Customization

More varieties of products Build-to-Order

Prohibits pooling orders to smooth requirements

Lean Prevents pooling releases to smooth demand on the supply chain

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Why Lean (Just-In-Time)?

Reduces inventory Capital requirements Etc

Reduces handling Direct-to-Line

Improves Quality See problems quickly

Increases launch speed15.057 Spring 03 Vande Vate 10

Why Not Lean? Capacity

Changes in requirements create upstream inventory Changes in requirements raise transport costs

Reliability Distant suppliers subject to disruption

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Release VariabilityDaily Receipt

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0 01-Apr-02 06-Apr-02 11-Apr-02 16-Apr-02 21-Apr-02 26-Apr-02

Managing Variability

Capacity Buffer Inventory Buffer Time Buffer

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Freight Cost

Capacity

Utilized Capacity

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Expediting Expedited Service

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Lower Capacity

Utilized Capacity

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Ideal Supply Chain

Same requirements every day

No excess capacity

No inventory No service failures

Minimum Cost

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Buffer Inventory with Constant Supply

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Vol

ume

Time

Variation in Demand

Variation in Buffer

A Financial Model

From Revenues

Cash Expenses

Cash Acct15.057 Spring 03 Vande Vate 18

A Financial Model

From Revenues

Cash Expenses

Sell Assets

Invest

Cash Acct15.057 Spring 03 Vande Vate 19

Controls When Cash

Invest balance reaches enough to bring it to here

here

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Controls

When Cash balance falls to here

Sell assets to bring it to here

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Controls

T

b t

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Trade-offs

Opportunity cost of Cash Balance Transaction costs of investing andselling assets Set the controls, T, t and b to balance 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 Balance Transaction costs of investing andselling assets

Cost of holdingInventory Supply chaincosts of expeditingand curtailingorders

Set the controls, T, t and b to balance these costs

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The Traditional Model

1

0 1 2 k M … … … p1 p2 pk

q2 qk

1-(p1+ q1)

q1 1

A Markov Model15.057 Spring 03 Vande Vate 26

Challenges

Data intensive: pi’s and qi’s Computationally intensive Alternative

Brownian motion Inventory behaves like

a random walk Model of a particle in space

Two parameters: mean and variance Advanced calculus methods make it “easy” to work with

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Release VariabilityDaily Receipt

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µ = 367

σ = 412

68% of time usage is between 0 and 800

0

01-Apr-02 06-Apr-02 11-Apr-02 16-Apr-02 21-Apr-02 26-Apr-02

The EOQ as a Special Case

Average usage rate µ

Variance in usage σ2

Nominal release rate λ < µ

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/(µ – λ) Order frequency is (µ – λ)/Q Average Inventory is Q/2 + σ2/2(µ – λ) Average Cost is

Expediting Cost: (F+fQ)(µ – λ)/Q Inventory Cost: h(Q/2 + σ2/2(µ – λ))

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The Total Cost Formula

hQ/2 + F(µ – λ)/Q + hσ2/2(µ – λ) + f(µ – λ)

EOQ: Transaction Constant that doesn’t depend on Q EOQ: Inventory

The best Q balances inventory and ordering costs:

hQ/2 = F(µ – λ)/Q Q2 = 2F(µ – λ)/h Q = √2F(µ – λ)/h

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Fixed Expediting Quantity

Find the best nominal release rate λ

to get the right frequency of expediting

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The Total Cost Formula

hQ/2 + hσ2/2r + fr + Fr/Q

EOQ: Transaction EOQ: Inventory Constant that doesn’t depend on r

The best drift rate r = µ − λ balances inventory and ordering costs:

hσ2/2r = fr + Fr/Q r2 = hσ2Q/2(F+fQ) r = √hσ2Q/2(F+fQ)

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Two-sided Version

If inventory grows too large, curtail shipments What’s too large? How much should we curtail? If expediting is expensive

create a positive drift order more than you need curtail shipments when inventory is too high

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Differences

Constant Stream of Releases punctuated by 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: Inventory1000

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