SHORT-TERM SCHEDULI NG CARLOS A. MENDEZ CARLOS A. MENDEZ Instituto de Desarrollo Tecnológico para la Industria Química (INTEC) Universidad Nacional de Litoral (UNL) – CONICET Güemes 3450, 3000 Santa Fe, Argentina cmendez@intec.unl.edu.ar PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
OUTLINE PROBLEM STATEMENT MAJOR FEATURES AND CHALLENGES SOLUTION METHODS MILP-BASED MODELS EXAMPLES AND COMPUTATIONAL ISSUES INDUSTRIAL-SCALE PROBLEMS PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
LITERATURE. REVIEW PAPERS Pekny, J.F., & Reklaitis, G.V. (1998). Towards the convergence of theory and practice: A technology guide for scheduling/planning methodology. In Proceedings of the third international conference on foundations of computer-aided process operations (pp. 91–111). Shah, N. (1998). Single and multisite planning and scheduling: Current status and future challenges. In Proceedings of the third international conference on foundations of computer-aided process operations (pp. 75–90). Pinto, J.M., & Grossmann, I.E. (1998). Assignments and sequencing models of the scheduling of process systems. Annals of Operations Research , 81 , 433–466. Kallrath, J. (2002). Planning and scheduling in the process industry. OR Spectrum , 24 , 219–250. Floudas, C A., & Lin, X. (2004). Continuous-time versus discrete-time approaches for scheduling of chemical processes: A review. Computers and Chemical Engineering , 28 , 2109–2129. Méndez, C.A., Cerdá, J., Harjunkoski, I., Grossmann, I.E. & Fahl, M. (2006). State-of-the-art review of optimization methods for short-term scheduling of batch processes. Computers and Chemical Engineering , 30, 6, 913 – 946, PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
TRADITIONAL "BIG PICTURE" � Plant Level: Multilevel/Hierarchical Decisions months, years Planning Economics Allocation of limited resources over time to perform a collection days, weeks Feasibility Scheduling Delivery of tasks secs, mins Dynamic Control Performance Information systems Optimization-based computer tools “Decision-making process with the goal of optimizing one or more objectives” PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
SHORT-TERM SCHEDULING Plant configuration Recipe data Demands Scheduler Production Scheduling Production Scheduling Detailed plant production scheduling Schedule PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
DECISION-MAKING PROCESS Batches or campaigns to be processed What What Where Where unit allocation resource allocation: steam, electricity, raw How How materials, manpower When Timing of manufacturing operations When MAIN CHALLENGES High combinatorial complexity Many problem features to be simultaneously considered Time restrictions PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
ILLUSTRATIVE EXAMPLE EQUIPMENT - HEATER - 2 REACTORS - STILL BATCH TASKS STN-REPRESENTATION - HEATING - 3 REACTIONS - SEPARATION GOAL MAXIMIZE PROFIT Reaction 1 DECISIONS Heating Heater Reaction 2 Reaction 3 Lot-sizing Reactor 1 Allocation Reactor 2 Separation profit = 2805 Sequencing Still Timing PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
PROBLEM STATEMENT - I � Given : � plant configuration � plant equipment (processing units, storage tanks, transfer units, connecting networks) � resources (electricity, manpower, heating/cooling utilities, raw materials) � product recipes � product precedence relations � demands What What PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
PROBLEM STATEMENT - II � Determine : Where Where � assignment of equipment and resources to tasks � production sequence � detailed schedule When When � start and end times � inventory levels � resources utilization profiles How How PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
PROBLEM STATEMENT - III � To optimize one or more objectives: � time required to complete all tasks (makespan) � number of tasks completed after their due dates � plant throughput � customer satisfaction � profit � costs PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
SCHEDULING & RE-SCHEDULING RESCHEDULING RESCHEDULING “Efficient resource Efficient resource “ dynamic & uncertain dynamic & uncertain relocation” ” relocation environment environment II I Execution Decision making When When Where Where Predictive What What schedule How How Unexpected Data ambiguous INFEASIBLE events outdated SCHEDULE incomplete PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
BATCH SCHEDULING FEATURES (1) Process topology Sequential Network (arbitrary) Single stage Multiple stages Single Parallel Multiproduct Multipurpose unit units (Flow-shop) (Job-shop) (2) Equipment assignment Fixed Variable (3) Equipment connectivity Partial Full (restricted) (4) Inventory storage policies Unlimited Non-Intermediate Finite Zero Intermediate Storage (NIS) Intermediate Wait (ZW) Storage (UIS) Storage (FIS) Dedicated Shared storage units storage units (5) Material transfer Instantaneous Time-consuming (neglected) No-resources Pipes Vessels (Pipeless) PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
BATCH SCHEDULING FEATURES Large diversity of factors ! (6) Batch size Fixed Variable Developing general methods (Mixing and Splitting) (7) Batch processing time is quite difficult … Fixed Variable (unit/batch-size dependent) Unit independent Unit dependent (8) Demand patterns Due dates Scheduling horizon Single product multiple product Fixed Minimum / maximum demand demands requirements requirements (9) Changeovers None Unit dependent Sequence dependent Product dependent Product and unit dependent (10) Resource Constraints None (only equipment) Discrete Continuous (11) Time Constraints None Non-working periods Maintenance Shifts (12) Costs Equipment Utilities Inventory Changeover (13) Degree of certainty Deterministic Stochastic PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
ROAD-MAP FOR BATCH SCHEDULING (1) TASK TOPOLOGY: 1 A B C 2 - Single Stage (single unit or parallel units) 3 - Multiple Stage (multiproduct or multipurpose) - Network (2) EQUIPMENT ASSIGNMENT - Fixed - Variable (3) EQUIPMENT CONNECTIVITY - Partial - Full (4) INVENTORY STORAGE POLICIES - Unlimited intermediate storage (UIS) - Finite intermediate storage (FIS): Dedicated or shared storage units - Non-intermediate storage (NIS) - Zero wait (ZW) 10% 2h 1h 90% S3 Separation S4 Reaction1 1h (5) MATERIAL TRANSFER 40% S1 S2 Heat - Instantaneous (neglected) 2h 3h 60% 70% S5 S7 Reaction2 Reaction 3 -Time consuming (no-resource, pipes, vessels) 30% S6 PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
ROAD-MAP FOR BATCH SCHEDULING (6) BATCH SIZE: - Fixed - Variable (mixing and splitting operations) (7) BATCH PROCESSING TIME ... - Fixed Due Due Due Due 0 date 1 date 2 date 3 date NO - Variable (unit / batch size dependent) Production (8) DEMAND PATTERNS Horizon - Due dates (single or multiple product demands) - Scheduling horizon (fixed, minimum/maximum requirements) (9) CHANGEOVERS i i’ ’ i changeover changeover i - None - Unit dependent - Sequence dependent (product or product/unit dependent) (10) RESOURCE CONSTRAINTS - None (only equipment) - Discrete (manpower) - Continuous (utilities) (Fixed or time dependent) PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
ROAD-MAP FOR BATCH SCHEDULING (11) TIME CONSTRAINTS - None - Non-working periods - Maintenance - Shifts (12) COSTS - Equipment - Utilities (fixed or time dependent) - Inventory - Changeovers (13) Degree of certainty - Deterministic - Stochastic PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
ROAD-MAP FOR SOLUTION METHODS (1) Exact methods (2) Constraint programming (CP) MILP Constraint satisfaction methods MINLP (3) Meta-heuristics (4) Heuristics Simulated annealing (SA) Dispatching rules Tabu search (TS) Genetic algorithms (GA) (5) Artificial Intelligence (AI) (6) Hybrid-methods Rule-based methods Exact methods + CP Agent-based methods Exact methods + Heuristics Expert systems Meta-heuristics + Heuristics Rigorous mathematical representation Non-linear constraints are avoided Discrete and continuous variables Mathematical-based solution methods Systematic solution search Feasibility and optimality PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
ROAD-MAP FOR OPTIMIZATION APPROACHES TIME DOMAIN REPRESENTATION - Discrete time Time interval duration ? TASK TIME - Continuous time TASK How many events ? TIME EVENTS TASK How many tasks ? TIME PASI 2008 - - Mar del Plata, Argentina Mar del Plata, Argentina PASI 2008
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