Mechanical Engineering 101 - University of California,...

© 2003‐2012, McMains, Dornfeld, MinME 101 lecture 18 1

Mechanical Engineering 101

University of California, Berkeley

Lecture #18

© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 2

Today’s lecture

• pull systems: kanban– Example– Parameters– Reliability– Scheduling, Assumptions, Variations


Kanban: a method for controlling pull system

• Japanese roughly translated as “card”– used for production authorization

• each kanban includes info on– part type– number of units authorized– possible additional info

• often used together with transport container– possibly color-coded to match– empty container “pulls” parts / triggers production– kanban card is “work order”– transfer lot size = container size


Kanban

Z

Step N manufacturer

• kanban card (and empty container) = request to supplier to make a container of “Z” and deliver ASAP– send request when remaining WIP/material just

covers lead time for replenishment

Z

Step N supplier


Kanban example [Mahoney]

• one-card kanban• low mix/high volume environment• products X and Z

– each has 3 steps performed at same 3 stations A,B,C

– one worker per station (aka Point Of Use, POU)

– storage after each station

Process A+B+CProcess A+BProcess A


Model number

Replenishment quantity

X

1

X1

“Z” product:

Kanban card for example

“X” product:

card located with product throughout the system


Product specific one-card kanban system

Product Zafter process A

Process AProcess BProcess C

Process A+B+CProcess A+B

Finished product X

Product Xafter process A

Finished product Z

product X kanban card

Process A

LMHV

Location after process A


Signals from parts and cards

Product Z removed from FGI

Product Z Kanban card put up at C

Z1

Authorizes another product Z to be started


More details……process B & C

Z1Completed Z after process C goes with card to FGI

Z1

Z1

Z kanban put up at B to schedule production of another Z product

C removes partially completed Z from input buffer


Moving further upstream….

Completed Z after process B goes with card to output buffer

Z1

Z kanban put up at A to schedule production of another Z product

Z1

B removes partially completed Z from input buffer


Last step……...

Z and kanban card placed in step A output buffer

process step A creates product Z


Idle state

• no kanban cards at any process stage– no production occurs– removing an X or Z from FGI would restart process


Today’s lecture

• pull systems: kanban– Intro– Parameters– Reliability– Scheduling, Assumptions, Variations


Kanban parameters

• container size– each kanban authorizes number of units that fit in container

• number of kanbans for each part type


i

iijij h

Dcn 22

cost/move container of part i with technology j

demand for product i

holding cost for i

Container size

• cost to move container based on– handling technology

• ideal container size n for part i, transfer technology j:– derived from minimizing total transfer & holding costs – (fixed costs = c1ij )


Number of kanbans

• supply of parts must be coordinated with demand during lead time

– process step i has demand D, lead time – how many parts will be removed during lead time?

1. D2. 3. D +

time

Inve

ntor

ypo

sitio

n

reorder point

Q

safety stock SS

lead time,

r


.Number of kanbans

• for process step i, lead time demand = iDi

• if we have ki containers (= ki kanbans), each holding ni parts, we’ll be ok if

ni * ki >= iDi

• number of kanbans:ki >= iDi / ni


.Number of kanbans

• real world: variability!

• measure variability of lead time demand iDi

• use to set a safety factor l :

iDi <= iDi (1 + l ) with some known probability

• if lead time demand iDi has mean 100, standard deviation 6, and we want to avoid shortages with ~97 1/2 % probability, what safety factor (l ) should we use?


.Number of kanbans

• total kanbans for step i:


Announcements

• HW 6 return• Midterm Thursday

– HW 1-6, movies, lecture material through this week

– Try the posted samples!!!Bring:– One 3x5 inch card of notes, handwritten, one side

only – An approved calculator:

• Hewlett Packard: The HP 33s and HP 35s models.• Texas Instruments: All TI-30X and TI-36X models.• Casio: All fx-115 models.


Today’s lecture



Process availability example

• 2 stage process– stage 1: 80 parts/hr

• but fails every 18 hrs w/ 2hrs downtime– stage 2: 80 parts/hr

• reliable

• constant demand 75 parts/hr

Demand 75/hour

80/hr 80/hr18hrs up/2 hrs down

1 2buffer


.Process availability example

• Do we have capacity to meet demand?

Demand 75/hour

80/hr 80/hr18 hrs up/2 hrs down

1 2buffer



• run stage 1 in fast mode– 125 parts/hr– fails every 8 hrs w/ 2 hrs downtime

• Average capacity?

Demand 75/hour


1 2buffer



• have capacity to meet demand if enough buffer inventory kept– since stage 1 faster, buffer will fill up


Demand 75/hour1 2buffer

time, hrs

0 1 2 8 9 10

Stage1 production

50

100

150



• kanban size is 5 parts/container for stage 1 output• how many kanbans (k) for stage 1?

– what is max (worst case) lead time to refill container?– what is max lead time demand?







0 1 2 3 4 5 6 7 8 9 10

50

Buffer inventory

100

150

0 1 2 3 4 5 6 7 8 9 10

Stage1 production

50

100

150

0 1 2 3 4 5 6 7 8 9 10

50

100

150Stage 2 production FGI

0 1 2 3 4 5 6 7 8 9 10

50

100

150

time, hrs


Capacity, previous example

• Average capacity– 80% of 125 = 100 parts/hr

Demand 75/hour


1 2buffer


.Preventive maintenance option

• slow machine to 110 parts/hr• 1/2 hr preventive maintenance every 2 hrs• Adequate capacity?


.Preventive maintenance option

• slow machine to 110 parts/hr• 1/2 hr preventive maintenance every 2 hrs• Adequate capacity?

• number kanbans?– max lead time = .5 hrs + 5/110 = .55 hrs– .55*75 = 41.3, so 9 kanbans


• Time check


Today’s lecture



Kanban scheduling rules

• several choices– FCFS

• first come first served– SPT

• shortest processing time– families

• often FCFS between families– EMQ

• wait until EMQ orders accumulated


Kanban scheduling rules• yet more choices

– cyclical production– fixed, repeating sequence (most efficient sequence)

• continuous time– production quantity set to total number outstanding authorizations

» but often have a min and a max• periodic review

– do one full sequence per production period» based on outstanding orders at start of period

• variation: signal kanbans– send signal kanban at reorder point– with earlier material kanban signals


Signal kanbans

• signal authorizes production of entire EMQ

signalkanban

signalkanban

signalkanban

Part A Part B Part C


Signal kanbans

• signal authorizes production of entire EMQ• possibly preceded by material order authorization

signalkanban

materialkanban

signalkanban

materialkanban

signalkanban

materialkanban

Part A Part B Part C


Oatmeal kanban


Kanban systems

• one card system– supplier makes parts in response to arrival of kanban

card– inventory stored in buffers between stages

• at user

• kanban squares– empty spot triggers production

• signal kanbans


Kanban systems

• two card system– both input (user) and output (producer) buffers

maintained• Useful with multiple work centers using same part

– parts already waiting in output buffer when “withdrawal” kanban arrives from user

– producer makes parts in response to “production” kanban posted when a previous order was filled

• could have been triggered by any work center using part


PM2

WM2 M

PX1

WX1 X

PV1

WV1 V

PY1

WY1 Y

PW1

WW1 W

PZ1

WZ1 Z

Inter-process inventory

2‐card kanban example

• withdrawal kanban(aka transport) kanban

• production kanban• products M,V,W,X,Y,Z

M


WM2 M

WX1 X

WV1 V

WY1 Y

WW1 W

WZ1 Z

PM2

M

PX1

XPV1

V

PY1

YPW1

W

PZ1

Z

WM2 M

WX1 X

WV1 V

WY1 Y

WW1 W

WZ1 Z

i input buffer

process i transit

i+1 input buffer

Steady statei output buffer

M M M


Assumptions needed for efficient use of kanbans

• demand and demand mix approximately constant– otherwise need to adjust # kanbans

• short setup times– allows rapid response to actual demand– or you’ll need large buffers (lots of inventory)

• disciplined workforce– proper transfer of kanbans– produce only if kanban

• available, flexible capacity– cross-trained workers– maintenance

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