Hybrid Technologies for Supply
Chain Planning and Scheduling
Alkis Vazacopoulos
Director
Dash Optimization
www.dashoptimization.com
Agenda
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•
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Background
CP versus MIP
CP and MIP
Case Studies
Further Developments
Agenda
•
•
•
•
•
Background
CP versus MIP
CP and MIP
Case Studies
Further Developments
Background
• MIP
– Solves specific class of problems
– Standard search procedure
– Very good for finding optimum
• CP
– Solves wide class of problems
– Flexible/bespoke search procedure
– Very good for finding feasible points
Agenda
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•
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Background
CP versus MIP
CP and MIP
Case Studies
Further Developments
Languages
MIP
CP
Variables
Real + Integer
Finite Domain
Constraints
Linear Equations and
inequalities
Arithmetic constraints
Symbolic/Global constraints
Example
• Variables
:
• Constraint
:
x 1 ,.., x n ∈ {0 ,..... m − 1 }
Pair wise different values
Algorithms
MIP
CP
Inference
Pre-solve, LP
cutting planes
Domain filtering
Constraint propegation
Search
Branch-and-relax
Branch-and-cut
Branch-and-bound
Inference
y
Linear arithmetic constraints
3x + y ≤ 7
3y + x ≤ 7
x+ y = z
x, y ∈ {0,...,3}
CP (filtering)
LP
: x, y ≤ 2, z ≤ 4
: x, y ≤ 2, z ≤ 3.5
MIP (cutting plane) : x, y ≤ 2, z ≤ 3
x
Formulation
Integer programming:
only linear equations
and inequalities
xi ≠ x
•
Additional Constraints
xi − x j +1≤ myi , x j − xi +1≤ my j , yi + y j =1,
yi , y j ∈{0 ,1},
0≤ xi , x j ≤ m −1
•
Additional Variables
•
Constraint programming
Symbolic constraint
zik =1 iff xi = k , i =1,...., n , k = 0 ,...., m −1
zi 0 +..... zim−1 =1, z ik +....+ z nk ≤1
•
j
⇔ xi < x j ∨ xi > x
j
⇔ x i ≤ x j −1∨ x i ≥ x j + 1
alldifferent ( x1 ,.....xn )
Cumulative (Disjunctive)
Resources
Cumulative constraint
Limit
resource
resource
duration
time
start
End
Machine Choice (Speed)
Diffn (2D)
machine
M6
M5
M4
duration
1
machine
M3
M2
M1
start
time
Consumable Resources
Storage
Max capacity
Min capacity
Product/Machine Dependent
Setup Times
cycle with distance matrix
variable time
forbidden sequence
Agenda
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•
•
•
•
Background
CP versus MIP
CP and MIP
Case Studies
Further Developments
CP, MIP and their combination
•
Optimization Technologies
– Mixed Integer Programming: MIP
– Finite Domain Constraint Programming: CP
•
Planning & Scheduling
CP
CP+MIP
– Long and mid-term planning: MIP
– Short-term planning, scheduling: CP
Supply chain optimization
Requires MIP, CP, and their combination
Time Horizon
MIP
Planning & Scheduling Problems
• Model building
• Model solving
• Problem decomposition
• Communication between solvers
– Generic modeling and solution approaches for MIP,
CP, MIP + CP
Typical Architecture
Scheduling Model
Planning Model
MANUAL
ITERATION
LP/MIP
CP
Ideal Architecture
INTEGRATED ENVIRONMENT
Common Planning and Scheduling Model
LP/MIP
CP
Combining MIP & CP
Master problem
MIP
Sub problem
CP
Feasible
(OK)
Infeasible
Add Cut to MIP
Mixed logical/Linear Programming framework (Hooker et al)
Agenda
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•
•
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•
Background
CP versus MIP
CP and MIP
Case Studies
Further Developments
Background
• LISCOS Project
– European Union 5th Framework
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BASF - Chemicals
P&G - Food
PSA - Cars
Barbot - Paint
Barbot
• paint is produced in
batches which are
composed by a sequence
of operations (tasks)
weighing
pre-mixing
dispersion
milling
finishing
colour
tinting
quality
control
filling
Process
• solvent based production line
Traditional Methodology
Production Department
Sales Department
• forecasting
• lot-sizing
(quantity-batches to
be produced each
day)
• end products inventory
• distribution
• ...
production
• raw materials inventory
orders
• scheduling of
batches
on machines
• ...
Traditional Methodology
• Machine capacity depends on the way production orders
are scheduled
• Batching and lot-sizing does not consider subsequent
scheduling, thus machine capacity cannot be correctly
estimated:
– overestimation: work overload and eventually rescheduling of production orders;
– underestimation: productivity losses;
– both cases may contribute to delivery delays.
New Methodology
• Decision support system that solves the
problems in an integrated fashion:
– determine the batches and lot sizes for each
product;
– schedule the resulting tasks optimising the
use of resources;
– scheduling constraints are considered at the
lot-sizing level.
New Methodology
– In general, a single model comprising
both lot-sizing and scheduling is too
large
– Lot-sizing is well solved by MIP
– Scheduling is best solved by CP
– Methodology solves each problem using
the best technique
Technical Solution
production orders
production
planning
scheduling
Information on
(un)feasibility
Mixed Integer Programming
(Xpress-MP)
Constraint Programming
(CHIP)
Technical Solution
• Some test results:
– scheduling daily problems (20 machines/80
tasks) are solved by CHIP within seconds
– lot-sizing problems (2 days) are solved by
XPRESS Branch and Cut within seconds
– a 2 day integrated lot-sizing/scheduling
problem is solved by the combined approach
within a few minutes
Benefits
• More efficient use of production capacity;
• Reduction on waste of materials in the
process of cleaning the machines;
• Reduction of delivery times;
• Prevention of shortages
• 10% capacity increase.
Conclusions
• The integration of lot-sizing and
scheduling gives better solutions than
using the two models separatley
• The combined MIP/CP approach allows
solving an integrated model, that is to big
to be solved by one technique alone
BASF
Segments
Products (examples)
Chemicals
Petrochemical feedstocks, plasticizers, electronic
grade chemicals, glues and resins, amines, diols,
intermediates for paints, fibers and fine chemicals
Plastics & Fibers
Styrene, styrene-based polymers, specialty foams,
engineering plastics, polyols, isocyanates, polyurethane systems and polyurethane specialty
elastomers, fiber intermediates, nylon-based fibers
Performance Products Textile and leather chemicals, pigments, raw
materials for detergents, gasoline and diesel
additives, refinery chemicals, superabsorbents,
adhesive raw materials, paper chemicals,
construction chemicals, automotive coatings
Agricultural Products
& Nutrition
Herbicides, fungicides, insecticides, vitamins,
pharmaceutical active ingredients, UV absorbers
Oil & Gas
Crude oil and natural gas
(exploration, production and trading)
Case study - Polypropylene
Polypropylenes are mostly “commodities”: competition is keen, customers decide
mostly by price, in the second
order by service and flexibility.
First Stage
Manual planning (without
optimisation):
Intermediate
products
Raw
materials
Raw
materials
Second Stage
• needed three days
• no chance to consider quality
aspects
• low flexibility at the occurence
of disturbances
• difficulties to react to shortterm demands
ex. 9
500 t
500 t
ex. 10
Intermediate
products
ex. 11
20 tanks = 2000t
ex. 12
ex. 13
ex. 14
Raw
materials
Final
product
P1
P2
.
.
.
Pn
Polymerisation Stage
Raw
materials
• Continuous production on 24 hours/day
• Campaign production with variable size
• Sequence-dependent changeover times
Intermediates
Intermediate Storage
Intermediates
I1
I2
.
.
.
I7
• Storage of intermediate products before the second
stage
• Limited capacity
• Only one product per silo
Extrusion Stage
Raw materials
End
products
P1
P2
.
.
.
Pn
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• Continuous production on 24 hours/day
• Campaign production with variable size
• Production rate depends on product and machine
The Optimization Problem
Lot-Sizing Problem:
Distribute anticipated customer demand for the next three
months into campaigns of variable size
Assignment problem: Determine the machine for each campaign
Sequencing problem: Find a valid sequence for each individual machine
Global objective: Minimize inventory while respecting the customers due dates
We can not
• solve lot-sizing without assignment, because machines are very different in speed
• solve assignment without sequencing, because of strong restrictions on changeovers
• solve sequencing without lot-sizing, because of the limited buffer size for intermediates
and complex temporal relationships between campaigns
We have to solve all three problems simultaneously!
The Planning Problem
Lot-Sizing Problem:
Suitable for MIP, but not CP.
Assignment problem: Suitable for MIP and CP.
}
}
Sequencing problem: Suitable for CP, but not MIP
MIP Model (Master)
CP Model (Slave)
use MIP and CP
Now
We can
we can
not solve
solve all
all three
three problems
problems simultaneously!
simultaneously!
Implementation and Results
SAP R/3
Software:
• XPRESS-MP (Dash Optimisation) for MIP
• CHIP (Cosytec) for CP
AviS/3
• Advanced Visual Scheduler (BIS) for Visualisation
Benefits:
• Optimal plan (w.r.t objective function) available in less
than 10 minutes
• Total planning process needs a few hours
• Flexibility, Reactivity
Optimizer
Outlook
Supply chain optimisation problems in process industry often involve
lot-sizing
assignment
sequencing
Combined MIP/CP algorithm with Mosel allows very complex supply
chain planning problems to be formulated and solved with a few
hundred lines of code.
A second implementation of the combined approach is already being
implemented at BASF
Agenda
•
•
•
•
•
Background
CP versus MIP
CP and MIP
Case Studies
Further Developments
General Conclusions
• Solve problems (that could not be
solved)
• Solve problems quicker
⇒
• Better plans
• More responsive operation
• Increase capacity
Current Developments: Xpress-CP
Architecture
Mosel/IVE ENVIRONMENT
Mosel Planning and Scheduling Model
Xpress-MP
CHIP
Summary
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•
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CP & MIP can work together
Master/slave architecture works
Proven on planning and scheduling
New product under development
Acknowledgements
Barbot www.barbot.pt
BASF www.basf.com
PSA Peugeot Citroën www.psa-peugeot-citroen.com
Procter & Gamble www.pg.com
CORE, University of Louvain-la-Neuve www.core.ucl.ac.be
DEIO, University of Lisbon www.deio.fc.ul.pt
LORIA, University of Henri-Poincare www.loria.fr
COSYTEC www.cosytec.com