9-Manufacturing Lead Time and Inventory Costs

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1 Prepared by Dr. ule Itr Satolu

Manufacturing Lead Time Total time elapsed for completion of a batch in a

production system.

m

iii

n

i

noosu TQTTMLT1

2

i= Operation index; i=1,, nm

Q: Batch size

To= Operation time at a given workcenter.

Tno= Non-Operational time at the workcenter (quality control,

material handling, process delay etc.)

Tsui= Setup time Prepared by Dr. ule Itr Satolu

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Manufacturing Lead Time (MLT) MLT is comprised of

Processing time:

Proportional with the batch size (Q)!

Batch delay: Parts waiting the rest of the batch to be completed.

Reasons: Large batch sizes, large transfer batch sizes.

Proportional with the batch size (Q)!

Process delay: Whole batch waiting. Reasons:

Machine breakdown, line imbalance etc.

Defects, rework.


Manufacturing Lead Time By means of cellular manufacturing, process and batch

delay are reduced considerably!

Therefore, manufacturing lead time also decreases, significantly!

In 1989, a research in USA: Reduction of MLT is between 5 and 91%, in 20 manufacturing companies. Average: 46%.


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Production Lead Time = MLT + order processing (lead) time +

waiting time before production + storage time + transportation time


Production Lead Time (Durmuolu, 1998)

Order

Processing

Process

Delay

Process

Delay

Process

Transportation

Ord

er

Pro

ce

ssi

ng

Tim

e

Wa

iting

time

be

fore

pro

du

ctio

n

Ma

nu

factu

ring

Le

ad

Tim

eS

tora

ge

Tim

eT

ran

sp

ort

Tim

e

Order preparation

Waiting for the Raw Material

Delay due to congestion

Waiting for the next period

Process Delay

Urgent work orders

Defects, rework

Machine breakdown

Line imbalance

Poor production control

Early order release

Early starting the order to balance workload

Batch Delay

Large batch sizes

Large tranfer batch sizes

Processing Time

Accepting The

Order

Delivery

Production

Lead Time


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Manufacturing Lead Time Cost

Cm

Process-0 Process-1 Process-2

Tsu+Q*To+Tno

Co*Tp+Cno

(C

o*T

p+

Cn

o)

Process-nmTime

Cost

7

Cm: Material cost

Co: Cost of worker

and machine per unit

time

Cno: Cost of non-

operational time

Tp: Processing time

Tp=Tsu+Q*To

Q: Batch size

(Durmuolu, 1998)

Prepared by Dr. ule Itr Satolu

Manufacturing Lead Time Cost Cno: Non-operational activities cost i: Index of operation-i

Co: Cost of worker and machine per unit time i=1,,nm Q: Batch size Cpc: Total cost of one piece of part Cm: Material cost

Tp=Tsu+Q*To

8

m

ii

n

i

nopompc CTCCC1

If Tp and Cno are assumed to be equal for all operations;

nopommpc CTCnCC


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Manufacturing Lead Time Cost

Cost

t

Cm

nm(Tp*Co+Cno)

Manufacturing Lead

Time

MLT

Cum. Cost at a given time-t= Cm+[nm(Tp*Co+Cno)/MLT]*t


Other Costs These are proportional with the time the order spends in

the system.

Cost of Investment in WIP: Cost incurred before delivery to the customer. Includes: Cm Cumulative cost of order * internal rate of return (i)

In Process Handling (Storage) Cost of WIP Occurs due to space occupied by the WIP.

Proportional with the size and storage position of the WIP, measured by storage ratio (s).

Cumulative cost of order * storage ratio (s).

h=i+s where h is inventory holding cost ratio.


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Total MLT and WIP Inventory Cost

MLT

nopommnopommpc dthtMLTCTCnCCTCnCTC0

.*]/)([

nopom CTCnC 1

MLT

mmpc dthMLTtCCCCTC0

11 .]/*[

MLThCCCCTC

hMLTMLTCMLTCCCTC

mmpc

mmpc

*]2/[

]2*/*[*

11

2

11

11

TCpc= Total MLT and WIP holding cost for one piece of part.

Inventory (WIP) holding cost


Total MLT and WIP Inventory Cost Cost

t

Cm

nm(Tp*Co+Cno)=C1

MLT

WIP (Inventory) Holding Cost=

(Cm+C1 / 2)*h*MLT


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Littles Law Littles Law represents the relationship between

throughput rate (TH), lean time (LT) , and WIP level in a manufacturing system.

WIP=TH*LT

Prepared by Dr. ule Itr Satolu 13

LT

Homework How do you interpret the relation between the TC per

piece of part and

MLT,

total processing time,

non-operational time,

batch size?

Please make at least 4 sentences.


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Example Cost of worker and machines per unit time

Direct workers cost = $ 7.00 / hour

Workers overhead ratio for the factory = 60%

Machine investment cost = $ 100.000

Machine lifecycle = 8 years

Salvage value = 0 Machines overhead ratio for the factory= 50% Internal rate of return= 10% 8 hours/shift/day = working hours.


Example Workers cost/hour= 7(1+0.60) = $11.20/h

Annual uniform cost of machines (AUC):

AUC= 100.000*(A/P, 10%, 8)

AUC= 100.000*(0.18744)= $18744/year

Annual Working hours= 8*250=2000 h/year

18744 / 2000= $9.37 / h

Machines cost per hour= 9.37*(1+0.5) =

$ 14.06 / h

Cost of workers and machines per hour= 14.06+11.20= $ 25.26 / h


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Example

Raw material cost of a part= 100 $

20 operations needed for that part

MLT=15 weeks

0.8 hour/operation

Machine and worker cost / hour= 25 $

Cost of non-operational activities / operation =10 $

Internal rate of return= 20 %

Storage ratio= 13 %

Determine cost of each piece of part.


Example Cpc = Cm + nm (Tp*Co + Cno)

Cpc = 100 + 20 (0.8*25 + 10)= $ 700 / part

C1 = nm (Tp*Co + Cno)

C1 = 20 (0.8*25 + 10) =$ 600 /part

h = 20 + 13 = 33% per year

h=33%/ 52= 0.6346% per week

Inventory holding cost = (Cm + C1/2)*h*MLT

=(100+600/2)*0.6346%*15 = 38.08 $/part

TCpc=Cm + C1+ (Cm + C1/2)*h*MLT

TCpc=700 + 38.08 = 738.08 $/part


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Example Inventory holding cost/part= 38.08 $

5000 parts/year*38.08 $= 190.400$/year

However, inventory holding cost usually not considered at the companies!

If MLT was reduced by 50%, inventory holding cost would be also decreased by 50%.



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Effect of Lot-Size Reduction Operation (units/day)

Product A B C

X 1000 2000 1000

Y 2000 2000 2000

21

8000 units of each of X and Y should be produced. X first and then Y.


Schedule

22 Process batches=Transfer batches=8000.

(Nicholas, 1998)


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Schedule-2

23

Schedule with process batches=4000, transfer batches=2000.

(Nicholas, 1998)


Lead Time Production lead time for X reduced from 20 days to 13

days.

That for Y reduced from 24 days to 15 days.

This is dueto smaller process batches and transfer batches.

Besides, we assumed that operations not busy with other parts, and no process time variability!


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Carrying Cost

25

Bottom: Inventory level of complete units, when process batches= transfer batches=8000. Top: Inventory level (process wide)

(Nicholas, 1998)


Carrying Cost

26

Inventory when process batches=4000 and transfer batches=2000.

(Nicholas, 1998)


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Practical Strategies for Lead Time Reduction 1. Look for the WIP

2. Keep things moving

3. Synchronize production

4. Smooth the workflow

5. Eliminate variability.


Look for the WIP Excess inventory is the root of evil. Suzaki.

Inventory=Production rate*Lead Time(Littles Law)

Any action that reduces lead time also decreases inventory.

Variance of flow times also affects amount of inventories.


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Look for the WIP


Keep Things Moving Continuous flow manufacturing

If product is always movig towards completion, both lead times and inventories will decrease.

Because almost 90-95% of time spent in the factory is (usually) waiting time!

Splitting jobs

Process and transfer batch sizes are different.

A process lot should be split into transfer lots as small as can be practically handled.

This is called also overlapping!


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Keep Things Moving Queue control

Maintain shorter queues.

In Kanban and CONWIP, amount of WIP is controlled.

Sharing Transfer Batches

If incoming transfer batches arev assigned to individual tools, lead time can be excessive.

If transfer batches are shared by more than one tool, the average lead time can be reduced.


Synchronize Production A part assembly cannot be completed until all

components are available.

So, synchronizaiton of components fabrication and assembly is important.

In Kanban and CONWIP, synchronization occurs naturally.


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Eliminate Variability Uncertainty is mother of inventory,

Prof. Martin Christopher

High Variability Uncertainty

Uncertainty Keeping more inventory, such as safety stock!


Eliminate Variability Variability in processing times are caused by rework,

downtime, lack of inconsistency in production methods.

Both mean and variance of lead time increase due to these.

Reduce rework: Quality checks before completion of the lot.

Improve machine reliability: Lead time variance can increase due to machine downtime.

A=MTBF/(MTBF+MTTR)


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Eliminate Variability Vendor (Supplier) Variability:

Variance of vendor lead time is as important as the cost of the parts, since highly variable vendors require more buffer lead time than the dependable ones.


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9-Manufacturing Lead Time and Inventory Costs