Embed Size (px)
Citation preview
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 1
Robust Production Planning:
Business Case TRW Automotive - Optimization and Simulation in a Real-World Environment -
TU Dresden
15. + 16. May, 2012
Robin Delius
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 2
PART 1
0 Problem Description
1 Production Model
2 Results
PART 2
3 Uncertainties in Plan Execution
4 Combination of Optimization and Simulation
5 Conclusions
Robust Production Planning:
Business Case TRW Automotive
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 3
Problem Description
Project is a cooperation between
Group of Business Computing esp. CIM
(Prof. Dr.-Ing. habil. Dangelmaier)
TRW Automotive GmbH, Gelsenkirchen
TRW Automotive GmbH in Gelsenkirchen is
manufacturing steering components
More than 700 employees
Sales: 294 Mio. €
Technological Portfolio (Steering):
Power Steering, EPHS-Systems, EPS-Systems
Tie Rods, Joints
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 4
Problem Description
Identification of problem area:
Composition of planning models under consideration of operational decision variables and their
corresponding decision context
IT Liquidity Knowhow Employment
Staff Planning
Material Planning
Machine Planning
De
cis
ion
Le
lve
ls
Strategic Success Factors
Cost-minimal
delivery
reliability
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 5
Problem Description
Models are a formal and mathematical description of the production and planning environment
Planning results are reusable within the following models
Production Capacities
Material
Capacities Staff Capacities
Production
Scheduling
Staff scheduling
Planning results for parameterization
Planning results for parameterization
M1
M2 M3 M4
M5
Operational
Planning
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 6
Problem Description
Production plan execution is influenced by several uncertainties
Machine failures
Late/missing deliveries
Scrap parts
…
Current planning methods do not consider such influences sufficiently
Optimization methods usually examine the best case only and are unable to offer alternatives
when issues occur
Stochastic optimization methods typically become to complex to solve efficiently
Which leads to high solution times and are in practice often not applicable
We propose a combination of optimization and material flow simulation to overcome these
obstacles
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 7
Production Model
Multi-stage production system of an automotive supplier as use case
Real world problem size
44 Products are manufactured on 21 machines.
External demands exist for 11 endproducts and are known for 56 periods beforehand
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 8
Production Model
The production plan is created with a mathematical programming model
The model is based on the standardized Multi-Level Capacitated Lot-Sizing Problem (MLCLSP)
Big bucket model which determines the daily lot-sizes
Model consists of ~500k (mixed-integer) variables
Several extensions assure its real world applicability
Planning Horizon of 8 weeks on daily basis
Determination of production, setup and maintenance activities
Multiple products can be manufactured on one machine and the same product may be made
on several, parallel machines.
Inclusion of backlog amounts with corresponding penalty costs
Work shift amounts are dynamically determined
Higher costs for late-, night and weekend shifts are incorporated
Inclusion of Production KPIs
Reduction of Capital Commitment in stock and production
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 9
Production Model
Restrictions within the model
𝐼𝑡−1,𝑝 + 𝑞𝑡−𝑛,𝑚,𝑝 − 𝑎𝑜,𝑝 ∗ 𝑞𝑡,𝑚,𝑜
ℙ𝑝
𝑜:𝑜≠𝑝
𝑀
𝑚
𝑀
𝑚
− 𝐼𝑡,𝑝 − 𝐵𝑡−1,𝑝 + 𝐵𝑡,𝑝 = 𝑑𝑡,𝑝 Inventory Equation
𝐼𝑡,𝑝 ≤ 𝑑𝑡′,𝑝𝑡+𝑟𝑡′=𝑡+1
𝑟∗ 𝑟𝑎𝑛𝑔𝑒𝑡,𝑝
𝑀𝐴𝑋
𝐼𝑡,𝑝 ≤ 𝑎𝑝,𝑜 ∗ 𝑞𝑡,𝑚,𝑜
ℙ𝑝𝑜:𝑜≠𝑝 𝑀
𝑚𝑡+𝑟𝑡′=𝑡+1
𝑟∗ 𝑟𝑎𝑛𝑔𝑒𝑡,𝑝
𝑀𝐴𝑋
Inventory Range (FG)
Inventory Range (WP)
𝐼𝑡,𝑝 ∗ 𝑠𝑒𝑙𝑙𝑖𝑛𝑔𝑃𝑟𝑖𝑐𝑒𝑝𝑝:𝑝∈𝐾
≤ 𝑐𝑎𝑝𝐶𝑜𝑚𝑚𝑖𝑡𝐾 Capital Commitment
𝑟 Range of preview within horizon
𝑟𝑎𝑛𝑔𝑒𝑡,𝑝𝑀𝐴𝑋
Acceptable inventory range for product p
in period t
𝑠𝑒𝑙𝑙𝑖𝑛𝑔𝑃𝑟𝑖𝑐𝑒𝑝 Price of product p
𝑐𝑎𝑝𝐶𝑜𝑚𝑚𝑖𝑡𝐾 Acceptable capital commitment
for key K
Inventory of product p in period t 𝐼𝑡,𝑝
𝑞𝑡,𝑚,𝑝 Production of product p in period t on
machine m
𝑎𝑜,𝑝 BOM: Number of pcs. Of product p, used
in product o
𝑑𝑡,𝑝 Demand for product p in period t
𝐵𝑡,𝑝 Backlog of product p in period t
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 10
Production Model
Solving the model with Cplex® (IBM Ilog Solver) on a multi-CPU-Server (4x Intel XEON®, 24 Core)
is impossible without decomposition or partial reformulation
Due to its realworld application, simplification of model is not an option!
Methods for decomposition are:
Timewise decomposition (model splitting on time axis)
„Relax & Fix“-Approach
Cut-Formulation
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 11
Production Model
Situation:
First Decomposition Timewise
Problem formulation with planning horizon of 8 weeks (56 Days)
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8
Splitting the planning horizon in „smaller chunks“ and generation smaller problem formulations
Subproblems are solved successively and combined afterwards, resulting in a feasible
solution for the overall problem formulation
Problem formulation with planning horizon of 8 weeks (56 Days)
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8
Subproblem 1 Subproblem 2 Subproblem 3 Subproblem 4 Subproblem 5 Subproblem 6 Subproblem 7 Subproblem 8
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8
Successive Planning
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 12
Production Model
Improving the planning relation between the subproblems …
… by overlapping planning of the subproblem
Subproblem 1 Subproblem 2 …
7 Tage
Subproblem 1 Subproblem 2 …
Overlapping SP 1
Overlapping SP 2
Subproblem 1 …
Gain of information can be used
for reformulation and
parameterization of the initial
subproblem
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 13
Production Model
Relaxation of subproblems
Adding hard restrictions in each successive planning step and fixing already determined
variable values with upper/lower bounds
• Level 1: Delivery reliability at all costs
Minimizing backlog variables
• Level 2: Reduction of capital commitment
Minimizing inventory stocks
• Level 3: Improvement of capacity usage
Cost-optimal decision of capacities
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 14
Integer solutions
Production Model
Closing gap between functional and formal solution quality
Without proof of optimality, existence of better solutions is possible
Adding „clique-cuts“ for solution confirmation
Dimension x
Dim
en
sio
n y
Real solution space
Binary variables form cliques with special properties:
Relaxation of model allows the following constellation:
Adding integer condition results in:
How to avoid this binary clique behaviour?
𝑏𝑖𝑛𝑛 + 𝑏𝑖𝑛𝑛+1 + 𝑏𝑖𝑛𝑛+2 + 𝑏𝑖𝑛𝑛+3 = 1
0,2 + 0,4 + 0,3 + 0,1 = 1
0 + 0 + 1 + 0 = 1
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 15
Production Model
Coupling of binary variables
Results in a symmetric variables assignment for a,b,c,d
• 3,-3,-1,1
Determination of absolute values for variables a,b,c,d
Specific formulation neccessary, because determination of absolute value is described by
a non-linear function (solution by objective function)
Mathematical problem is more difficult to solve, since adding new variables and equations
increases the problem complexity
Initial solution is already available, so finding a solution is not neccessary! Confirmation of
solution quality is sufficient.
𝑏𝑖𝑛𝑛 − 𝑏𝑖𝑛𝑛+1+𝑏𝑖𝑛𝑛 − 𝑏𝑖𝑛𝑛+2+𝑏𝑖𝑛𝑛 − 𝑏𝑖𝑛𝑛+3 + 𝑏𝑖𝑛𝑛+1 − 𝑏𝑖𝑛𝑛+2+𝑏𝑖𝑛𝑛+1 − 𝑏𝑖𝑛𝑛+3 + 𝑏𝑖𝑛𝑛+2 − 𝑏𝑖𝑛𝑛+3 = 𝑎
𝑏𝑖𝑛𝑛+1 − 𝑏𝑖𝑛𝑛+2+𝑏𝑖𝑛𝑛+1 − 𝑏𝑖𝑛𝑛+3+𝑏𝑖𝑛𝑛+1 − 𝑏𝑖𝑛𝑛 + 𝑏𝑖𝑛𝑛+2 − 𝑏𝑖𝑛𝑛+3+𝑏𝑖𝑛𝑛+2 − 𝑏𝑖𝑛𝑛 + 𝑏𝑖𝑛𝑛+3 − 𝑏𝑖𝑛𝑛 = 𝑏
𝑏𝑖𝑛𝑛+2 − 𝑏𝑖𝑛𝑛+3+𝑏𝑖𝑛𝑛+2 − 𝑏𝑖𝑛𝑛+𝑏𝑖𝑛𝑛+2 − 𝑏𝑖𝑛𝑛+1 + 𝑏𝑖𝑛𝑛+3 − 𝑏𝑖𝑛𝑛+𝑏𝑖𝑛𝑛+3 − 𝑏𝑖𝑛𝑛+1 + 𝑏𝑖𝑛𝑛 − 𝑏𝑖𝑛𝑛+1 = 𝑐
𝑏𝑖𝑛𝑛+3 − 𝑏𝑖𝑛𝑛+𝑏𝑖𝑛𝑛+3 − 𝑏𝑖𝑛𝑛+1+𝑏𝑖𝑛𝑛+3 − 𝑏𝑖𝑛𝑛+2 + 𝑏𝑖𝑛𝑛 − 𝑏𝑖𝑛𝑛+1+𝑏𝑖𝑛𝑛 − 𝑏𝑖𝑛𝑛+2 + 𝑏𝑖𝑛𝑛+1 − 𝑏𝑖𝑛𝑛+2 = 𝑑
𝑥 = 𝑥+ − 𝑥−
𝑥 = 𝑥+ + 𝑥−
𝑐 ∗ 𝑥+ + 𝑥−
𝑥𝑎+ + 𝑥𝑎
− + 𝑥𝑏+ + 𝑥𝑏
− + 𝑥𝑐+ + 𝑥𝑐
− + 𝑥𝑑+ + 𝑥𝑑
− = 8
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 16
Production Model
Run GAP 1 2 3 4 5 6 7 8 9 10 Average Min Max Intervall Dekomp. Rel.+Fix. Cuts
Sce
nar
io
S1 (low) 112 107 119 123 103 119 121 110 112 127 115,3 103 127 24
0,88-0,99 0,72-0,78 0,09-0,15 S2 (medium) 175 163 161 165 183 191 180 177 190 189 177,4 161 191 30 S3 (high) 223 245 212 229 232 241 231 218 217 230 227,8 212 245 33
Finding Solution in Minutes Quality
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 17
Results
Production
Capital Commitment
0
100
200
300
400
500
600
700
800
900
1000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55
Pro
du
ctio
n C
apac
itie
s
Planning horizon
K9098_P63473
K9098_P12139
K9098_P73444
K9098_P19183
K9098_P99593
K9098_P69014
K9098_P42120
K9098_P62400
K9098_P52466
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
0
50
100
150
200
250
300
350
400
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55
Cap
ital
in €
Inve
nto
ry
Planning horizon
LagerbestandP76313
zul. LagerreichweiteP76313
Kapitalbindungsgrenze
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 18
And now…
Part 2
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 19
Uncertainties in Production Plan Execution
The execution of a production plan rarely succeeds as planned before
Unforeseen events can influence the plan realization negatively
Results can be longer cycle times, machine blockage and scrap parts which are leading to
higher total production costs.
Replanning is inevitable to adapt to the new situation
To achieve a robust plan, which can handle unforeseen influences, two different planning targets
must be met:
Feasibility - the plan must be adhere to all given restriction and especially fulfill all demands
Result stability – the resulting plan‘s costs must not deviate far from the best case scenario in
any circumstances
A high feasibility robustness can lead to a lower result stability robustness.
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 20
Combination of Optimization and Simulation
The execution of an production plan under stochastic influences can be simulated quickly.
Many replications allow a sufficient coverage of possible stochastic events
The simulation results can be aggregated to a new, more robust production plan
Single simulation runs can be used as pre-planned alternatives for edge cases
The simulation models must be generated correspondingly to the optimization model, containing
all constraints and objective measurements to achieve comparable results.
Our simulation is based on d³FACT, a high-performance, petri-net-based material flow simulation
framework by our workgroup, Business Computing, esp. CIM.
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 21
Combination of Optimization and Simulation
The initial production plan is created with IBM Ilog CPLEX 12.2 and loaded afterwards into the
simulation by converting the resulting solution file.
The material flow simulator performes several simulation iterations with a different random
number seed each, to generate diverse scenarios
During the simulation, the resulting plans are recorded and stored for postprocessing
Postprocessing allows for the simulation external manipulation of the underlying plan
Extension of planned capacities and shifts to provide sufficient buffer times
The evaluation calculates performance figures for the validity and result robustness upon the
plan’s performance in the different simulated scenarios.
CPLEX MST-File ConverterProduction
Pland³FACT
Production Plan including uncertainties
Evaluation
DB
Evaluated Production Plans
Postprocessing
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 22
Combination of Optimization and Simulation
The simulation applies stochastic influences on the initial production plan.
Cycle, maintenance and setup times are randomly prolonged to imitate machine failures and
disturbances on the production process.
Due to the lack of accurate historical machine failure data, we took the failure rate and the
standard deviation by which the process times were prolonged as parameters for the
stochastical disturbance.
For our test cases we assumed:
The failure rate is 10% of total lots.
The planned process times are extended using a standard deviation of 15% and 30% of the
planned time.
Machines can react in two different ways when necessary materials are missing.
Naive machine control – waits until all parts for a lot are in place.
Rule-based machine control – skips the scheduled lot and produces the next, when all needed
materials are in place.
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 26
Conclusions
Increase of delivery reliability (+~2.5%) and planning efficiency (+~12.5%)
Simulations can be used to evaluate a production plan‘s robustness
Optimization results can easily be transferred into our simulation framework
Weak spots can be determined and fixed through automatic post processing and rule based
machine controls to decrease internal delays and increase the overall robustness
Performing a large number of simulations is substantially faster than running another instance of
the optimization problem
© P
rof.
Dr.
-Ing.
habil.
W. D
angelm
aie
r, H
ein
z N
ixdorf
Institu
te, U
niv
ers
ity o
f P
aderb
orn
TU Dresden, 15. + 16. May 27
Heinz Nixdorf Institute
University of Paderborn
Business Computing, esp. CIM
Fuerstenallee 11
33102 Paderborn
Phone: +49 5251 606479
Fax.: +49 5251 606483
E-mail: [email protected]
www.hni.uni-paderborn.de/en/cim
Thank you for your attention!
