Inventory and Variability - LGO-SDM PROGRAM AT MIT · c2010StanleyB.Gershwin. Allrightsreserved....

Inventory and Variability

Stanley B. [email protected]

http://web.mit.edu/manuf-sys

Massachusetts Institute of Technology

December 13, 2010

Inventory and Variability 1/29 Copyright c©2010 Stanley B. Gershwin. All rights reserved.

Inventory

◮ Inventory is a necessary evil, and we do our best to minimize it.

◮ Variability makes inventory necessary.

◮ Variability is the enemy of manufacturing.


InventoryCosts

◮ Financial: raw materials have been paid for, but no revenue comes inuntil the finished product is sold.

◮ Demand risk: a product may not be sold due to (for example):◮ time value (newspaper)◮ obsolescence◮ going out of fashion◮ spoilage (food)

The longer an item is in storage, the more likely that one of these willoccur.


InventoryCosts

◮ Holding cost (warehouse space)

◮ Damage/theft/loss

◮ Reduction of yield when inspection is not immediate.

◮ Concealment of causes of problems — the sources of variability.


InventoryBenefits and Motivation

◮ The purpose of storage is to allow systems to survive even whenimportant events are unsynchronized.

◮ Storage improves system performance by decoupling parts of thesystem from one another.

◮ Storage reduces the propagation of disturbances, and thus reducesinstability and the fragility of complex, expensive systems.

◮ Storage allows production systems (of energy or goods) to be builtwith capacity less than the peak demand.


InventoryBenefits and Motivation

◮ Reduces the propagation of disturbances (eg, machine failures).

◮ Allows economies of scale:◮ volume purchasing◮ set-ups

◮ Helps manage seasonality and limited capacity.

◮ Helps manage uncertainty:◮ Short term: random arrivals of customers or orders.◮ Long term: Total demand for a product next year.


VariabilityCauses

◮ Random (uncontrollable)

◮ random demand◮ random supply◮ machine failures◮ human variability

◮ Deterministic (controllable)◮ setups◮ batches◮ order costs◮ MRP nervousness


VariabilityHow variability causes inventory

B1

B2

largepipes

smallpipe

75

100

75

100

75

100

No variability:

◮ Assume the small pipe is thebottleneck.

◮ There is no accumulation of waterin either tank.

◮ The outflow rate in the third pipe isalways the same as the rate of flowinto the first pipe.

◮ Call this Case 1 .



M2

M1

M3

B1

B2

largepipes

all valves closed

0

0

0

Variable valves, Case 2

◮ In this figure, all valves are closed.

◮ While the system is in this state,the water level does not change inany tank, and there is no inflow oroutflow.

◮ But it does not stay in this stateforever.



M1

M 2

M3

B1

B2

0 100

0

0


◮ Now the second valve is opened.

◮ While the system is in this state,the first tank loses water and thesecond tank gains water, and thereis no inflow or outflow.

◮ If it stays in this state long enough,the first tank becomes empty orthe second tank becomes full.

◮ But it does not stay in this stateforever either.



M1

M 2

M3

B1

B2

0 100

0

0 100


◮ Now the second and third valvesare opened.

◮ While the system is in this state,the first tank loses water. The levelsecond tank stays constant. Thereis no inflow but there is outflow atmaximum rate ...

◮ until the first tank becomes empty,and then the second tank loseswater until it becomes empty.

◮ But it leaves this state eventuallyalso.



M2

M1

M3

B1

B2

0

0 100

0 100


◮ There are a total of eight valve states.For each state, the flow rate in eachpipe is either 0 or 100.

◮ Think of an open valve as operationaland a closed valve as failed. Then thevalves are characterized by MTTF,MTTR.

◮ For some set of MTTFs and MTTRs,the average flow rate of Case 2 is thesame as the flow rate of Case 1...

◮ ... but Case 2 has inventory and Case1 does not.



Conclusions:

◮ Variability causes inventory.

◮ The tanks in Case 1 are always empty.

◮ The tanks in Case 2 gain or lose material due to the unsynchronizedvalve behavior.

◮ Variability makes inventory necessary.

◮ We would get the same flow rate in Case 1 if the tanks were not there.

◮ The flow rate in Case 2 is a function of the valve behavior (MTTF andMTTR) and the sizes of the tanks. To make the average flow rate ofCase 2 the same as the flow rate of Case 1, tanks may be necessary.


What is an Operation?

OperationPart Part

Waste

MachineOperator

Consumable

Nothing happens until everything is present.


What is an Operation?Waiting

Whatever does not arrive last must wait.

◮ Inventory: parts waiting.

◮ Under-utilization: machines waiting.

◮ Idle work force: operators waiting.


What is an Operation?Waiting

OperationPart Part

Waste

MachineOperator

Consumable

◮ Reductions in the availability, or ...

◮ Variability in the availability ...

... of any one of these items causes waiting in the rest of them and reduces

performance of the system.


Variability — Causes and CuresCreation

Causes

◮ random demand

◮ random supply

◮ machine failures

◮ human variability

◮ setups

◮ batches

◮ order costs

Cures

◮ manage demand,

◮ find a more reliable supplier

◮ improve machines

◮ improve human management

◮ reduce setup and order costs

◮ increase capacity and flexibility


Variability — Causes and CuresPropagation

Causes

◮ blockage and starvation

Cures

◮ in-process inventory buffers


Variability — Causes and CuresAmplification

Causes

◮ MRP nervousness – changes inschedule in the presence ofbatching

Cures

◮ reduce setup and order costs

◮ develop improved schedulingmethods


Variability — Causes and CuresConclusion:

Therefore, factories should be

◮ designed and operated

to minimize the

◮ creation, propagation, and amplification

of uncertainty, variability, and randomness.


How inventory and variability interactSimulations: Buffer Level vs. time

0

2

4

6

8

10

0 200 400 600 800 1000

n(t)

t

MTTRi = 10,MTTFi = 100, i = 1, 2;N = 10

Small buffer

0

20

40

60

80

100

0 2000 4000 6000 8000 10000n(

t)t

MTTRi = 10,MTTFi = 100, i = 1, 2;N = 100

Large buffer


How inventory and variability interactSimulations: Buffer Level vs. time

0

20

40

60

80

100

0 2000 4000 6000 8000 10000

n(t)

t

MTTRi = 10, i = 1, 2,

MTTF1 = 50,

MTTF2 = 100;N = 100

First Machine is Bottleneck

0

20

40

60

80

100

0 2000 4000 6000 8000 10000

n(t)

t

MTTRi = 10, i = 1, 2,

MTTF1 = 100,

MTTF2 = 50;N = 100

Second Machine is Bottleneck


How inventory and variability interactProduction Rate vs. Buffer Size

N

P

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0 20 40 60 80 100 120 140 160 180 200

Increasing a small buffer may pay off; increasing a large buffer will not.


How inventory and variability interactAverage Inventory vs. Buffer Size

N

nBottleneck at first machine.

Bottleneck at second machine.

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100 120 140 160 180 200

There will be less inventory if the bottleneck is upstream.


WIP and Buffer Size in Long linesAll buffer sizes = 23, total buffer space = 437

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18 20

aver

age

inve

ntor

y

Production Rate = 0.8806


WIP and Buffer Size in Long linesTotal buffer space = 414

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18 20

optim

al b

uffe

r si

ze



WIP and Buffer Size in Long linesAll buffer sizes = 37, total buffer space = 703

0

10

20

30

40

50

0 2 4 6 8 10 12 14 16 18 20

aver

age

inve

ntor

y



WIP and Buffer Size in Long linesTotal buffer space = 510

0

10

20

30

40

50

0 2 4 6 8 10 12 14 16 18 20

optim

al b

uffe

r si

ze



WIP and Buffer Size in Long linesConclusions

◮ Buffer space is not needed where inventory is greatest;

◮ Buffer space is needed where inventory variability is greatest.


Inventory and Variability - LGO-SDM PROGRAM AT MIT · c2010StanleyB.Gershwin. Allrightsreserved....

Documents

Transcript of Inventory and Variability - LGO-SDM PROGRAM AT MIT · c2010StanleyB.Gershwin. Allrightsreserved....