Application of Optimization-Based Production
Loading at Toshiba Corp.
Michael Ball, Zhenying Zhao, U of Maryland; Hideo Mizusawa, Yoshinori Shirasu, Toshiba Corporation
Background
• UMD and Toshiba have collaboratively developed advanced
• Material change from black (B) to white (W) should be done in
Available to Promise (ATP) and Production Capacity Planning (PCP)
parallel with die change, unless initial matl is B and there is no W
with initial die.
• Optimization-based Production Loading (OPL) extends ATP to shopfloor level by considering detailed production information.
Time period t
Planning Sales
(Head quarters)
Die A
(End die of t-1)
Die B
Die C
Die D
(End die of t)
Black :
Showing Production
Capability
Planning
Planning
System
System
Production
Advanced
ATP
Production
Capability
Demand, Forecast
mon tue wed thu
Die
changeover
(parallel)
M/C Clean-up
from W ÎB
White :
fri
• Data was collected from an electric appliance company
9 OPL time horizon: 15 days
9 Total number of machines: 80
9 Total number of dies: 870
9 Total number of component types: 870
9 Total number of material types: 2 (black or white)
9 Possible component, machine die combination: 1300
9 Variation of the total number of orders per day: 1 ~ 287
9 Quantity variation of orders: 750 ~ 210,000
UMD
Minimize:
Due date violation + Inventory holding cost + Change-over time
Production
UMD Loading
Major Decision Variables
Concept of OPL
2nd stage comp: s
Demand Order
B
A
p
r
q
t
A:120pcs/ Due date:Jun.10
B:70pcs/ Due date Jun.9
u
• Q( m ,d , j ) ( t ) : Quantity produced by using of machine m, die d and
component j in time period t.
60000
M/C
S1
S2
1st stage assy
M/C
Jun7
Jun6
Jun7
u:120
s:100
U1
p:40
t:120
U2
r:70
q:100
s:20
u:150
M/C
Jun8
p:80
F1
F2
q:100
Jun8
Jun9
B:50
A:50
B:20
q:90
u:20
Scope of SPL
Major Constraints
• Develop OPL prototype for single bottleneck stage
• A factory producing electronic appliance from Toshiba Corp. is
selected as motif for the development.
• Changeover loss including die changeover and material changeover
when switching products are significant.
-11
-10
-9
-7
-6
-5
-4
C j (t , t k )
t
k
3,000,000
300,000
2,500,000
T
• Capacity balance :
Q( m ,d , j ) ( t ) c( m ,d , j )
200,000
SPL
DBS
150,000
SPL
1,500,000
DBS
1,000,000
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
1
2
3
4
5
6
7
8
9
10
11
12
13 14
15
Day
• Production Lot Sizing :
Total number of lots in SPL is 14.5% less than the ones in DRBS.
Lot Sizing
Number of lots
450
am ( t ) Om ( t )
400
350
300
Frequency
• Changeover calculation constraints
9 Available combinations of die and machine for each component
9 Ending die for each machine and day
22,446
2,147,220
2,000,000
500,000
0
( m ,d ) MD
-1
2,761,980
50,000
nd Q( m ,d , j ) ( t )
-2
Accumulated Change-over Time
Change-over Time
350,000
Day
I j ( t 1)
-3
Day
100,000
• Production conservation :
8,094
17,379
879
6,100
-12
1,353
439
0
-13
1,129
293
0
-14
DBS
• Changeover Loss:
Total changeover time can be reduced 18.2% by using SPL
compared to DRBS.
( d , j ) DJ ,
• One product can be produced with multiple available combinations
of machine, die (injection module), and material.
8
0
Leftover
7
0
0
• Demand commitments :
C j (t , t k ) L j (t k ) rj (t k )
I j (t )
-8
10000
t T
Single-Stage OPL (SPL) and Motif
0
0
Qty
20000
250,000
A:50
A:20
SPL
40000
30000
material change-over between component group j` at
machine m and die d in time period t.
FAT assy
2nd stage assy
50000
85
0
• Om (t )
: Total changeover time on machine m in time period t.
• Z ( m ,d ) ( t ) : Die indicator, equal to 1 as die d is allocated to
machine m in time period t.
• Zˆ ( m ,d ) ( t ) : Ending die indicator, equal to 1 as die d is allocated as
ending die to machine m in time period t.
X
(
t
)
• ( m ,d , j ) : Material change indicator, equal to 1 as there is
70000
CO Time (ACC) [sec]
Manufacturing-BoM
Product(FAT) :
1st stage comp:
80000
0
0
• The goal of this project is to develop optimization-based OPL
prototype to reduce production lead-time and total inventory level, to
improve throughput and order commitments (customer service level).
• C j ( t , t ) : Quantity committed for component j in time period t.
CO Time [sec]
• Model should determine optimal daily production schedule for each
production stage based on Final Assembly and Testing requirements.
73,614
Due Date Violation and Left-over
k
0
0
Factory capacity
• Total computation time of SPL including pre-possessing, database
querying and optimization: 180 minutes
• Demand Commitment:
Total quantity of the violated orders and left-over orders is reduced
6.2% by using SPL compared to DRBS.
0
0
Procurement status,
Material inventory
Objective Function
MES
Production
Order
50,921
FAT Request
16,710
Production
Capability
Planning (PCP)
17
0
Material
Material
System
System
Supplier
Real time
due date
promising
UMD
(Captive factory and
affiliated plant)
MRP
MRP
Experimental Comparison with a Commercial
Dispatching Rule Based Scheduler (DRBS)
Mixed Integer Programming (MIP) Formulation
250
DBS
1,789
SPL
1,529
SPL
DBS
200
150
Average lots
100
50
0
100
200
300
400
500
600
700
Production Lot Size
800
900
1000
Over
1000
DRBS
662
SPL
770