Y Pochet Lhoist Group IP at CORE May

Y. Pochet, Lhoist Group IP at CORE May 27 -29, 2009 From PW and MIP to PP by MIP From Production Waste and Milling Intermediate Products To Production Performance by Milling Inequality Polyhedron

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 2

Lhoist Group Lhoist 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 Lhoist 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. 3

Why Supply Chain Network Optimization? Impact on EBITDA & ROCE Operational buy Tactical Material planning make Scheduling Master Planning move Transportation Scheduling Transport & Resource Planning store Inventory Management Distribution Planning sell partner Strategic Supply Chain Network Optimisation Forecasting & Order Promising Collaborative Planning, Forecasting & Replenishment 4

European Lime Production & Delivery SC Network : From the Quarry to the Customer 5

Lime Production: Plant Mass Flows 6

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 7

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! 8

This is not only about science This is about something else … 9

Y. Pochet, Lhoist Group IP at CORE May 27 -29, 2009 From PW and MIP to PP by MIP From (Pochet-) Wolsey and Mixed Integer Programming To Production Planning by Mixed Integer Programming

The Goal: Thank you Laurence for your exceptional guidance! • Laurence’s Ph. D Students (+ many others, sorry ! ) ü Work inspired by Laurence ü Constant drive to develop his students ü Fascination for the Lot-Sizing world • Area/Era 1: The Happy few or PP and MIP ü Single item planning models ü Specific Reformulations (cutting planes, extended, …) • Area/Era 2: The Happy many or PP by MIP ü Multi item production planning models ü Optimization algorithms & Systems ü Generalizations to MIPs & Generic reformulations • Area 3: The Happy all or MIP/IP ü ü ü Facility Location Scheduling and Constraint Programming Partitioning Problems Graphs with Bounded Decomposability ; Flows Markov and Groebner Bases 11

Laurence’s Ph. D Students 1. 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) 12

Laurence’s Ph. D 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) 13

Area 1: Lot Sizing Models LS-C • Single Item : LS-U ; 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 / ST Sales (profit max) [LS, WW, DLS]1 - [U, C, CC]1 / SL 1 - [U, C, CC]1 Safety Stocks [LS, WW, DLS] / SS 1 - [U, C, CC]1 Lower Bounds [LS, WW, DLS] / LB Research Stream on Algorithms ; Valid Inequalities ; Extended Reformulations 14

A long story … LAW’s Ph. D Di-graph V I Fixed Charge Problems ( SNF) [MP, ’ 85] Seminal Contributions APPLICATION THEORY COMPUTATION Padberg, Van Roy, Wolsey LS-U : Convex Hull [MP, ’ 84] V I Uncap. Fixed Charge Networks [ORL, ’ 85] Mixed 0 -1 Automatic Reformulation [OR, ’ 87] Barany, Van Roy, Wolsey Cap. Facility Loc. : [MOR, ’ 95] LS-B : [MP, ’ 88] ML-S : [? ? , ’ 87] LS-C : [ORL, ’ 88] P, Wolsey P P, Wolsey Aardal, P, Wolsey LS-C/ SC : [MP, ’ 96] Constantino LS-U/ concave [DAM, ’ 94] Aghezzaf, Wolsey LS-U / # set-ups : [ORL, ’ 92] Aghezzaf, Wolsey LS-CC : [MOR, ’ 93] P, Wolsey LS-C/ ST : [MS, ’ 98] Vanderbeck WW-U, CC, B, SC : [MP, ’ 94] IP Col. Generation : [ORL, ’ 96] P, Wolsey Vanderbeck, Wolsey 15

LAW’s Ph. D Di-graph APPLICATION THEORY LS-U / LS-CC WW-U, CC, B, SC Mixing MIR ineq: [MP, ’ 01] Günlük, P Mixing Sets : Van Vyve [MOR, ’ 05] Conforti, Wolsey Miller, Wolsey WW-CC/ LB : Constantino [MOR, ’ 98] Van Vyve [’ 03] WW-U/ B, SC : [ORL, ’ 99] Agra, Constantino LS-U/SL, SS : [MP, ’ 01] COMPUTATION 0 -1 continuous knapsack : [MP, ’ 99] BC-PROD : [MS, ’ 00] Marchand, Wolsey Belvaux, Wolsey C-MIR ineq. for MIPs : [OR, ’ 01] BC-OPT : [MP, ’ 99] Marchand, Wolsey Cordier, Wolsey Loparic, P, Wolsey LS / fixed charge networks : [DO, ’ 04] Ortega, Van Vyve LS-CC-B : Reform. [MP, ’ 06] Algor. [MOR, ’ 07] Van Vyve LS-C & Dynamic knapsack sets : [MP, ’ 03] Loparic, Marchand, Wolsey Lifting, MIR, SNF : [4 OR, ’ 03] LS-LIB : [Springer, ’ 08] Louveaux, Wolsey P, Van Vyve, Wolsey 16

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 17

Yves, Choaib, Jorge, Karen, El Houssaine, Cid, Michel, François, Miguel, Hugues, Gaëtan, Cécile, Marko, Francisco dit Pancho, Mathieu, Quentin, Jean-François, Ruslan, Peter. 18