© Muckstadt, Murray, Rappold. All Rights Reserved. The Laws of Supply Chain Physics John A. Muckstadt Cornell University December 6, 2001.

© Muckstadt, Murray, Rappold. All Rights Reserved.

The Laws of Supply Chain Physics

John A. MuckstadtCornell UniversityDecember 6, 2001


A Typical Supply Chain

Raw Material Suppliers(Internal or External)

Plants Downstream Customers

Raw

Ma

teri

als

Ran

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No

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ary

Co

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an

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Time


Traditional View of Decision Hierarchy

• Strategic Planning– Product markets, M&A, Allocation of Assets

• Tactical Planning– Sales & Operations Planning– Plant Operations Planning

• Operations– Detailed Scheduling– Execution


Planning Issues• Customer demand is highly uncertain and non-stationary.


Demand Estimates by Quarter

Planned Production CapacityDemand Estimates by Quarter


Actual Demand by Day

Nominal Production CapacityActual Demand


Planning Issues• Customer demand is highly uncertain and non-stationary.• Product-level forecasts are uncertain over short time

horizons.


Customer Demand


The Effect of Product Level Forecasts on Production


Planning Issues• Customer demand is highly uncertain and non-stationary.• Product-level forecasts are uncertain over short time

horizons.

• Limited production capacity necessitates inventory in certain products in order to meet customer service objectives.

• Uncertainty in production capacity, yields, and supplier delivery performance also dictates additional safety stock.

• The supply chain planner must be able to gather and assimilate state-of-the-world data and to make resource allocation decisions under uncertainty that will have far-reaching consequences in future time periods.

• The supply chain planner must adhere to the laws of supply chain physics.





Raw

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Time


Local optimization results in global disharmony

First Law of Supply Chain Physics





Raw

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Time


Second Law of Supply Chain Physics

• The average amount of inventory in a system is equal to the product of the demand rate and the average time a unit is in the system (Little’s Law)

L = W


The Impact of Uncertainty and Limited Capacity

• Consider a single plant location subject to random customer demands received periodically.

• The plant has a finite production capacity in each period.

• Demand must be satisfied in the period in which it arises.

• Question: What are the relationships among:

– customer service,

– inventory requirements, and

– production capacity usage? Random customer demand

Finished goods inventory

Production facility with limited capacity


Central Issue

• How much inventory is required to minimize costs or to support a specific customer service level objective?


Customer Demand

0

10

20

30

40

50

60

70

80

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191

Day

Un

its

49.99

7.12

0.14

Mean demand 50 units/periodStd Dev 7.1 units/periodMax Capacity 58 units / period

Period


Production

0

10

20

30

40

50

60

70

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191

Day

Un

its

49.99

6.22

0.12

Period


Inventory Level

-20

-15

-10

-5

0

5

10

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191

Day

Un

its

Customer Service (Fill Rate)99.5%

4.24

2.39

0.56

Mean demand 50 units/dayStd Dev 7.1 units/day

Period


Inventory Level

-120

-100

-80

-60

-40

-20

0

20

40

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191

Day

Un

its


5.60

35.69

6.38

Mean demand 50 units/dayStd Dev 23 units/dayMax Capacity 58 units / day

Period


Inventory Level

-250

-200

-150

-100

-50

0

50

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191

Day

Un

its


(47.48)

84.50

1.78

Mean demand 50 units/dayStd Dev 23 units/dayMax Capacity 53 units / day

Period


ExampleFill Rate vs. Inventory Investment

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

0 100 200 300 400 500Inventory

Fill

Ra

te

Demand Mean is 100 units/periodDemand StdDev is 30 unitsCapacity Utilization is 85%

Need 60 units to support a 90% service level.Need 77 units to support a 95% service level.Need 100 units to support a 98% service level.


Fill Rate vs. Inventory Investment

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

0 100 200 300 400 500Inventory

Fill

Ra

teCapacity Utilization increased to 95%

Demand Mean is 100 units/periodDemand StdDev is 30 unitsCapacity Utilization is 95%

Need 198 units to support a 90% service level.Need 258 units to support a 95% service level.Need 335 units to support a 98% service level.

or roughly 330% more inventory for the same level of service.


• Inventories are a consequence of supply chain design and customer service objectives.

• Supply chains are dynamic systems.– Capacity Utilization– Inventory Levels– Customer Service

• Pick any two, and the other is determined.

• The exact mathematical representation depends on the forms of the stochastic processes generating demands and governing productive capacity.

are NOT independent

Third Law of Supply Chain Physics


The value of collaboration and information sharing diminish as the

capacity utilization is either extremely high or extremely low.

Fourth Law of Supply Chain Physics


Sources and Effects of Supply Chain Uncertainty

• Supply chain design and management are significant determinants of operational uncertainty.

• Uncertainty is often created by the structure and rules employed in the operation of a supply chain.– Lead times– Forecasting mechanisms– Capacity allocation rules– Inventory stocking policies


An Example Supply Chain Environment

Order

CustomerOperations

ProductionLead Time

Product

Lead TimeDownstreamBU

ConsumerDemand

( Mean, Variance )

Order

Demand

Time

Information Sharing

Product

Information

• Forecasting mechanism• Stocking policies

• Forecasting mechanism• Stocking policies• Level of information sharing


Customer Demand


Central Warehouse Demand


Factory Demand


Factory Demand with Information Sharing


Lead Time Reduction and No Information Sharing


Lead Time Reduction with Information Sharing


• Effective supply chain design will reduce uncertainty dramatically and improve operational and financial performance significantly.

• However, residual uncertainty will exist and must be effectively considered in a decision support environment.

Fifth Law of Supply Chain Physics


Historical Demand by Quarter

Mean = 741.2

StdDev = 69.1

Coeff Var = 0.09

units per day

units per day

Production CapacityDemand


Historical Demand by Month

Mean = 741.2

StdDev = 131.1

Coeff Var = 0.18

units per day

units per day



Historical Demand by Day

Mean = 741.2

StdDev = 771.8

Coeff Var = 1.04

units per day

units per day



Complications

• All products are not demanded equally.

• All customers do not behave in the same manner.

• Operating strategies and implementing decision support systems must contend with these differences and respect the operational trade-offs throughout the supply chain.


0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321

Rank

Cu

mu

lati

ve %

of

To

tal

Cap

acit

y D

eman

ded

Distribution of Products


Total Demand

0

10

20

30

40

50

60

70

80

09/01/98 10/21/98 12/10/98 01/29/99 03/20/99 05/09/99 06/28/99 08/17/99 10/06/99

Day

To

tal Q

ty

1.0

6.4

6.4

289

Average =

StdDev =

CV =

Total Units =

39- Part X700P220A1B

Example Product A


Total Demand

0

10

20

30

40

50

60

70

80

90

100

09/01/98 10/21/98 12/10/98 01/29/99 03/20/99 05/09/99 06/28/99 08/17/99 10/06/99

Day

To

tal Q

ty

1.2

6.1

5.3

338

Average =

StdDev =

CV =

Total Units =


Example Product B


Total Demand

0

20

40

60

80

100

120

140

09/01/98 10/21/98 12/10/98 01/29/99 03/20/99 05/09/99 06/28/99 08/17/99 10/06/99

Day

To

tal Q

ty

3.6

13.4

3.7

1,051

Average =

StdDev =

CV =

Total Units =

15- Part X700PPTA1C

Example Product C


Total Demand

0

10

20

30

40

50

60

70

80

90

100

09/01/98 10/21/98 12/10/98 01/29/99 03/20/99 05/09/99 06/28/99 08/17/99 10/06/99

Day

To

tal Q

ty

1.3

8.9

6.6

390

Average =

StdDev =

CV =

Total Units =


Example Product D


• Accurate item level forecasts are often not statistically accurate for most items over a short-time horizon.

Sixth Law of Supply Chain Physics


Dealing With Residual Uncertainty: The No B/C Production-Inventory

Strategy

• Store capacity only in items for which it is possible to estimate demand distributions and to use capacity effectively to produce requirements for other items upon demand.

• Keep inventory to mitigate against the uncertainty in the total demand for capacity. The amount of inventories kept depends on the variation in aggregate demand for capacity and the variation in the available capacity in each time period.


• Keep your assets in their most flexible form for as long as it is economically and operationally possible.

Seventh Law of Supply Chain Physics


Summary: Guiding Principles

1. Know customer requirements.

2. Construct a lean supply chain organization.

3. Build tightly-coupled information infrastructures.

4. Build tightly-coupled business processes.

5. Construct tightly-coupled decision support systems.


“There is nothing more difficult to plan,nor more dangerous to manage,

nor more doubtful of success,than the creation of a new order of things.

For the reformer has fierce enemies in all who would profit from the preservation of the old,

and only lukewarm defenders in those who would gain from the new.

This lukewarmness arises partly from the fear of their adversaries, who have law in their favor, and partly

from the incredulity of mankind, who do not truly believe in anything new until they have had an actual

experience of it.”

Niccolo Machiavelli - 1513

© Muckstadt, Murray, Rappold. All Rights Reserved. The Laws of Supply Chain Physics John A. Muckstadt Cornell University December 6, 2001.

Documents

customer demand slide

production slide

mean demand

limited capacity slide

quarter slide

units period period

unitsday period slide

w slide