Mixed Integer Linear Programming in Process Scheduling: Modeling, Algorithms, and Applications
 Christodoulos A. Floudas,
 Xiaoxia Lin
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This paper reviews the advances of mixedinteger linear programming (MILP) based approaches for the scheduling of chemical processing systems. We focus on the shortterm scheduling of general network represented processes. First, the various mathematical models that have been proposed in the literature are classified mainly based on the time representation. Discretetime and continuoustime models are presented along with their strengths and limitations. Several classes of approaches for improving the computational efficiency in the solution of MILP problems are discussed. Furthermore, a summary of computational experiences and applications is provided. The paper concludes with perspectives on future research directions for MILP based process scheduling technologies.
 Applequist, G., O. Samikoglu, J. Pekny, and G. Reklaitis. (1997). “Issues in the Use, Design and Evolution of Process Scheduling and Planning Systems.” ISA Transactions 36, 81–121. CrossRef
 Bassett, M.H., P. Dave, F.J.D. III, G.K. Kudva, J.F. Pekny, G.V. Reklaitis, S. Subrahmanyam, D.L. Miller, and M.G. Zentner. (1996a). “Perspectives on Model Based Integration of Process Operations.” Computers & Chemical Engineering 20, 821–844. CrossRef
 Bassett, M.H., J.F. Pekny, and G.V. Reklaitis. (1996b). “Decomposition Techniques for the Solution of LargeScale Scheduling Problems.” AIChE Journal 42, 3373–3387. CrossRef
 Blömer, F. and H.O. Günther. (2000). “LPBased Heuristics for Scheduling Chemical Batch Processes.” International Journal of Production Research 38, 1029–1051. CrossRef
 Bok, J. and S. Park. (1998). “ContinuousTime Modeling for ShortTerm Scheduling of Multipurpose Pipeless Plants.” Industrial & Engineering Chemistry Research 37, 3652–3659. CrossRef
 Bowman, E.H. (1959). “The ScheduleSequencing Problem.” Operations Research 7, 621–624.
 Burkard, R.E., T. Fortuna, and C.A.J. Hurkens. (2002). “Makespan Minimization for Chemical Batch Processes Using NonUniform Time Grids.” Computers & Chemical Engineering 26, 1321–1332. CrossRef
 Castro, P., A.P.F.D. BarbosaPóvoa, and H. Matos. (2001). “An Improved RTN ContinuousTime Formulation for the ShortTerm Scheduling of Multipurpose Batch Plants.” Industrial & Engineering Chemistry Research 40, 2059–2068. CrossRef
 Castro, P., H. Matos, and A.P.F.D. BarbosaPóvoa. (2002). “Dynamic Modeling and Scheduling of an Industrial Batch System.” Computers & Chemical Engineering 26, 671–686. CrossRef
 Cerdá, J., G.P. Henning, and I.E. Grossmann. (1997). “A MixedInteger Linear Programming Model for ShortTerm Scheduling of SingleStage Multiproduct Batch Plants with Parallel Lines.” Industrial & Engineering Chemistry Research 36, 1695–1707. CrossRef
 Dedopoulos, I.T. and N. Shah. (1995). “Optimal ShortTerm Scheduling of Maintenance and Production for Multipurpose Plants.” Industrial & Engineering Chemistry Research 34, 192–201. CrossRef
 Dimitriadis, A.D., N. Shah, and C.C. Pantelides. (1997). “RTNBased Rolling Horizon Algorithms for Medium Term Scheduling of Multipurpose Plants.” Computers & Chemical Engineering 21, S1061–S1066.
 Elkamel, A. and G. AlEnezi. (1998). “Structured Valid Inequalities and Separation in Optimal Scheduling of the ResourceConstrained Batch Chemical Plant.” Mathematical Engineering in Industry 6, 291– 318.
 Elkamel, A., M. Zentner, J.F. Pekny, and G.V. Reklaitis. (1997). “A Decomposition Heuristic for Scheduling the General Batch Chemical Plant.” Engineering Optimization 28, 299–330.
 Floudas, C.A. (1995). Nonlinear and MixedInteger Optimization. Oxford University Press.
 Floudas, C.A. and X. Lin. (2004). “ContinuousTime versus DiscreteTime Approaches for Scheduling of Chemical Processes: A Review.” Computers & Chemical Engineering 28, 2109–2129. CrossRef
 Garey, M.R. and D.R. Johnson. (1979). Computers and Intractability: A Guide to the Theory of NPCompleteness. New York: W. H. Freeman.
 Georgiadis, M.C., L.G. Papageorgiou, and S. Macchietto. (2000). “Optimal Cleaning Policies in Heat Exchanger Networks under Rapid Fouling.” Industrial & Engineering Chemistry Research 39, 441–454. CrossRef
 Glismann, K. and G. Gruhn. (2001). “ShortTerm Scheduling and Recipe Optimization of Blending Processes.” Computers & Chemical Engineering 25, 627–634. CrossRef
 Glover, F. (1975). “Improved Linear Integer Programming Formulations of Nonlinear Integer Problems.” Management Science 22, 455–460.
 Grossmann, I.E., I. Quesada, R. Raman, and V.T. Voudouris. (1996). “MixedInteger Optimization Techniques for the Design and Scheduling of Batch Processes.” In G. V. Reklaitis, A. K. Sunol, D. W. T. Rippin and O. Hortacsu (ed.), Batch Processing Systems Engineering, Berlin: Springer, pp. 451– 494.
 Harjunkoski, I. and I.E. Grossmann. (2001). “A Decomposition Approach for the Scheduling of a Steel Plant Production.” Computers & Chemical Engineering 25, 1647–1660. CrossRef
 Hui, C. and A. Gupta. (2001). “A Biindex ContinuousTime MixedInteger Linear Programming Model for SingleStage Batch Scheduling with Parallel Units.” Industrial & Engineering Chemistry Research 40, 5960–5967. CrossRef
 Hui, C., A. Gupta, and H.A.J. van der Meulen. (2000). “A Novel MILP Formulation for ShortTerm Scheduling of MultiStage MultiProduct Batch Plants with SequenceDependent Constraints.” Computers & Chemical Engineering 24, 2705–2717. CrossRef
 Ierapetritou, M.G. and C.A. Floudas. (1998a). “Effective ContinuousTime Formulation for ShortTerm Scheduling: 1. Multipurpose Batch Processes.” Industrial & Engineering Chemistry Research 37, 4341–4359. CrossRef
 Ierapetritou, M.G. and C.A. Floudas. (1998b). “Effective ContinuousTime Formulation for ShortTerm Scheduling: 2. Continuous and SemiContinuous Processes.” Industrial & Engineering Chemistry Research 37, 4360–4374. CrossRef
 Ierapetritou, M.G. and C.A. Floudas. (2001). Comments on “An Improved RTN ContinuousTime Formulation for the Shortterm Scheduling of Multipurpose Batch Plants.” Industrial & Engineering Chemistry Research 40, 5040–5041. CrossRef
 Ierapetritou, M.G., T.S. Hené, and C.A. Floudas. (1999). “Effective ContinuousTime Formulation for ShortTerm Scheduling: 3. Multiple Intermediate Due Dates.” Industrial & Engineering Chemistry Research 38, 3446–3461. CrossRef
 Janak, S.L., X. Lin, and C.A. Floudas. (2004). “Enhanced ContinuousTime UnitSpecific EventBased Formulation for ShortTerm Scheduling of Multipurpose Batch Processes: Resource Constraints and Mixed Storage Policies.” Industrial & Engineering Chemistry Research 43, 2516–2533. CrossRef
 Karimi, I.A. and C.M. McDonald. (1997). “Planning and Scheduling of Parallel SemiContinuous Processes. 2. ShortTerm Scheduling.” Industrial & Engineering Chemistry Research 36, 2701–2714. CrossRef
 Kondili, E., C.C. Pantelides, and R.W.H. Sargent. (1988). “A General Algorithm for Scheduling Batch Operations.” In Proceedings of the Third International Symposium on Process Systems Engineering, Sydney, Australia, pp. 62–75.
 Kondili, E., C.C. Pantelides, and R.W.H. Sargent. (1993). “A General Algorithm for ShortTerm Scheduling of Batch Operations  I. MILP Formulation.” Computers & Chemical Engineering 17, 211– 227. CrossRef
 Ku, H. and I.A. Karimi. (1988). “Scheduling in Serial Multiproduct Batch Processes with Finite Interstage Storage: A Mixed Integer Linear Programming Formulation.” Industrial & Engineering Chemistry Research 27, 1840–1848. CrossRef
 Lamba, N. and I.A. Karimi. (2002a). “Scheduling Parallel Production Lines with Resource Constraints. 1. Model Formulation.” Industrial & Engineering Chemistry Research 41, 779–789. CrossRef
 Lamba, N. and I.A. Karimi. (2002b). “Scheduling Parallel Production Lines with Resource Constraints. 2. Decomposition Algorithm.” Industrial & Engineering Chemistry Research 41, 790–800. CrossRef
 Lee, K., S. Heo, H. Lee, and I. Lee. (2002). “Scheduling of SingleStage and Continuous Processes on Parallel Lines with Intermediate Due Dates.” Industrial & Engineering Chemistry Research 41, 58– 66. CrossRef
 Lee, K., H.I. Park, and I. Lee. (2001). “A Novel Nonuniform Discrete Time Formulation for ShortTerm Scheduling of Batch and Continuous Processes.” Industrial & Engineering Chemistry Research 40, 4902–4911. CrossRef
 Lin, X. and C.A. Floudas. (2001). “Design, Synthesis and Scheduling of Multipurpose Batch Plants via an Effective ContinuousTime Formulation.” Computers & Chemical Engineering 25, 665–674. CrossRef
 Lin, X., C.A. Floudas, S. Modi, and N.M. Juhasz. (2002). “ContinuousTime Optimization Approach for MediumRange Production Scheduling of a Multiproduct Batch Plant.” Industrial & Engineering Chemistry Research 41, 3884–3906. CrossRef
 Majozi, T. and X.X. Zhu. (2001). “A Novel ContinuousTime MILP Formulation for Multipurpose Batch Plants. 1. ShortTerm Scheduling.” Industrial & Engineering Chemistry Research 40, 5935–5949. CrossRef
 Manne, A.S. (1960). “On the JobShop Scheduling Problem.” Operations Research 8, 219–223.
 Maravelias, C.T. and I.E. Grossmann. (2003). “A New General ContinuousTime State Task Network Formulation for ShortTerm Scheduling of Multipurpose Batch Plants.” Industrial & Engineering Chemistry Research 42, 3056–3074. CrossRef
 Méndez, C.A. and J. Cerdá. (2000a). “Optimal Scheduling of a ResourceConstrained Multiproduct Batch Plant Supplying Intermediates to Nearby EndProduct Facilities.” Computers & Chemical Engineering 24, 369–376. CrossRef
 Méndez, C.A., G.P. Henning, and J. Cerdá. (2000b). “Optimal Scheduling of Batch Plants Satisfying Multiple Product Orders with Different DueDates.” Computers & Chemical Engineering 24, 2223–2245. CrossRef
 Méndez, C.A., G.P. Henning, and J. Cerdá. (2001). “An MILP ContinuousTime Approach to ShortTerm Scheduling of ResourceConstrained Multistage Flowshop Batch Facilities.” Computers & Chemical Engineering 25, 701–711. CrossRef
 Mockus, J., W. Eddy, A. Mockus, L. Mockus, and R.V. Reklaitis. (1997). Bayesian Heuristic Approach to Discrete and Global Optimization: Algorithms, Visualization, Software, and Applications. Kluwer Academic Publishers.
 Mockus, L. and G.V. Reklaitis. (1997). “Mathematical Programming Formulation for Scheduling of Batch Operations Based on Nonuniform Time Discretization.” Computers & Chemical Engineering 21, 1147–1156. CrossRef
 Mockus, L. and G.V. Reklaitis. (1999a). “Continuous Time Representation Approach to Batch and Continuous Process Scheduling. 1. MINLP Formulation.” Industrial & Engineering Chemistry Research 38, 197–203. CrossRef
 Mockus, L. and G.V. Reklaitis. (1999b). “Continuous Time Representation Approach to Batch and Continuous Process Scheduling. 2. Computational Issues.” Industrial & Engineering Chemistry Research 38, 204–210. CrossRef
 Moon, S. and A.N. Hrymak. (1999). “MixedInteger Linear Programming Model for ShortTerm Scheduling of a Special Class of Multipurpose Batch Plants.” Industrial & Engineering Chemistry Research 38, 2144–2150. CrossRef
 Moon, S., S. Park, and W.K. Lee. (1996). “New MILP Models for Scheduling of Multiproduct Batch Plants under ZeroWait Policy.” Industrial & Engineering Chemistry Research 35, 3458–3469. CrossRef
 Orçun, S., I.K. Altinel, and Ö Hortaçsu. (1999). “Reducing the Integrality Gap with a Modified ReFormulation Linearization Approach.” Computers & Chemical Engineering Supplement, pp. S539–S542.
 Orçun, S., I.K., Altinel, and Ö Hortaçsu. (2001). “General Continuous Time Models for Production Planning and Scheduling of Batch Processing Plants: Mixed Integer Linear Program Formulations and Computational Issues.” Computers & Chemical Engineering 25, 371–389. CrossRef
 Pantelides, C.C. (1993). “Unified Frameworks for Optimal Process Planning and Scheduling.” In D.W.T. Rippin, J.C. Hale, and J. Davis (eds.), Proceedings of the Second International Conference on Foundations of ComputerAided Process Operations, Crested Butte, Colorado, pp. 253–274.
 Pekny, J.F. and G.V. Reklaitis. (1998). “Towards the Convergence of Theory and Practice: A Technology Guide for Scheduling/Planning Methodology.” In J.F. Pekny and G.E. Blau (eds.), Proceedings of the Third International Conference on Foundations of ComputerAided Process Operations, Snowbird, Utah, pp. 91–111.
 Pekny, J.F. and M.G. Zentner. (1993). “Learning to Solve Process Scheduling Problems: The Role of Rigorous Knowledge Acquisition Frameworks.” In D.W.T. Rippin, J.C. Hale, and J. Davis (eds.), Proceedings of the Second International Conference on Foundations of ComputerAided Process Operations, Crested Butte, Colorado, pp. 275–309.
 Pinto, J.M. and I.E. Grossmann. (1995). “A Continuous Time Mixed Integer Linear Programming Model for Short Term Scheduling of Multistage Batch Plants.” Industrial & Engineering Chemistry Research 34, 3037–3051. CrossRef
 Pinto, J.M. and I.E. Grossmann. (1996). “An Alternate MILP Model for ShortTerm Scheduling of Batch Plants with Preordering Constraints.” Industrial & Engineering Chemistry Research 35, 338–342. CrossRef
 Pinto, J.M. and I.E. Grossmann. (1998). “Assignment and Sequencing Models for the Scheduling of Process Systems.” Annals of Operations Research 81, 433–466. CrossRef
 Pinto, J.M., A. Türkay, B. Bolio, and I.E. Grossmann. (1998). “STBS: A ContinuousTime MILP Optimization for ShortTerm Scheduling of Batch Plants.” Computers & Chemical Engineering 22, 1297–1308. CrossRef
 Pritsker, A.A.B., L.J. Watters, and P.M. Wolfe. (1969). “Multiproject Scheduling with Limited Resources: A ZeroOne Programming Approach.” Management Science 16, 93–108. CrossRef
 Reklaitis, G.V. (1992). “Overview of Scheduling and Planning of Batch Process Operations.” NATO Advanced Study Institute—Batch Process Systems Engineering, Antalya, Turkey.
 Rippin, D.W.T. (1993). “Batch Process Systems Engineering: A Retrospective and Prospective Review.” Computers & Chemical Engineering 17, S1–S13. CrossRef
 Sahinidis, N.V. and I.E. Grossmann. (1991b). “Reformulation of Multiperiod MILP Models for Planning and Scheduling of Chemical Processes.” Computers & Chemical Engineering 15, 255–272. CrossRef
 Schilling, G. (1997). “Optimal Scheduling of Multipurpose Plants.” PhD thesis, University of London.
 Schilling, G. and C.C. Pantelides. (1996). “A Simple ContinuousTime Process Scheduling Formulation and a Novel Solution Algorithm.” Computers & Chemical Engineering 20, S1221–S1226. CrossRef
 Schilling, G. and C.C. Pantelides. (1996b). “A Hybrid Branch and Bound Algorithm for ContinuousTime Process Scheduling Formulations.” AIChE 1996 Annual Meeting, Chicago, IL, November 1996, Paper 171d.
 Shah, N. (1998). “Single And Multisite Planning and Scheduling: Current Status and Future Challenges.” In J.F. Pekny and G.E. Blau (eds.), Proceedings of the Third International Conference on Foundations of ComputerAided Process Operations, Snowbird, Utah, pp. 75–90.
 Shah, N., C.C. Pantelides, and R.W.H. Sargent. (1993). “A General Algorithm for ShortTerm Scheduling of Batch OperationsII. Computational Issues.” Computers & Chemical Engineering 17, 229– 244. CrossRef
 Sherali, H.D. and W.P. Adams. (1994). “A Hierarchy of Relaxations and ConvexHull Characterizations for MixedInteger ZeroOne Programming Problems.” Discrete Applied Mathematics 52, 83–106. CrossRef
 Wang, S. and M. Guignard. (2002). “Redefining Event Variables for Efficient Modeling of ContinuousTime Batch Processing.” Annals of Operations Research 116, 113–126. CrossRef
 Wilkinson, S.J., A. Cortier, N. Shah, and C.C. Pantelides. (1996). “Integrated Production and Distribution Scheduling on a EuropeanWide Basis.” Computers & Chemical Engineering 20, S1275–S1280. CrossRef
 Wilkinson, S.J., N. Shah, and C.C. Pantelides. (1995). “Aggregate Modelling of Multipurpose Plant Operation.” Computers & Chemical Engineering 19, S583–S588. CrossRef
 Yee, K.L. and N. Shah. (1998). “Improving the Efficiency of Discrete Time Scheduling Formulation.” Computers & Chemical Engineering 22, S403–S410. CrossRef
 Yi, G., K. Suh, B. Lee, and E.S. Lee. (2000). “Optimal Operation of Quality Controlled Product Storage.” Computers & Chemical Engineering 24, 475–480. CrossRef
 Zentner, M.G., A. Elkamel, J.F. Pekny, and G.V. Reklaitis. (1998). “A Language for Describing Process Scheduling Problems.” Computers & Chemical Engineering 22, 125–145. CrossRef
 Zentner, M.G., J.F. Pekny, G.V. Reklaitis, and J.N.D. Gupta. (1994). “Practical Considerations in Using ModelBased Optimization for the Scheduling and Planning of Batch/Semicontinuous Processes.” Journal of Process Control 4, 259–280. CrossRef
 Zhang, X. (1995). “Algorithms for Optimal Scheduling Using Nonlinear Models.” PhD thesis, University of London.
 Zhang, X. and R.W.H. Sargent. (1996). “The Optimal Operation of Mixed Production Facilities—A General Formulation and Some Solution Approaches for the Solution.” Computers & Chemical Engineering 20, 897–904. CrossRef
 Zhang, X. and R.W.H. Sargent. (1998). “The Optimal Operation of Mixed Production Facilities—Extensions and Improvements.” Computers & Chemical Engineering 22, 1287–1295. CrossRef
 Title
 Mixed Integer Linear Programming in Process Scheduling: Modeling, Algorithms, and Applications
 Journal

Annals of Operations Research
Volume 139, Issue 1 , pp 131162
 Cover Date
 20051001
 DOI
 10.1007/s104790053446x
 Print ISSN
 02545330
 Online ISSN
 15729338
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 chemical process scheduling
 mixedinteger linear programming (MILP)
 discretetime model
 continuoustime model
 branch and bound
 Industry Sectors
 Authors

 Christodoulos A. Floudas ^{(1)}
 Xiaoxia Lin ^{(1)}
 Author Affiliations

 1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 085445263, USA