Multiobjective decision processes under uncertainty: Applications, problem formulations, and solution strategies

Industrial and Engineering Chemistry Research

Volumn 44, Issue 8, 2005, Pages 2405-2415

  Cheng, Lifei ^a   Subrahmanian, Eswaran ^a   Westerberg, Arthur W ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ARCHITECTURE; ITERATIVE SOLUTION PROCESSES; MULTIOBJECTIVE DECISION PROCESSES; PARETO FRONTS BACKWARD;

APPROXIMATION THEORY; DECISION MAKING; INVENTORY CONTROL; ITERATIVE METHODS; MATHEMATICAL MODELS;

UNCERTAIN SYSTEMS;

DECISION SUPPORT SYSTEM;

EID: 18144375620     PISSN: 08885885     EISSN: None     Source Type: Journal    
DOI: 10.1021/ie049622+     Document Type: Article

References (89)

1. Kall, P.; Wallace, S. W. Stochastic Programming; John Wiley & Sons: New York, 1994.
2. Birge, J. R.; Louveaux, F. Introduction to Stochastic Programming; Springer: New York, 1997.
3. Birge, J. R. Current Trends in Stochastic Programming Computation and Applications; Technical Report; Dept of Industrial and Operations Engineering, University of Michigan: Ann Arbor, MI, 1995.
4. Cheng, L.; Subrahmanian, E.; Westerberg, A. W. Design and Planning under Uncertainty: Issues on Problem Formulations and Solutions. Comput. Chem. Eng. 2003, 27, 781-801.
5. Cheng, L.; Subrahmanian, E.; Westerberg, A. W. Multi-Objective Decisions on Capacity Planning and Inventory Control. Ind. Eng. Chem. Res. 2004, 43, 2192-2208.
6. Cheng, L.; Subrahmanian, E.; Westerberg, A. W. A Comparison of Optimal Control and Stochastic Programming from a Formulation and Computation Perspective. Comput. Chem. Eng. 2004, 29, 149-164.
7. Cheng, L.; Duran, M. A. Logistics for World Wide Crude Oil Transportation based on Discrete Event Simulation and Optimal Control. Foundations of Computer-Aided Process Operations 2003 Conference, January, 2003. Comput. Chem. Eng. 2004, 28, 897-911.
8. Cheng L.; Duran, M. A. Just-in-Time Refinery Operation Strategy: A Hybrid Make-to-Order and Make-to-Stock System; Technical Report; ExxonMobil Research and Engineering Company, in preparation for publication, 2004.
9. Scarf, H. The Optimality of (s, S) Policies in the Dynamic Inventory Problem. In Mathematics Methods in the Social Sciences; Stanford University Press: Palo Alto. CA. 1960: pp 196-202.
10. Porteus, E. L. On the Optimality of Generalized (s, S) Policies. Manage. Sci. 1971, 17 (7). 411-426.
11. DeCroix, G. A.; Arreola-Risa, A. Optimal Production and Inventory Policy for Multiple Products under Resource Constraints. Manage. Sci. 1998, 44 (7), 950-961.
12. Glasserman, P.; Tayur, S. Sensitivity Analysis for Basestock Levels in Multiechelon Production-inventory Systems. Manag. Sci. 1995, 41 (2), 263-281.
13. Kapuscinski, R.; Tayur, S. A Capacitated Production-Inventory Model with Periodic Demand. Oper. Res. 1998, 46 (6), 899-911.
14. Bashyam, S.; Fu, M. C.; Kaku, B. K. Application of Perturbation Analysis to Multiproduct Capacitated Production-Inventory Control. Int. J. Operations Quantitative Manage., submitted.
15. Braun, M. W.; Rivera, D. E.; Flores, M. E.; Carlyle, W. M.; Kempf, K. G. A Model Predictive Control Framework for Robust Management of Multi-Product, Multi-Echelon Demand Networks. Annu. Rev. Control 2003, 27 (2), 229-245.
16. Eppen, G. D.; Martin, R. K.; Schrage, L. A Scenario Approach to Capacity Planning. Oper. Res. 1989, 37 (4), 517-527.
17. Barahona, F.; Bermon, S.; Gunluk, O.; Hood, S. Robust Capacity Planning in Semiconductor Manufacturing; IBM report RC22196, 2001.
18. Ahmed, S.; Sahinidis, N. V. An Approximation Scheme for Stochastic Integer Programs Arising in Capacity Expansion. Oper. Res. 2003, 51, 461-471.
19. Ahmed, S.; King, A. J.; Parija, G. A Multi-Stage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty. J. Global Optimization 2002, 26, 3-24.
20. Manne, A. S. Capacity Expansion and Probabilistic Growth. Econometrica 1961, 29 (4), 632-649.
21. Bean, J. C.; Higle, J. L.; Smith, R. L. Capacity Expansion under Stochastic Demands. Oper. Res. 1992, 40 (2), S210-S216.
22. Davis, M. H. A.; Dempster, M. A. H.; Sethi, S. P.; Vermes, D. Optimal Capacity Expansion under Uncertainty. Adv. Appl. Prob. 1987, 19, 156-176.
23. Eberly, J. C.; Van Mieghem, J. A. Multi-factor Dynamic Investment under Uncertainty. J. Economic Theory 1997, 75, 345-387.
24. Harrison, J. M.; Van Mieghem, J. A. Multi-resource Investment Strategies: Operational Hedging under Demand Uncertainty. Eur. J. Oper. Res. 1999, 113, 17-29.
25. Angelus, A.; Porteus, E. L.; Wood, S. C. Optimal Sizing and Timing of Capacity Expansions with Implications for Modular Semiconductor Wafer Fabs; Research Paper No. 1479R; Graduate School of Business, Stanford University: Stanford, CA, 1999.
26. Rajagopalan, S.; Singh, M. R.; Morton, T. E. Capacity Expansion and Replacement in Growing Markets with Uncertain Technological Breakthroughs. Manage. Sci. 1998, 44 (1), 12-30.
27. Angelus, A.; Porteus, E. L. Simultaneous Production and Capacity Management under Stochastic Demand for Produced to Stock Goods; Research Paper No. 1419R; Graduate School of Business, Stanford University: Stanford, CA, 2000.
28. Rajagopalan, S.; Swaminathan, J. M. A Coordinated Production Planning Model with Capacity Expansion and Inventory Management. Manage. Sci. 2001, 47 (11), 1562-1580.
29. Bradley, J. R.; Glynn, P. W. Managing Capacity and Inventory Jointly in Manufacturing Systems. Manage. Sci. 2002, 48 (2), 273-288.
30. Schmidt, C. W.; Grossmann, I. E. Optimization Models for the Scheduling of Testing Tasks in New Product Development. Ind. Eng. Chem. Res. 1996, 35, 3498-3510.
31. Jain, V.; Grossmann, I. E. Resource-Constrained Scheduling of Tests in New Product Development. Ind. Eng. Chem. Res. 1999, 38, 3013-3026.
32. Maravelias, C. T.; Grossmann, I. E. Simultaneous Planning for New Product Development and Batch Manufacturing Facilities. Ind. Eng. Chem. Res. 2001, 40, 6147-6164.
33. Subramanian D.; Pekny, J. F.; Reklaitis, G. V. A Simulation-Optimization Framework for Addressing Combinatorial and Stochastic Aspects of an R&D Pipeline Management Problem. Comput. Chem. Eng. 2000, 24, 1005-1011.
34. Dantzig, G. B.; Infanger, G. Multi-stage stochastic linear programs for portfolio optimization. Ann. Oper. Res. 1993, 45, 59-76.
35. Kusy, M. I.; Ziemba. W. T. A bank asset and liability management model. Oper. Res. 1986, 34, 356-376.
36. Carino, D. R.; Kent, T.; Meyers, D. H.; Stacy, C.; Sylvanus, M.; Turner, A. L.; Watanabe, K.; Ziemba, W. T. The Russell-Yasuda Kasai Model: An Asset/Liability Model for a Japanese Insurance Company using Multi-stage Stochastic Programming. Interfaces 1994, 24 (1), 29-49.
37. Hoyland, K. Asset liability management for a life insurance company: A stochastic programming approach. Ph.D. Dissertation, Norwegian University of Science and Technology, Trondheim, Norway, 1998.
38. Mulvey, J. M.; Gould, G.; Morgan, C. An Asset and Liability Management System for Towers Perrin-Tillinghast. Interfaces 2000, 30 (1), 96-114.
39. Dort, C. Asset liability management for pension funds: A multistage chance constrained programming approach. Ph.D. Thesis, Erasmus University Rotterdam, Department of Mathematics, Rotterdam, The Netherlands.
40. Consigli, G.; Dempster, M. A. H. Dynamic Stochastic Programming for Asset-liability Management. Ann. Oper. Res. 1998, 81, 131-161.
41. Zenios, S.; Homer, M.; McKendall, R.; Vassiadou-Zeniou, C. Dynamic Models for Fixed-Income Portfolio Management Under Uncertainty. J. Econ. Dyn. Control 1998, 22 (10), 1517-1541.
42. Ziemba, W. T.; Mulvey, J. M. Worldwide Asset and Liability Modeling; Cambridge University Press: New York, 1998.
43. Ferguson, A.; Dantzig, G. B. The Allocation of Aircraft to Routes: An Example of Linear Programming under Uncertain Demands. Manage. Sci. 1956, 3, 45-73.
44. Kleywegt, A. J.; Nori, V. S.; Savelsbergh, M. W. P. The Stochastic Inventory Routing Problem with Direct Deliveries. Transport. Sci. 2002, 36, 94-118.
45. Laporte, G.; Louveaux, F. V.; Mercure, H. The Vehicle Routing Problem with Stochastic Travel Times. Transport. Sci. 1992, 26, 161-170.
46. Kenyon, A.; Morton, D. P. A Survey on Stochastic Location and Routing Problems. Central Eur. J. Oper. Res. 2002, 9, 277-328.
47. Powell, W. B. A Comparative Review of Alternative Algorithms for the Dynamic Vehicle Allocation Problem. Vehicle Routing: Methods and Studies; Golden, B., Assad, A., Eds.; North-Holland: Amsterdam, 1988; pp 249-291.
48. Takriti, S.; Birge, J.; Long, E. A Stochastic Model for the Unit Commitment Problem. IEEE Trans. Power Syst. 1996, 11 (3), 1497-1508.
49. Pereira, M. V. F.; Pinto, L. M. V. G. Multi-stage Stochastic Optimization Applied to Energy Planning. Math. Programming 1991, 52, 359-375.
50. Nowak, M. P.; Romisch, W. Stochastic Lagrangian Relaxtion Applied to Power Scheduling in a Hydro-Thermal System under Uncertainty. Ann. Oper. Res. 2001, 100, 251-272.
51. Gollmer, R.; Nowak, M. P.; Römisch, W.; Schultz, R. Unit Commitment in Power Generation: A Basic Model and Some Extensions. Ann. Oper. Res. 2000, 96, 167-189.
52. Gröwe-Kuska, N.; Römisch, W. Stochastic Unit Commitment in Hydro-thermal Power Production Planning. Preprint 02-3, Institut für Mathematik, Humboldt-Universität Berlin, 2002 and Applications of Stochastic Programming; Wallace, S. W., Ziemba, W. T., Eds.; MPS-SIAM Series in Optimization.
53. Dupacova, J.; Gaivoronski, A.; Kos, Z.; Szantai, T. Stochastic programming in water management: A case study and a comparison of solution techniques. Eur. J. Oper. Res. 1991, 52, 28-44.
54. Lasdon, L. S.; Watkins, D.; McKinney, D.; Nielsen, S.; Martin, Q. A Scenario-Based Stochastic Programming Model for Water Supplies from the Highland Lakes. Int. Trans. Oper. Res. 2000, 7 (3), 211-230.
55. Pistikopoulos, E. N.; Ierapetritou, M. G. A Novel Approach for Optimal Process Design under Uncertainty. Comput. Chem. Eng. 1995, 19, 1089-1110.
56. Schultz, R.; Stougie, L.; van der Vlerk. M. H. Two-stage Stochastic Integer Programming: A Survey. Statistica Neerlandica 1996, 50 (3), 404-416.
57. Caroe, C. C.; Schultz, R. A Two-stage Program for Unit Commitment under Uncertainty in a Hydro-Thermal Power System. Preprint SC 98-11, Konrad-Zuse- Zentrum für Informationstechnik, Berlin, 1998.
58. Romisch W.; Schultz. R. Multi-stage Stochastic Integer Programs: An Introduction. Online Optimization of Large Scale Systems: Grötschel, M., Krurnke, S. O., Rambau, J., Eds.; Springer-Verlag: Berlin. 2001: pp 579-598.
59. Klein Haneveld, W. K.; van der Vlerk, M. H. Stochastic Integer Programming: General Models and Algorithms. Ann. Oper. Res. 1999, 85, 39-57.
60. Lokketangen, A.; Woodruff, D. L. Progressive Hedging and Tabu Search Applied to Mixed Integer (0, 1) Multi-stage Stochastic Programming. J. Heuristics 1996, 2, 111-123.
61. Hoyland, K.; Wallace, S. W. Generating Scenario Trees for Multi-stage Decision Problems. Manage. Sci. 2001, 47 (2), 295-307.
62. Shapiro, A.; Homem-de-Mello, T. A Simulation-based Approach to Two-stage Stochastic Programming with Recourse. Math. Programming 1998, 81, 301-325.
63. Shapiro, A.; Homem-de-Mello, T. On the Rate of Convergence of Optimal Solutions of Monte Carlo Approximations of Stochastic Programs. SIAM J. Optimization 2000, 11, 70-86.
64. Dupacova, J. Stochastic Programming: Approximation via Scenarios; 3rd International Conference on Approximation, Puebla, 1995.
65. Bertsekas, D. P. Dynamic Programming and Optimal Control, Vols. I and II; Athena Scientific: Belmont, MA, 2000.
66. Puterman, M. L. Markov Decision Processes: Discrete Stochastic Dynamic Programming; John Wiley & Sons: New York, 1994.
67. Bellman, R. E. Dynamic Programming; Princeton University Press: Princeton, NJ, 1957.
68. Li, D.; Haimes, Y. Y. Multi-objective Dynamic Programming: The State of the Art. Control-Theory Adv. Technol. 1989, 5 (4), 471-483.
69. Li, D. Multiple Objectives and Non-Separability in Stochastic Dynamic Programming. Int. J. Syst. Sci. 1990, 21 (5), 933-950.
70. Bertsekas, D. P.; Tsitsiklis, J. N. Neuro-Dynamic Programming; Athena Scientific: Belmont, MA, 1996.
71. Tsitsiklis, J. N.; Van Roy, B. Feature-Based Method for Large Scale Dynamic Programming. Machine Learning 1996, 22, 59-94.
72. Tesauro, G. J. Practical Issues in Temporal-Difference Learning. Machine Learning 1992, 8, 257-277.
73. Gordon, G. J. Approximate Solutions to Markov Decision Processes. Ph.D. Thesis in School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 1999.
74. Marbach, P. Simulation-Based Methods for Markov Decision Processes. Ph.D. Thesis in Department of Electrical Engineering and Computer Science, MIT, Cambridge, MA, 1998.
75. Dupacova, J.; Consigli, G.; Wallace, S. W. Generating Scenarios for Multi-stage Stochastic Programs. Ann. Oper. Res. 2000, 100, 25-53.
76. Fu, M. C. Sample Path Derivatives for (s, S) Inventory Systems. Oper. Res. 1994, 42 (2), 351-364.
77. Ruszczyński, A. Decomposition Methods in Stochastic Programming. Math. Programming 1997, 79, 333-353.
78. Van Slyke, R.; Wets, R. J. B. L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J. Appl. Math. 1969, 17 (4), 638-663.
79. Birge, J. R. Decomposition and Partitioning Methods for Multi-stage Stochastic Linear Programs. Oper. Res. 1985, 33, 989-1007.
80. Gassman, H. I. MSLiP: A Computer Code for the Multi-stage Stochastic Linear Programming Problem. Math. Programming 1990, 47, 407-423.
81. Ruszczyński, A. Parallel Decomposition of Multi-stage Stochastic Programming Problems. Math. Programming 1993, 58 (2), 201-228.
82. Rosa, C. H.; Ruszczynski, A. On Augmented Lagrangian Decomposition Methods for Multi-stage Stochastic Programs. Ann Oper. Res. 1996, 64, 289-309.
83. Mulvey, J. M.; Ruszczynski, A. A New Scenario Decomposition Method for Large Scale Stochastic Optimization Oper Res. 1995, 43, 477-490.
84. Caroe, C. C.; Schultz, R. Dual Decomposition in Stochastic Integer Programming. Oper. Res. Lett. 1999, 24, 37-45.
85. Rockafellar R. T.: Wets, R. J.-B. Scenario and Policy Aggregation in Optimization under Uncertainty. Math. Oper. Res. 1991, 16, 119-147.
86. Markowitz. H. M. Portfolio Selection. 1st ed.; John Wiley and Sons: New York, 1959.
87. Sortino, F. A.; Van Der Meer, R. Downside Risk. J. Portfolio Manage. 1991, 17 (4), 27-32.
88. Chankong, V.; Haimes, Y. Y. Multi-objective Decision Making Theory and Methodology; North-Holland Series in System Science and Engineering; North-Holland: Amsterdam, 1983.
89. Deb, K.; Agrawal, S.; Pratap, A.; Meyarivan, T. A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II. In Proceedings of the Parallel Problem Solving from Nature VI; Springer: Berlin, 2000; pp 849-858.