9-manufacturing lead time and inventory costs
DESCRIPTION
lead time ve stok costTRANSCRIPT
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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.
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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
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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
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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
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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
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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
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TCpc= Total MLT and WIP holding cost for one piece of part.
Inventory (WIP) holding cost
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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
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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.
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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.
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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
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8000 units of each of X and Y should be produced. X first and then Y.
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Schedule
22 Process batches=Transfer batches=8000.
(Nicholas, 1998)
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Schedule-2
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Schedule with process batches=4000, transfer batches=2000.
(Nicholas, 1998)
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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
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Bottom: Inventory level of complete units, when process batches= transfer batches=8000. Top: Inventory level (process wide)
(Nicholas, 1998)
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Carrying Cost
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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.
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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
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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.
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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!
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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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