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