Challenges in the application of mathematical programming in the enterprise-wide optimization of process industries

Theoretical Foundations of Chemical Engineering

Volumn 48, Issue 5, 2014, Pages 555-573

  Grossmann, Ignacio E ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

control; decomposition methods; enterprise wide optimization; mathematical programming; mixed integer linear and nonlinear optimization methods; modeling; planning; process industries; real time optimization; scheduling; stochastic programming

Indexed keywords

CONTROL ENGINEERING; ENVIRONMENTAL IMPACT; MATHEMATICAL PROGRAMMING; MODELS; NONLINEAR PROGRAMMING; PLANNING; SCHEDULING; STOCHASTIC PROGRAMMING; STOCHASTIC SYSTEMS;

DECOMPOSITION METHODS; ENTERPRISE-WIDE OPTIMIZATION; NONLINEAR OPTIMIZATION METHODS; PROCESS INDUSTRIES; REAL-TIME OPTIMIZATION;

INTEGER PROGRAMMING;

EID: 84910004281     PISSN: 00405795     EISSN: 16083431     Source Type: Journal    
DOI: 10.1134/S0040579514050182     Document Type: Article

References (150)

1. Grossmann, I.E., Enterprise-wide optimization: a new frontier in process systems engineering, AIChE J., 2005, vol. 51, pp. 1846–1857.
2. Varma, V.A., Reklaitis, G.V., Blau, G.E., and Pekny, J.F., Enterprise-wide modeling and optimization—an overview of emerging research challenges and opportunities, Comput. Chem. Eng., 2007, vol. 31, pp. 692–711.
3. Grossmann, I.E., Advances in mathematical programming models for enterprise-wide optimization, Comput. Chem. Eng., 2012, vol. 47, pp. 2–22.
4. Shapiro, J.F., Modeling of the Supply Chain, Duxbury, Mass.: Pacific Grove, 2001.
5. Shah, N.K., Li, Z., and Ierapetritou, M.G., Petroleum refining operations: key issues, advances and opportunities, Ind. Eng. Chem. Res., 2011, vol. 50, pp. 1161–1170.
6. Shah, N.K., Pharmaceutical supply chains: key issues and strategies for optimization, Comput. Chem. Eng., 2004, vol. 28, pp. 929–941.
7. Pistikopoulos, E., Georgiadis, M., and Papageorgiou, L., Supply-Chain Optimization, New York: Wiley, 2007.
8. Wassick, J.M., Enterprise-wide optimization in an integrated chemical complex, Comput. Chem. Eng., 2009, vol. 33, pp. 1950–1963.
9. Lainez, J.M., Guillen, G., Badell, M., Espuna, A., and Puigjaner, L., Enhancing corporate value in the optimal design of chemical supply chains, Ind. Eng. Chem. Res., 2007, vol. 46, pp. 7739–7757.
10. Pinedo, M., Scheduling: Theory, Algorithms, and Systems, Prentice Hall, 2001.
11. Mendez, C.A., Cerda, J., Grossmann, I.E., Harjunkoski, I., and Fahl, M., State-of-the-art review of optimization methods for short-term scheduling of batch processes, Comput. Chem. Eng., 2006, vol. 30, pp. 913–946.
12. Floudas, C.A. and Lin, X., Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review, Comput. Chem. Eng., 2004, vol. 28, pp. 2109–2129.
13. Pochet, Y. and Wolsey, L.A., Production Planning by Mixed Integer Programming, New York: Springer, 2006.
14. Glover, F., Improved linear integer programming formulations of nonlinear integer problems, Manage. Sci., 1975, vol. 22, pp. 455–460.
15. Wolsey, L.A., Integer Programming, New York: Wiley, 1998.
16. Johnson, E.L., Nemhauser, G.L., and Savelsbergh, M.W.P., Progress in linear programming based on the branchand-bound algorithms: an exposition, INFORMS J. Comput., 2000, vol. 12, pp. 243–263.
17. Bixby, R.E., Solving real-world linear programs: a decade and more of progress, Oper. Res., 2002, vol. 50, pp. 3–15.
18. Bixby, R.E. and Rothberg, E., Progress in computational mixed integer programming—a look back from the other side of the tipping point, Ann. Oper. Res., 2007, vol. 49, pp. 37–41.
19. Kondili, E., Pantelides, C.C., and Sargent, R., A general algorithm for short-term scheduling of batch operations. I. MILP Formulation, Comput. Chem. Eng., 1993, vol. 17, pp. 211–227.
20. Shah, N., Pantelides, C.C., and Sargent, W.H., A general algorithm for short-term scheduling of batch operations. II. Computational issues, Comput. Chem. Eng., 1993, vol. 17, pp. 229–244.
21. Achterberg, T., Koch, T., and Martin, A., MIPLIB 2003, Oper. Res. Lett., 2006, vol. 34, pp. 361–372.
22. Grossmann, I.E., Review of non-linear mixed integer and disjunctive programming techniques, Optim. Eng., 2002, vol. 3, pp. 227–252.
23. Leyffer, S., Integrating SQP and branch and bound for mixed integer nonlinear programming, Comput. Optim. Appl., 2001, vol. 18, pp. 295–309.
24. Stubbs, R. and Mehrotra, S., A branch-and-cut method for 0–1 mixed convex programming, Math. Program., 1999, vol. 86, pp. 515–533.
25. Geoffrion, A.M., Generalized Benders decomposition, J. Optim. Theory Appl., 1972, vol. 10, pp. 237–260.
26. Geoffrion, A.M., Lagrangean relaxation for integer programming, Math. Program. Study, 1974, vol. 2, pp. 82–114.
27. Duran, M.A. and Grossmann, I.E., An outer-approximation algorithm for a class of mixed-integer non-linear programs, Math. Program., 1986, vol. 36, pp. 307–339.
28. Fletcher, R. and Leyffer, S., Solving mixed integer nonlinear programs by outer approximation, Math. Program., 1994, vol. 66, pp. 327–349.
29. Quesada, I. and Grossmann, I.E., An LP/NLP based branch and bound algorithm for convex MINLP optimization problems, Comput. Chem. Eng., 1992, vol. 16, pp. 937–947.
30. Bonami, P., Biegler, L.T., Conn, A.R., Cornuejols, G., Grossmann, I.E., Laird, C.D., Lee, J., Lodi, A., Margot, F., Sawaya, N., and Wachter, A., An algorithmic framework for convex mixed integer nonlinear programs, Discrete Optim., 2008, vol. 5, pp. 186–204.
31. Westerlund, T. and Pettersson, F., An extended cutting plane method for solving convex MINLP problems, Comput. Chem. Eng., 1995, vol. 19, pp. 131–136.
32. Westerlund, T. and Pörn, R., Solving pseudo-convex mixed integer optimization problems by cutting plane techniques, Optim. Eng., 2002, vol. 3, pp. 253–280.
33. Viswanathan, J.V. and Grossmann, I.E., A combined penalty function and outer-approximation method for MINLP optimization, Comput. Chem. Eng., 1990, vol. 14, pp. 769–778.
34. Brooke, A., Kendrick, D., Meeraus, A., and Raman, R., GAMS: A User’s Guide, Washington, DC: GAMS Development Corp., 1998.
35. Schweiger, C.A. and Floudas, C.A., Process synthesis, design and control: a mixed integer optimal control framework, Proc. DYCOPS-5 on Dynamics and Control of Process Systems, Corfu, Greece, 1998, pp. 189–194.
36. Abhishek, K., Leyffer, S., and Linderoth, J.T., FilMINT: an outer approximation-based solver for convex mixed-integer nonlinear programs, INFORMS J. Comput., 2010, vol. 22, pp. 555–567.
37. Biegler, L.T., Nonlinear Programming: Concepts, Algorithms and Applications to Chemical Processes, Philadelphia, Pa.: SIAM, 2010.
38. Drud, A., Conopt—A GRG code for large sparse dynamic nonlinear optimization problems, Math. Program., 1985, vol. 31, pp. 153–191.
39. Gill, P.E., Murray, W., and Saunders, M.A., SNOPT: an SQP algorithm for large-scale constrained optimization, SIAM J. Optim., 2002, vol. 12, pp. 979–1006.
40. Byrd, R.H., Hribar, M.E., and Nocedal, J., An interior point algorithm for large-scale nonlinear programming, SIAM J. Optim., 1999, vol. 9, pp. 877–900.
41. Wächter, A. and Biegler, L.T., On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math. Program., 2006, vol. 106, pp. 25–57.
42. Tawarmalani, M. and Sahinidis, N., Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming, Amsterdam: Kluwer, 2002.
43. Sahinidis, N., BARON: A General Purpose Global Optimization Software Package, J. Global Optim., 1996, vol. 8, pp. 201–205.
44. LINDOGlobal Solver, Chicago, Ill.: Lindo Systems, 2010.
45. Misener, R. and Floudas, C., GloMIQO: Global mixed-integer quadratic optimizer, J. Global Optim., 2013, vol. 57, pp. 3–50.
46. Belotti, P., Lee, J., Liberti, L., Margot, F., and Wächter, A., Branching and bounds tightening techniques for non-convex MINLP, Optim. Methods Software, 2009, vol. 24, pp. 597–634.
47. Vigerese, S., Ballerstein, M., Berthold, T., Gamrath, G., Gleixner, A.M., Heinz, S., Humpola, J., Lehmann, T., Michaels, D., Pfetsch, M.E., Shinano, Y., Weltge, S., and Winkler, M., Solving MINLPs with SCIP, Berlin: Inat. Math., 2012. http://www.math.hu-berlin.de/~stefan/SCIP-ISMP12.pdf
48. Balas, E., Disjunctive programming, Ann. Discrete Math., 1979, vol. 5, pp. 3–51.
49. Adams, J., Balas, E., and Zawack, D., The shifting bottleneck procedure for job shop scheduling, Manage. Sci., 1988, vol. 34, pp. 391–401.
50. Beaumont, N., An algorithm for disjunctive programs, Eur. J. Oper. Res., 1991, vol. 48, pp. 362–371.
51. Raman, R. and Grossmann, I.E., Modeling and computational techniques for logic-based integer programming, Comput. Chem. Eng., 1994, vol. 18, pp. 563–578.
52. Grossmann, I.E. and Trespalacios, F., Systematic modeling of discrete-continuous optimization models through generalized disjunctive programming, AIChE J., 2013, vol. 59, pp. 3276–3295.
53. Lee, S. and Grossmann, I.E., New algorithms for nonlinear generalized disjunctive programming, Comput. Chem. Eng., 2000, vol. 24, pp. 2125–2141.
54. Sawaya, N. and Grossmann, I.E., A hierarchy of relaxations for linear generalized disjunctive programming, Eur. J. Oper. Res., 2012, vol. 216, pp. 70–82.
55. Ruiz, J.P. and Grossmann, I.E., A hierarchy of relaxations for nonlinear convex generalized disjunctive programming, Eur. J. Oper. Res., 2012, vol. 218, pp. 38–47.
56. Trespalacios, F. and Grossmann, I.E., Algorithmic approach for improved mixed-integer reformulations of convex generalized disjunctive programs, INFORMS J. Comput. (in press).
57. Castro, P.M. and Grossmann, I.E., Generalized disjunctive programming as a systematic modeling framework to derive scheduling formulations, Ind. Eng. Chem. Res., 2012, vol. 51, p. 5781–5792.
58. Vecchietti, A. and Grossmann, I.E., LOGMIP: A disjunctive 0–1 nonlinear optimizer for process systems models, Comput. Chem. Eng., 1999, vol. 23, p. 555–565.
59. Ferris, M.C., Dirkse, S.P., and Jagla, J.-H., and Meeraus, A., An extended mathematical programming framework, Comput. Chem. Eng., 2009, vol. 33, pp. 1973–1982.
60. Hooker, J.N., Logic-Based Methods for Optimization: Combining Optimization and Constraint Satisfaction, New York: Wiley, 2000.
61. Hooker, J.N., Logic, optimization and constraint programming, INFORMS J. Comput., 2002, vol. 14, pp. 295–347.
62. Constraint and Integer Programming: Toward a Unified Methodology, Milano, M., Ed., Amsterdam: Kluwer, 2003.
63. Jain, V. and Grossmann, I.E., Algorithms for hybrid MILP/CP models for a class of optimization problems, INFORMS J. Comput., 2001, vol. 13, pp. 258–276.
64. Maravelias, C.T. and Grossmann, I.E., A Hybrid MILP/CP decomposition approach for the continuous time scheduling of multipurpose batch plants, Comput. Chem. Eng., 2004, vol. 28, pp. 1921–1949.
65. Hooker, J.N., Planning and scheduling by logic-based Benders decomposition, Oper. Res., 2007, vol. 55, pp. 588–602.
66. Van Hentenryck, P., The OP—Optimization Programming Language, Cambridge, Mass.: MIT Press, 1999.
67. Birge, J.R. and Louveaux, F., Introduction to Stochastic Programming, New York: Springer, 1997.
68. Sahinidis, N.V., Optimization under uncertainty: state of the art and opportunities, Comput. Chem. Eng., 2004, vol. 28, pp. 971–983.
69. Ruszczynski, A., Decomposition methods in stochastic programming, Math. Program., Ser. B, 1997, vol. 79, pp. 333–353.
70. Jonsbraten, T.W., Wets, R.J.B., and Woodruff, D.L., A class of stochastic programs with decision dependent random elements, Ann. Oper. Res., 1998, vol. 82, pp. 83–106.
71. Ben-Tal, A., El Ghaoui, L., and Nemirovski, A., Robust Optimization, Princeton, N.J.: Princeton Univ. Press, 2009.
72. Soyster, A.L., Convex programming with set-inclusive constraints and applications to inexact linear programming, Oper. Res., 1973, vol. 21, pp. 1154–1157.
73. Bertsimas, D. and Sim, M., Robust discrete optimization and network flows, Math. Program., Ser. B, 2003, vol.98, pp. 49–71.
74. Li, Z., Ding, R., and Floudas, C.A., A comparative theoretical and computational study on robust counterpart optimization: I. Robust linear optimization and robust mixed integer linear optimization, Ind. Eng. Chem. Res., 2011, vol. 50, pp. 10567–10603.
75. Guignard, M., Lagrangean Relaxation, Top, 2003, pp. 151–228.
76. Terrazas-Moreno, S., Trotter, P., and Grossmann, I.E., Temporal and spatial Lagrangean decompositions in multi-site, multi-period production planning problems with sequence-dependent changeovers, Comput. Chem. Eng., 2011, vol. 35, pp. 2913–2928.
77. Held, M. and Karp, R.M., The traveling-salesman problem and minimum spanning trees: Part 2, Math. Program., 1971, vol. 1, pp. 6–25.
78. Held, M., Wolfe, P., and Crowder, H.P., Validation of subgradient optimization, Math. Program., 1974, vol. 6, pp. 62–86.
79. Fisher, M.L., An application oriented guide to Lagrangean relaxation, Interfaces, 1985, vol. 15, pp. 10–21.
80. Cheney, E.W. and Goldstein, A.A., Newton’s method for convex programming and Tchebycheff approximation, Numer. Math., 1959, vol. 1, pp. 253–268.
81. Kelley, J.E., The cutting-plane method for solving convex programs, J. Soc. Ind. Appl. Math., 1960, vol. 8, pp. 703–712.
82. Benders, J.F., Partitioning procedures for solving mixed variables programming problems, Numer. Math., 1962, vol. 4, pp. 238–252.
83. Van Slyke, R.M. and Wets, R., L-shaped linear programs with applications to optimal control and stochastic programming, SIAM J. Appl. Math., 1969, vol. 17, pp. 638–663.
84. Straub, D.A. and Grossmann, I.E., Design optimization of stochastic flexibility, Comput. Chem. Eng., 1993, vol. 17, pp. 339–347.
85. Pistikopoulos, E.N., Uncertainty in process design and operations, Proc. Eur. Symp. Comput. Aided Process Eng., 1995, pp. S553–S563.
86. Ierapetritou, M.G. and Pistikopoulos, E.N., A novel optimization approach of stochastic planning models, Ind. Eng. Chem. Res., 1994, vol. 33, pp. 1930–1942.
87. Ierapetritou, M.G., Acevedo, J., and Pistikopoulos, E.N., An optimization approach for process engineering problems under uncertainty, Comput. Chem. Eng., 1996, vol. 20, pp. 703–709.
88. Birge, J.R. and Louveaux, F.V.A., Multicut algorithm for two-stage stochastic linear programs, Eur. J. Oper. Res., 1988, vol. 34, pp. 384–392.
89. Magnanti, T.L. and Wong, R.T., Accelerating Benders decomposition: algorithmic enhancement and model selection criteria, Oper. Res., 1981, vol. 29, pp. 464–484.
90. Saharidis, G.K.D., Minoux, M., and Ierapetritou, M.G., Accelerating Benders method using covering cut bundle generation, Int. Trans. Oper. Res., 2010, vol. 17, pp. 221–237.
91. Iyer, R.R. and Grossmann, I.E., A bilevel decomposition algorithm for long-range planning of process networks, Ind. Eng. Chem. Res., 1998, vol. 37, pp. 474–481.
92. Bok, J.-K., Grossmann, I.E., and Park, S., Supply chain optimization in continuous flexible process networks, Ind. Eng. Chem. Res., 2000, vol. 39, pp. 1279–1290.
93. You, F., Grossmann, I.E., and Wassick, J.M., Multisite capacity, production and distribution planning with reactor modifications: MILP model, bilevel decomposition algorithm versus Lagrangean decomposition scheme, Ind. Eng. Chem. Res., 2011, vol. 50, pp. 4831–4849.
94. Erdirik-Dogan, M.E. and Grossmann, I.E., A decomposition method for the simultaneous planning and scheduling of single-stage continuous multiproduct plants, Ind. Eng. Chem. Res., 2006, vol. 45, pp. 299315.
95. Bassett, M.H., Pekny, J.F., and Reklaitis, G.V., Decomposition techniques for the solution of largescale scheduling problems, AIChE J., 1996, vol. 42, pp. 3373–3387.
96. Dimitriadis, A.D., Shah, N., and Pantelides, C.C., RTN-based rolling horizon algorithms for medium term scheduling of multipurpose plants, Comput. Chem. Eng., 1997, vol. 21, pp. S1061–S1066.
97. Ehrgott, M., Multicriteria Optimization, Berlin: Springer, 2000.
98. Deb, K., Multi-Objective Optimization Using Evolutionary Algorithms, New York: Wiley, 2008.
99. Pistikopoulos, E., Georgiadis, M., and Dua, V., MultiParametric Programming: Theory, Algorithms, and Applications,, New York: Wiley, 2007, Vol. 1.
100. Pantelides, C.C., Unified Frameworks for Optimal Process Planning and Scheduling, in Foundations of Computer-Aided Process Operations, New York: CACHE, 1994, pp. 253–274.
101. Ierapetritou, M.G. and Floudas, C.A., Effective continuous-time formulation for short-term scheduling. 1. Multipurpose batch processes, Ind. Eng. Chem. Res., 1998, vol. 37, pp. 4341–4359.
102. Sundaramoorthy, A. and Maravelias, C.,T., A general framework for process scheduling, AIChE J., 2011, vol. 57, pp. 695–710.
103. You, F. and Grossmann, I.E., Mixed-integer nonlinear programming models and algorithms for large-scale supply chain design with stochastic inventory management, Ind. Eng. Chem. Res., 2008, vol. 47, pp. 7802–7817.
104. Mendez, C.A., Grossmann, I.E., Harjunkoski, I., and Kabore, P., A simultaneous optimization approach for off-line blending and scheduling of oil-refinery operations, Comput. Chem. Eng., 2006, vol. 30, pp. 614–634.
105. Mouret, S., Grossmann, I.E., and Pestiaux, P., A novel priority-slot based continuous-time formulation for crude-oil scheduling problems, Ind. Eng. Chem. Res., 2009, vol. 48, pp. 8515–8528.
106. Misener, R., Thompson, J.P., and Floudas, C.A., APOGEE: global optimization of standard, generalized, and extended pooling problems via linear and logarithmic partitioning schemes, Comput. Chem. Eng., 2011, vol. 35, pp. 876–892.
107. Pinto, J. and Grossmann, I.E., Optimal cyclic scheduling of multistage multiproduct continuous plants, Comput. Chem. Eng., 1994, vol. 18, p. 797–816.
108. Bhatia, T. and Biegler, L.T., Dynamic optimization in the design and scheduling of multiproduct batch plants, Ind. Eng. Chem. Res., 1996, vol. 35, pp. 2234–2246.
109. Nystrom, R.H., Franke, R., Harjunkoski, I., and Kroll, A., Production campaign planning including grade transition sequencing and dynamic optimization, Comput. Chem. Eng., 2005, vol. 29, pp. 2163–2179.
110. Flores-Tlacuahuac, A. and Grossmann, I.E., Simultaneous cyclic scheduling and control of a multiproduct CSTR, Ind. Eng. Chem. Res., 2006, vol. 45, pp. 6698–6712.
111. Graves, S, Using Lagrangean techniques to solve hierarchical production planning problems, Manage. Sci., 1982, 28, pp. 260–275.
112. Gupta, A. and Maranas, C.D., A hierarchical Lagrangean relaxation procedure for solving midterm planning problems, Ind. Eng. Chem. Res., 1999, vol. 38, pp. 1937–1947.
113. Jackson, J.R. and Grossmann, I.E., Temporal decomposition scheme for nonlinear-multisite production planning and distribution models, Ind. Eng. Chem. Res., 2003, vol. 42, pp. 3045–3055.
114. Neiro, S.M.S. and Pinto, J.M., Lagrangean decomposition applied to multiperiod planning of petroleum refineries under uncertainty, Latin Amer. Appl. Res., 2006, vol. 36, pp. 213–220.
115. Li, Z. and Ierapetritou, M., Production planning and scheduling integration through augmented Lagrangean optimization, Comput. Chem. Eng., 2010, vol. 34, pp. 996–1006.
116. Liu, S., Pinto, J.M., and Papageorgiou, L.G., TSP-based MILP model for medium term planning of single-stage continuous multiproduct plants, Ind. Eng. Chem. Res., 2008, vol. 47, pp. 7733–7743.
117. Verderame, P.M. and Floudas, C.A., Integrated operational planning and medium-term scheduling for large-scale industrial batch plant, Ind. Eng. Chem. Res., 2008, vol. 47, pp. 4845–4860.
118. Maravelias, C.T. and Sung, C., Integration of planning and scheduling: overview, challenges, and opportunities, Comput. Chem. Eng., 2009, vol. 33, pp. 1919–1930.
119. Lima, R., Grossmann, I.E., and Jiao, Y., Long-term scheduling of a single-stage multi-product continuous process to manufacture high performance glass, Comput. Chem. Eng., 2011, vol. 35, pp. 554–574.
120. Terrazas-Moreno, S. and Grossmann, I.E., A multiscale decomposition method for the optimal planning and scheduling of multisite continuous multiproduct plants, Chem. Eng. Sci., 2011, vol. 66, pp. 4307–4518.
121. Li, Z. and Ierapetritou, M., Robust optimization for process scheduling under uncertainty, Ind. Eng. Chem. Res., 2008, vol. 47, pp. 4148–4157.
122. Liu, M.L. and Sahinidis, N.V., Optimization in process planning under uncertainty, Ind. Eng. Chem. Res., 1996, vol. 35, pp. 4154–4165.
123. You, F., Wassick, J.M., and Grossmann, I.E., Risk management for a global supply chain planning under uncertainty: models and algorithms, AIChE J., 2009, vol. 55, pp. 931–971.
124. Goel, V., Grossmann, I.E., El-Bakry, A.S., and Mulkay, E.L., A novel branch and bound algorithm for optimal development of gas fields under uncertainty in reserves, Comput. Chem. Eng., 2006, vol. 30, pp. 1076–1092.
125. Colvin, M. and Maravelias, C.T., A stochastic programming approach for clinical trial planning in new drug development, Comput. Chem. Eng., 2008, vol. 32, pp. 2626–2642.
126. Linderoth, J. and Wright, S.J., Implementing a decomposition algorithm for stochastic programming on a computational grid, Comput. Optim. Appl., 2003, vol. 24, pp. 207–250.
127. Wassick, J.M. and Ferrio, J., Extending the resource task network for industrial applications, Comput. Chem. Eng., 2011, vol. 35, pp. 2124–2140.
128. Pekny, J.F., Miller, D.L., and McRae, G.J., An exact parallel algorithm for scheduling when production costs depend on consecutive system states, Comput. Chem. Eng., 1990, vol. 14, pp. 1009–1023.
129. Kelly, J.D., Chronological decomposition heuristic for scheduling: divide and conquer, AIChE J., 2002, vol. 48, pp. 2995–2999.
130. Castro, P.M., Harjunkoski, I., and Grossmann, I.E., Greedy algorithm for scheduling batch plants with sequence-dependent changeovers, AIChE J., 2011, vol. 57, pp. 373–387.
131. Goux, J.-P. and Leyffer, S., Solving large MINLPs on computational grids, Optim. Eng., 2003, vol. 3, pp. 327–354.
132. Ferris, M.C. and Munson, T.S., Modeling languages and Condor: metacomputing for optimization, Mathem. Program., 2000, vol. 88, pp. 487–506.
133. KPMG: The Outlook for the US Chemical Industry. http://www.kpmg.de/docs/20101028US_chemical_industry_outlook_2010.pdf
134. Langevin, A., Mbaraga, P., and Campbell, J.F., Continuous approximation models for freight distribution: an overview, Transport. Res., Part B: Methodol., 1996, vol. 30, pp. 163–188.
135. Pinto-Varela, T., Barbosa-Póvoa, A.P.F.D., and Novais, A.Q., Bi-objective optimization approach to the design and planning of supply chains: economic versus environmental performances, Comput. Chem. Eng., 2011, vol. 35, pp. 1454–1468.
136. Alattas, A., Grossmann, I.E., and Palou-Rivera, I., Integration of nonlinear CDU models in refinery planning optimization, Ind. Eng Chem. Res., 2011, vol. 50, pp. 6860–6870.
137. Geddes, R.L., A general index of fractional distillation power for hydrocarbon mixtures, AIChE J., 1958, vol. 4, pp. 389–392.
138. Erdirik-Dogan, M. and Grossmann, I.E., Simultaneous planning and scheduling of single-stage multi-product continuous plants with parallel lines, Comput. Chem. Eng., 2008, vol. 32, p. 2664–2683.
139. Mitra, S., Grossmann, I.E., Pinto, J.M., and Arora, N., Optimal production planning under time-sensitive electricity prices for continuous power-intensive processes, Comput. Chem. Eng., 2012, vol. 38, pp. 171–184.
140. Gupta, V. and Grossmann, I.E., Offshore Oilfield Development Planning under Uncertainty and Fiscal Considerations, in Optimization and Analytics in the Oil and Gas Industry, Furman, K., Song, H., and El-Bakry, A., Eds., Berlin: Springer, 2011.
141. Kelly, J.D., Logistics: the missing link in blend scheduling optimization, Hydrocarbon Process., 2006, pp. 45–51.
142. Perea, E., Ydstie, E., and Grossmann, I.E., A model predictive control strategy for supply chain optimization, Comput. Chem. Eng., 2003, vol. 27, pp. 1201–1218.
143. Harjunkoski, I., Nystrom, R., and Horch, A., Integaration of scheduling and control: theory or practice, Comput. Chem. Eng., 2009, vol. 33, pp. 1909–1918.
144. Hugo, A. and Pistikopoulos, E., Environmentally conscious long-range planning and design of supply chain networks, J. Cleaner Prod., 2005, vol. 13, pp. 1428–1448.
145. Bojarski, A.D., Lainez, J.M., Espuna, A., and Puigjaner, L., Incorporating environmental impacts and regulations in holistic supply chains modeling: an LCA approach, Comput. Chem. Eng., 2009, vol. 33, pp. 1747–1759.
146. Grossmann, I.E. and Guillen-Gosalbez, G., Scope for the application of mathematical programming techniques in the synthesis and planning of sustainable processes, Comput. Chem. Eng., 2010, vol. 34, pp. 1365–1376.
147. Elia, J.A., Baliban, R.C., Xiao, X., and Floudas, C.A., Optimal energy supply network determination and life cycle analysis for hybrid coal, biomass and natural gas to liquid (CBGTL) plants using carbon-based hydrogen production, Comput. Chem. Eng., 2011, vol. 35, pp. 1399–1430.
148. You, F., Tao, L., Graziano, D.J., and Snyder, S.W., Optimal design of sustainable cellulosic biofuel supply chains: multiobjective optimization coupled with life cycle assessment and input-output analysis, AIChE J., 2012, vol. 58, pp. 1157–1180.
149. Castro, P.M., Harjunkoski, I., and Grossmann, I.E., New continuous-time scheduling formulation for continuous plants under variable electricity cost, Ind. Eng. Chem. Res., 2009, vol. 48, pp. 6701–6714.
150. Quantitative Models for Supply Chain Management, Ed. by Tayur, S., Ganeshan, R., and Magazine, M., Massachusetts: Kluwer Academic, 1999.