Hybrid Technologies for Supply Chain Planning and Scheduling
Alkis VazacopoulosDirectorDash Optimizationwww.dashoptimization.com
Agenda
• 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
• Background• CP versus MIP• CP and MIP• Case Studies• Further Developments
LanguagesMIP CP
Variables Real + Integer Finite Domain
Constraints Linear Equations andinequalities
Arithmetic constraintsSymbolic/Global constraints
Example
• Variables :
• Constraint : Pair wise different values
{ }1,.....0,..,1 −∈ mxx n
Algorithms
MIP CP
Inference Pre-solve, LP cutting planes
Domain filteringConstraint propegation
Search Branch-and-relaxBranch-and-cut
Branch-and-bound
Inferencey
{ }
3,2, : plane) (cutting MIP5.3,2, : LP
4,2, : )(filtering CP
3,...,0,
73 73
sconstraint arithmeticLinear
≤≤≤≤≤≤
∈=+≤+≤+
zyxzyxzyx
yxzyx
xyyx
x
Formulation• Integer programming:
only linear equations and inequalities
• Additional Constraints
• Additional Variables
• Constraint programming Symbolic constraint
11 +≥∨−≤⇔
>∨<⇔≠
jiji
jijiji
xxxx
xxxxxx
{ } 1,0,1,0, ,1 ,1 ,1
−≤≤∈=+≤+−≤+−
mxxyyyymyxxmyxx
jiji
jijijiji
( )nxx ,.....nt alldiffere 1
1....,1..... 1,....,0 ,,....,1 , iff 1
10 ≤++=+−====
− nkikimiiik
zzzzmknikxz
Cumulative (Disjunctive) Resources
Cumulative constraint
resourceLimit
resource
duration
starttime
End
Machine Choice (Speed)
Diffn (2D)machine
M6
start
duration 1M5
machineM4
M3
M2
M1
time
Consumable Resources
Storage
Max capacity
Min capacity
Product/Machine Dependent Setup Times
cycle with distance matrix
variable time
forbidden sequence
Agenda
• Background• CP versus MIP• CP and MIP• Case Studies• Further Developments
• Optimization Technologies
– Mixed Integer Programming: MIP– Finite Domain Constraint Programming: CP
• Planning & Scheduling
– Long and mid-term planning: MIP– Short-term planning, scheduling: CP
Supply chain optimizationRequires MIP, CP, and their combination
CP, MIP and their combination
CP MIPCP+MIP
Time Horizon
Planning & Scheduling Problems• Model building
• Model solving
• Problem decomposition
• Communication between solvers
– Generic modeling and solution approaches for MIP, CP, MIP + CP
Typical Architecture
MANUAL ITERATION
Planning Model
LP/MIP
Scheduling Model
CP
Ideal Architecture
Common Planning and Scheduling Model
INTEGRATED ENVIRONMENT
LP/MIP CP
Combining MIP & CP
Feasible(OK)
Sub problemCP
Master problemMIP
InfeasibleAdd Cut to MIP
Mixed logical/Linear Programming framework (Hooker et al)
Agenda
• Background• CP versus MIP• CP and MIP• Case Studies• Further Developments
Background
• LISCOS Project– European Union 5th Framework
• BASF - Chemicals• P&G - Food• PSA - Cars• Barbot - Paint
Barbotweighing• paint is produced in
batches which are composed by a sequence of operations (tasks)
pre-mixing
dispersion
milling
finishing
colour tinting
quality control
filling
Process• solvent based production line
Traditional Methodology
Production DepartmentSales Department
• forecasting
• lot-sizing(quantity-batches to
be produced each day)
• end products inventory
• distribution
• ...
• raw materials inventory
• scheduling of batches
on machines
• ...
production
orders
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 re-
scheduling 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
productionplanning
production orders
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
Segments Products (examples)BASF
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, poly-urethane 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 Herbicides, fungicides, insecticides, vitamins, & Nutrition pharmaceutical active ingredients, UV absorbers
Oil & Gas Crude oil and natural gas (exploration, production and trading)
Case study - Polypropylene
First StageRaw
materials
20 tanks = 2000t
ex. 9
ex. 10
ex. 11
ex. 12
ex. 13
ex. 14Raw
materials
Raw materials
Final product
P1P2...
Pn
Intermediate products
Intermediate products
Second Stage
500 t 500 t
Polypropylenes are mostly “commodities”: competition is keen, customers decidemostly by price, in the second order by service and flexibility.
Manual planning (without optimisation):
• needed three days
• no chance to consider quality aspects
• low flexibility at the occurence of disturbances
• difficulties to react to short-term demands
Polymerisation Stage
• Continuous production on 24 hours/day• Campaign production with variable size• Sequence-dependent changeover times
Raw materials Intermediates
Intermediate Storage
• Storage of intermediate products before the second stage
• Limited capacity• Only one product per silo
IntermediatesI1I2...
I7
Extrusion Stage
• Continuous production on 24 hours/day• Campaign production with variable size• Production rate depends on product and machine
Raw materials
End products
P1P2...
Pn•••
The Optimization ProblemLot-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
use MIP and CP
MIP Model (Master)
CP Model (Slave)}}
We can not solve all three problems simultaneously!Now we can solve all three problems simultaneously!
Software:
• XPRESS-MP (Dash Optimisation) for MIP
• CHIP (Cosytec) for CP
• 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
Implementation and Results
OptimizerAviS/3
SAP R/3
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 Planning and Scheduling Model
Mosel/IVE ENVIRONMENT
Xpress-MP CHIP
Summary
• 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