From PW and MIP to PP by MIP

From Production Waste and Milling Intermediate Products

To Production Performance by Milling Inequality Polyhedron

Y. Pochet, Lhoist GroupIP at COREMay 27-29, 2009

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Outline

• Supply Chain Network at Lhoist• Lime Basics• Production Waste Constraint and Model for the Milling

Process• Milling Inequality Polyhedron • Improved Production Performance using the Milling Inequality

Polyhedron

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Lhoist GroupLhoist is a privately held lime company

•Headquarters in Limelette, Belgium, Europe

Lhoist is the leading lime manufacturer in the world with over 70 operations in: •Belgium, France, Germany, Denmark, •Poland, Czech Republic, England, Spain, Portugal, North- and Central America•Brazil

Supply Chain Network Optimization at LhoistLhoist Group is using an APS (Advanced Planning Software) as part of its DSS (Decision Support System) for its strategic and tactical “supply chain network optimizations”. Development started in 1991, research project Lhoist (P. Sevrin) – UCL (Y. Pochet) Specificity: divergent product structure with linked co-products (grain size, physical and chemical quality, variable recipes,…)

difficult flow balance constraints within the plants.

The system and the optimization approach have been used extensively within Lhoist Group for many strategic studies. The system will never be a “decision system” and will remain a support to challenge creativity and entrepreneurship.

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buybuy

makemake

storestore

movemove

sellsell

partnerpartner

Material planningMaterial planning

SchedulingScheduling Master PlanningMaster Planning

Inventory ManagementInventory Management Distribution PlanningDistribution Planning

Transportation SchedulingTransportation Scheduling

Forecasting & Order PromisingForecasting & Order Promising

Collaborative Planning, Forecasting & ReplenishmentCollaborative Planning, Forecasting & Replenishment

SupplyChain

NetworkOptimisation

SupplyChain

NetworkOptimisation

Transport & ResourcePlanning

Transport & ResourcePlanning

Impact on EBITDA &

ROCE

Operational Tactical Strategic

Why Supply Chain Network Optimization?

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European Lime Production & DeliverySC Network : From the Quarry to the Customer

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Lime Production: Plant Mass Flows

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Outline

• Supply Chain Network at Lhoist• Lime Basics• Production Waste Constraint and Model for the Milling

Process• Milling Inequality Polyhedron • Improved Production Performance using the Milling

Inequality Polyhedron

8

Outline

• Supply Chain Network at Lhoist• Lime Basics• Production Waste Constraint and Model for the Milling

Process• Milling Inequality Polyhedron • Improved Production Performance using the Milling

Inequality Polyhedron

• As Karen would say:

I don’t have the foggiest idea what this is about…

Let’s try again!

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This is not only about science This is about something else …

From PW and MIP to PP by MIP

From (Pochet-) Wolsey and Mixed Integer Programming

To Production Planning by Mixed Integer Programming

Y. Pochet, Lhoist GroupIP at COREMay 27-29, 2009

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The Goal: Thank you Laurence for your exceptional guidance!

• Laurence’s PhD Students (+ many others, sorry ! ) Work inspired by Laurence Constant drive to develop his students Fascination for the Lot-Sizing world

• Area/Era 1: The Happy few or PP and MIP Single item planning models Specific Reformulations (cutting planes, extended,…)

• Area/Era 2: The Happy many or PP by MIP Multi item production planning models Optimization algorithms & Systems Generalizations to MIPs & Generic reformulations

• Area 3: The Happy all or MIP/IP Facility Location Scheduling and Constraint Programming Partitioning Problems Graphs with Bounded Decomposability ; Flows Markov and Groebner Bases

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Laurence’s PhD Students1. Y. Pochet, Lot-Sizing Problems: Reformulations and Cutting Plane

Algorithms (1987)

2. C. Bousba, Planification des Réseaux Electriques de Distribution à Basse Tension: une Approche par la Programmation Mathématique (1989)

3. J.P. de Sousa, Time Indexed Formulations of Non-Preemptive Single-Machine Scheduling Problems (1989)

4. K. Aardal, On the Solution of One and Two-Level Capacitated Facility Location Problems by the Cutting Plane Approach (1992)

5. E-H Aghezzaf, Optimal Constrained Rooted Subtrees and Partitioning Problems on Tree Graphs (1992)

6. C. de Souza, The Graph Equipartition Problem: Optimal Solutions, Extensions and Applications (1993)

7. M. Schaffers, On Links between Graphs with Bounded Decomposability, Existence of Efficient Algorithms, and Existence of Polyhedral Characterizations (1994)

8. F. Vanderbeck, Decomposition and Column Generation for Integer Programs (1994)

9. M. Constantino, A Polyhedral Approach to Production Planning Models: Start-Up Costs and Times, Upper and Lower Bounds on Production (1995)

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Laurence’s PhD Students

10.H. Marchand, A Polyhedral Study of the Mixed Knapsack Set and its Use to Solve Mixed Integer Programs (1998)

11.G. Belvaux, Modelling and Solving Lot-Sizing Problems by Mixed Integer Programming (1999)

12.C. Cordier, Development and Experimentation with a Branch and Cut System for Mixed Integer Programming (1999)

13.M. Loparic, Stronger Mixed 0-1 Models for Lot-Sizing Problems (2001)

14.F. Ortega, Formulations and Algorithms for Fixed Charge Networks and Lot-Sizing Problems (2001)

15.M. Van Vyve, A Solution Approach of Production Planning Problems based on Compact Formulations for Single-Item Lot-Sizing Models (2003)

16.Q. Louveaux, Exploring Structure and Reformulations in Different Integer Programming Algorithms(2004)

17.J-F. Macq, Optimization of Multimedia Flows over Data Networks (2005)

18.R. Sadykov, Integer Programming-based Decomposition Approaches for Solving Machine Scheduling Problems (2006)

19.P. Malkin, Computing Markov bases, Groebner bases and extreme rays (2007)

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Area 1: Lot Sizing Models LS-C

• Single Item : LS-U ; LS-C ; LS-CC (Wagner-Whitin costs WW ; Discrete Prod. DLS) Variants : Backlogging [LS,WW,DLS]1 - [U,C,CC]1 / B Start-Up Costs [LS,WW,DLS]1 - [U,C,CC]1 / SC

Start-Up Times [LS,WW,DLS]1 - [U,C,CC]1 / STSales (profit max) [LS,WW,DLS]1 - [U,C,CC]1 / SLSafety Stocks [LS,WW,DLS]1 - [U,C,CC]1 / SSLower Bounds [LS,WW,DLS]1 - [U,C,CC]1 / LB

Research Stream on Algorithms ; Valid Inequalities ; Extended Reformulations

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A long story … LAW’s PhD Di-graph

LS-U : Convex Hull [MP, ’84]

Barany, Van Roy, Wolsey

Seminal Contributions

Mixed 0-1 Automatic Reformulation [OR, ’87]

Van Roy, Wolsey

V I Uncap. Fixed Charge Networks [ORL, ’85]

Barany, Van Roy, Wolsey

V I Fixed Charge Problems ( SNF) [MP, ’85]

Padberg, Van Roy, Wolsey

LS-B : [MP, ’88]

P, Wolsey

LS-C : [ORL, ’88]

P, Wolsey

ML-S : [??, ’87]

P

Cap. Facility Loc.: [MOR, ’95]

Aardal, P, Wolsey

LS-U/ concave [DAM, ’94]

Aghezzaf, Wolsey

LS-CC : [MOR, ’93]

P, Wolsey

WW-U,CC,B,SC : [MP, ’94]

P, Wolsey

LS-U / # set-ups : [ORL, ’92]

Aghezzaf, WolseyLS-C/ ST : [MS, ’98]

Vanderbeck

IP Col. Generation : [ORL, ’96]

Vanderbeck, Wolsey

LS-C/ SC : [MP, ’96]

Constantino

APPLICATION THEORY COMPUTATION

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LAW’s PhD Di-graph

WW-CC/ LB :

Constantino [MOR, ’98]Van Vyve [’03]

WW-U/ B,SC : [ORL, ’99]

Agra, Constantino

0-1 continuous knapsack : [MP, ’99]

Marchand, Wolsey

C-MIR ineq. for MIPs : [OR, ’01]

Marchand, Wolsey

BC-PROD : [MS, ’00]

Belvaux, Wolsey

BC-OPT : [MP, ’99]

Cordier, Wolsey

LS-LIB : [Springer, ’08]

P, Van Vyve, Wolsey

LS-U/SL, SS : [MP, ’01]

Loparic, P, WolseyLS-C & Dynamic knapsack

sets : [MP, ’03]

Loparic, Marchand, Wolsey

LS / fixed charge networks : [DO, ’04]

Ortega, Van Vyve

LS-CC-B : Reform. [MP, ’06] Algor. [MOR, ’07]

Van Vyve

Lifting, MIR, SNF : [4OR, ’03]

Louveaux, Wolsey

Mixing MIR ineq: [MP, ’01]

Günlük, P

Mixing Sets :

Van Vyve [MOR,’05]Conforti, Wolsey

Miller, Wolsey

LS-U / LS-CC

WW-U,CC,B,SC

APPLICATION THEORY

COMPUTATION

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Thank you so much Laurence for your

• Patience (personal comment)• Permanent challenging mindset: Asking (us) the right - but

tough - questions at the right time

• Constant Drive• Intuition and deep knowledge of the field• Continuous source of inspiration and intellectual motivation

• Guidance• Friendship

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Matrix Pulsar/ Alpine

/ Futur (50 Tons)

Colouring Unit (16 Tons/ hour)

NIPAG (3.5

tons/ hour)

PULSAG (10 tons/ hour)

NIPAG Buffer

(70 Tons 200 Tons

MAx)

PULSAG Buffer

150 tons

Matrix Buffer Japanese (80 Tons)

GREEN Buffer

Storage

Re-Blend Storage

White Buffer

Storage50-60 Tons/ Hour

Brand Change-over 15 Min.

Dry Material Addition

15 % FUTUR 10 % PULSAR

8 EURO PULSAR

3 JAPAN PULSAR

7 FUTUR

Yves, Choaib, Jorge, Karen,

El Houssaine, Cid, Michel,

François, Miguel, Hugues,

Gaëtan, Cécile, Marko,

Francisco dit Pancho,

Mathieu, Quentin,

Jean-François, Ruslan, Peter.