An Algorithm for the Solution of Multiparametric Mixed Integer Linear Programming Problems

Annals of Operations Research

Volumn 99, Issue 1-4, 2000, Pages 123-139

  Dua, Vivek ^a   Pistikopoulos, Efstratios N ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Multiparametric mixed integer linear programming

Indexed keywords

EID: 0042188408     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1023/a:1019241000636     Document Type: Article

References (57)

1. J. Acevedo and E.N. Pistikopoulos, A parametric MINLP algorithm for process synthesis problems under uncertainty, Ind. Eng. Chem. Res. 35 (1996) 147-158.
2. J. Acevedo and E.N. Pistikopoulos, A multiparametrie programming approach for linear process engineering problems under uncertainty, Ind. Eng. Chem. Res. 36 (1997) 717.
3. J. Acevedo and E.N. Pistikopoulos, An algorithm for multiparametric mixed-integer linear programming problems, Operations Research Letters 24 (1999) 139-148.
4. M.G. Bailey and B.E. Gillet, Parametric integer programming analysis: a contraction approach, J. Oper. Res. 31 (1980) 257-262.
5. C. Blair, Integer and mixed-integer programming, in: Advances in Sensitivity Analysis and Parametric Programming, eds. T. Gal and H.J. Greenberg (Kluwer Academic, Dordrecht, The Netherlands, 1997).
6. A. Brooke, D. Kendrick and A. Meeraus, GAMS: A Users Guide (Scientific Press, California, 1988).
7. P.J. Carstensen, Complexity of some parametric integer and network programming problems, Mathematical Programming 26 (1983) 64-75.
8. V. Chankong, Y.Y. Haimes and D.M. Gemperline, A multiobjective dynamic programming method for capacity expansion, IEEE Transactions on Automatic Control 26 (1981) 1195-1207.
9. G.B. Dantzig, Linear Programming and Extensions (Princeton Univ. Press, NJ, 1963).
10. J. Dauer and Y.-H. Liu, Multi-criteria and goal programming, in: Advances in Sensitivity Analysis and Parametric Programming, eds. T. Gal and H.J. Greenberg (Kluwer Academic, Dordrecht, The Netherlands, 1997).
11. G.W. Evans, An overview of techniques for solving multiobjective mathematical programs, Management Science 30 (1984) 1268-1282.
12. R. Evren, Interactive compromise programming, J. Opl. Res. Soc. 38 (1987) 163-172.
13. A. V. Fiacco, Introduction to Sensitivity Analysis in Nonlinear Programming (Academic Press, New York, 1983).
14. T. Gal, Postoptimal Analyses, Parametric Programming, and Related Topics (de Gruyter, New York, 1995).
15. T. Gal and J. Nedoma, Multiparametric linear programming, Management Science 18 (1972) 406-422.
16. N. Ganesh and L.T. Biegler, A reduced Hessian strategy for sensitivity analysis of optimal flowsheets, AIChE J. 33 (1987) 282.
17. A.M. Geoffrion, J.S. Dyer and A. Feinberg, An interactive approach for multi-criterion optimization with an application to the operation of an academic department, Management Science 19 (1972) 357-367.
18. A.M. Geoffrion and G.W. Graves, Multicommodity distribution system design by Benders decomposition, Management Science 20 (1974) 822-844.
19. A.M. Geoffrion and R. Nauss, Parametric and postoptimality analysis in integer linear programming, Management Science 23 (1977) 453.
20. S. Holm and D. Klein, Discrete right hand side parametrization for linear integer programs, Europ. J. Oper. Res. 2 (1978) 50-53.
21. S. Holm and D. Klein, Three methods for post-optimal analysis in integer linear programming, Math. Prog. Study 21 (1984) 97.
22. B. Jansen, J.J. de Jong, C. Roos and T. Terlaky, Sensitivity analysis in linear programming: just be careful, Europ. J. Oper. Res. 101 (1997) 15-28.
23. L. Jenkins, Parametric mixed integer programming: an application to solid waste management, Management Science 28 (1982) 1270-1284.
24. L. Jenkins, Parametric methods in integer linear programming, Annals of Operations Research 27 (1990) 77.
25. P. Korhonen, J. Wallenius and S. Zionts, Solving the discrete multiple criteria problems using convex cones, Management Science 30 (1984) 1336-1345.
26. D. Li and Y.Y. Haimes, Hierarchical generating method for large-scale multiobjective systems, J. Optimization Theory and Applications 54 (1987) 303-333.
27. G.V. Loganathan and H.D. Sherali, A convergent interactive cutting-plane algorithm for multiobjective optimization, Operations Research 35 (1987) 365-377.
28. E. Loukakis and A.P. Muhlemann, Parameterisation algorithms for the integer linear programs in binary variables, Europ. J. Oper. Res. 17 (1984) 104-115.
29. L. Lovász, Certain duality principles in integer programming, Annals of Discr. Math. 1 (1977) 363-374.
30. T.J. Lowe, J.-F. Thisse, J.E. Ward and R.E. Wendell, On efficient solutions to multiple objective mathematical programs, Management Science 30 (1984) 1346-1349.
31. O. Marcotte and R.M. Soland, An interactive branch-and-bound algorithm for multiple criteria optimization, Management Science 32 (1986) 61-75.
32. R.E. Marsten and T.L. Morin, Parametric integer programming: the right-hand side case, Annals of Discr. Math. 1 (1977) 375-390.
33. K.G. Murty, Computational complexity of parametric linear programming, Mathematical Programming 19 (1980) 213-219.
34. K.G. Murty, Linear Programming (Wiley, New York, USA, 1983).
35. N. Nishida and Y Ohtake, A method for solution of the bicriterion mixed integer programming problems, Computers and Chemical Engineering 10 (1986) 119-122.
36. Y. Ohtake and N. Nishida, A branch and bound algorithm for 0-1 parametric mixed-integer programming, Oper. Res. Lett. 4 (1985) 41.
37. A. Palazoglu and Y. Arkun, A multiobjective approach to design chemical plants with robust dynamic operability characteristics, Computers and Chemical Engineering 10 (1986) 567-575.
38. K.P. Papalexandri and T.I. Dimkou, A parametric mixed-integer optimization algorithm for multiobjective engineering problems involving discrete decisions, Ind. Eng. Chem. Res. 37 (1998) 1866-1882.
39. S.A. Papoulias and I.E. Grossmann, A structural optimization approach in process synthesis-I: Utility systems, Computers and Chemical Engineering 7 (1983) 695.
40. A. Pertsinidis, On the parametric optimization of mathematical programs with binary variables and its application in the chemical engineering process synthesis., Ph.D. dissertation, Carnegie-Mellon University, Pittsburgh (1992).
41. A. Pertsinidis, I.E. Grossmann and G.J. McRae, Parametric optimization of MILP programs and a framework for the parametric optimization of MINLPs, Computers and Chemical Engineering 22 Suppl. (1998) S 205.
42. C.J. Piper and A.A. Zoltners, Some easy postoptimality analysis for zero-one programming, Management Science 22 (1976) 759-765.
43. G.M. Roodman, Postoptimality analysis in zero-one programming by implicit enumeration, Naval Res. Log. Quarterly 19 (1972) 435-447.
44. G.M. Roodman, Postoptimality analysis in integer programming by implicit enumeration: The mixed integer case, Naval Res. Log. Quarterly 21 (1974) 595.
45. P. Seferlis and A.N. Hrymak, Sensitivity analysis for chemical process optimization, Computers and Chemical Engineering 20 (1996) 1177.
46. J.F. Shapiro, Sensitivity analysis in integer programming, Annals of Discr. Math. 1 (1977) 467-477.
47. Y. Shimizu, Optimization of radioactive waste management system by application of multiobjective linear programming, J. Nuclear Sei. Tech. 18 (1981) 773-784.
48. A. Sophos, E. Rotstein and G. Stephanopoulos, Multiobjective analysis in modeling the petrochemical industry, Chemical Engineering Science 35 (1980) 2415-2426.
49. T. Tanino, Sensitivity analysis in multiobj ective optimization, J. Optimization Theory and Applications 56 (1988) 479-499.
50. T. Tanino and Y. Sawaragi, Duality theory in multiobj ective programming, J. Optimization Theory and Applications 27 (1979) 509-529.
51. G.K. Tayi, Sensitivity analysis of mixed integer programs: an application to environmental policy making, Europ. J. Oper. Res. 22 (1985) 224-233.
52. J. Teghem Jr., A survey of techniques for finding efficient solutions to multi-objective integer linear programming, Asia-Pacific J. Oper. Res. 3 (1986) 95-108.
53. A. Turgeon, An application of parametric mixed-integer linear programming to hydropower development, Water Resources Res. 23 (1987) 399-407.
54. A.C. Williams, Marginal values in mixed integer linear programming, Mathematical Programming 44 (1989) 67-75.
55. H.P. Williams, Duality in mathematics and linear and integer programming, J. Optimization Theory and Applications 90 (1996) 257-278.
56. H.P. Williams, The equivalence of two theorems of integer programming, Bull. London Math. Soc. 28 (1996) 311-316.
57. D. Wolbert, X. Joulia, B. Koehret and L.T. Biegler, Flowsheet optimization and optimal sensitivity analysis using analytical derivatives, Computers and Chemical Engineering 18 (1994) 1083.