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© 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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 3
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 4
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 5
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 6
Model number
Replenishment quantity
X
1
X1
“Z” product:
Kanban card for example
“X” product:
card located with product throughout the system
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 7
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 8
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 9
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 10
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 11
Last step……...
Z and kanban card placed in step A output buffer
process step A creates product Z
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 12
Idle state
• no kanban cards at any process stage– no production occurs– removing an X or Z from FGI would restart process
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 13
Today’s lecture
• pull systems: kanban– Intro– Parameters– Reliability– Scheduling, Assumptions, Variations
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 14
Kanban parameters
• container size– each kanban authorizes number of units that fit in container
• number of kanbans for each part type
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 15
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 )
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 16
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 19
.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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 23
.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?
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 27
.Number of kanbans
• total kanbans for step i:
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 29
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.
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 30
Today’s lecture
• pull systems: kanban– Intro– Parameters– Reliability– Scheduling, Assumptions, Variations
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 31
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 32
.Process availability example
• Do we have capacity to meet demand?
Demand 75/hour
80/hr 80/hr18 hrs up/2 hrs down
1 2buffer
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 35
.Process availability example
• run stage 1 in fast mode– 125 parts/hr– fails every 8 hrs w/ 2 hrs downtime
• Average capacity?
Demand 75/hour
125/hr 80/hr8 hrs up/2 hrs down
1 2buffer
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 37
Process availability example
• have capacity to meet demand if enough buffer inventory kept– since stage 1 faster, buffer will fill up
125/hr 80/hr8 hrs up/2 hrs down
Demand 75/hour1 2buffer
time, hrs
0 1 2 8 9 10
Stage1 production
50
100
150
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 38
.Process availability example
• 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?
125/hr 80/hr8 hrs up/2 hrs down
Demand 75/hour1 2buffer
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 47
Process availability example
125/hr 80/hr8 hrs up/2 hrs down
Demand 75/hour1 2buffer
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 48
Capacity, previous example
• Average capacity– 80% of 125 = 100 parts/hr
Demand 75/hour
125/hr 80/hr8 hrs up/2 hrs down
1 2buffer
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 49
.Preventive maintenance option
• slow machine to 110 parts/hr• 1/2 hr preventive maintenance every 2 hrs• Adequate capacity?
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 50
.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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 53
• Time check
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 55
Today’s lecture
• pull systems: kanban– Intro– Parameters– Reliability– Scheduling, Assumptions, Variations
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 56
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 57
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 58
Signal kanbans
• signal authorizes production of entire EMQ
signalkanban
signalkanban
signalkanban
Part A Part B Part C
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 59
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 60
Oatmeal kanban
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 61
Oatmeal kanban
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 62
Oatmeal kanban
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 63
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 64
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 65
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 66
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
© 2003‐2012, McMains, Dornfeld, Min ME 101 lecture 18 67
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