Modelling and solving environments for mathematical programming (MP): A status review and new directions

Journal of the Operational Research Society

Volumn 53, Issue 10 SPEC., 2002, Pages 1072-1092

  Dominguez Ballesteros, B ^a   Mitra, Gautam ^a   Lucas, C ^a   Koutsoukis, N S ^a  

^a BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

Algebraic modelling languages; Decision support; Linear programming; Optimisation; Planning

Indexed keywords

ALGEBRA; COMPUTER SIMULATION; COMPUTER SOFTWARE; CONSTRAINT THEORY; DATA STRUCTURES; DECISION SUPPORT SYSTEMS; GRAPHICAL USER INTERFACES; LINEAR PROGRAMMING; MATHEMATICAL MODELS; OPTIMIZATION; PROBLEM SOLVING; QUERY LANGUAGES; STOCHASTIC PROGRAMMING;

ALGEBRAIC MODELING LANGUAGES; ONLINE ANALYTICAL PROCESSING (OLAP) TOOLS;

INTEGER PROGRAMMING;

EID: 0036790044     PISSN: 01605682     EISSN: None     Source Type: Journal    
DOI: 10.1057/palgrave.jors.2601361     Document Type: Article

References (79)

1. Lucas C. and Mitra G. (1988). Computer-assisted mathematical programming (modelling) system (CAMPS). Comput J 31: 364-376.
2. Fourer R. (1983). Modelling languages versus matrix generators for linear programming. ACM Trans Math Software 9: 143-183.
3. IBM World Trade Corporation (1976). IBM Mathematical Programming System Extended/370 (MPSX/370) Program Reference Manual, 2nd edition. IBM Publication No. SH19-1095-1: New York, Paris.
4. Kuip C.A.C. (1993). Algebraic languages for mathematical programming. Eur J Opl Res 67: 25-51.
5. Birge J.R., Dempster M.A.H., Gassmann H.I., Gunn E.A., King A.J. and Wallace S.W. (1987). A standard input format for multi-period stochastic linear programs. Math Program Soc COAL Newslett 17: 1-19.
6. Aho A.H., Sethi R. and Ullman J.D. (1986). Compilers: Principles, Techniques, and Tools. Addison-Wesley Publishing Company: Reading, MA.
7. Maturana S.V. (1994). Issues in the design of modelling languages for Mathematical Programming. Eur J Opl Res 72: 243-261.
8. Moody S. (1994). Methods and tools for modelling linear and integer programming problems. PhD thesis, Department of Mathematics and Statistics, Brunel University.
9. Gilmore P.C. and Gomory R.E. (1961). A linear programming approach to the cutting stock problem. Part I. Opns Res 9: 849-859.
10. Mitra G. and Darby-Dowman K. (1985). Cru-Sched-A computer based bus crew scheduling system using integer programming. In: Rousseau J.M. (ed). Proceedings on the 3rd International Workshop on Transit Vehicle and Crew Scheduling. Computer Scheduling of Public Transport 2. Elsevier Science Publishers BV: Montreal, pp 223-232.
11. Darby-Dowman K., Fink R., Mitra G. and Smith J.W. (1995). An intelligent system for US Coast Guard cutter scheduling. Eur J Opl Res 87: 574-585.
12. Dantzig G.B. (1951). Maximisation of a linear function of variables subject to linear inequalities. In: T.C. Koopmans (ed). Activity Analysis of Production and Allocation. Wiley: New York.
13. Karmarkar N.K. (1984). A New Polynomial Time Algorithm for Linear Programming. Technical Report, AT & T Bell Laboratories, Murray Hill: New Jersey.
14. Mitra G., Andersen J. and Levkovitz R. (1992). The interior point method for LP on parallel computers. In: Kall P. (ed). Systems Modelling and Optimization. LNCIS180. Springer Verlag: Berlin, pp 241-250.
15. Levkovitz R. and Mitra G. (1993). Solution of large-scale linear programs: a review of hardware, software and algorithmic issues. In: Ciriani T. and Leachman R.C. (eds). Optimization in Industry, Mathematical Programming and Modelling Techniques in Practice. Wiley: Chichester, pp 139-171.
16. Maros I. and Mitra G. (1996). Simplex algorithms. In: Beasley J.E. (ed). Advances in Linear and Integer Programming. Oxford University Press: Oxford, pp 1-46.
17. ILOG CPLEX Division (2000). CPLEX 7.0. URL: http://www.ilog.com/products/cplex.
18. Ellison E.F.D., Hajian M., Jones H., Levkovitz R., Maros I., Mitra G. and Sayers D. (1999). FortMP Manual, Release 3. Numerical Algorithms Group (NAG) and Brunel University. URL: http://www.optirisk-systems.com.
19. Dash Associates (1999). XPRESS-MP Reference Manual, Release 11. Dash Associates: UK.
20. Shapiro J.F. (1998). Bottom-up vs. top-down approaches to supply chain management and modelling. Working Paper #4017, Sloan School of Management, Institute of Technology, Massachusetts.
21. Shapiro J.F. (1993). The decision database. Working Paper #3570-93-MSA, Sloan School of Management, Institute of Technology, Massachusetts.
22. Koutsoukis N.S., Mitra G. and Lucas C. (1999). Adapting on-line analytical processing (OLAP) for decision modelling: the interaction of information and decision technologies. Decis Support Sys 26: 1-30.
23. Mitra G. (1989). Tools for modelling support and construction of optimisation applications. In: Sharda R., Golden B.L., Wasil E., Balci O. and Stewart W. (eds). Impacts of Recent Computer Advances on Operations Research. Elsevier Science Publishing CO. Inc: North Holland, pp 484-496.
24. Mousavi H. (1998). Data and optimisation modelling for decision support. PhD thesis, Department of Mathematics and Statistics, Brunel University.
25. Koutsoukis N.S., Dominguez-Ballesteros B., Lucas C. and Mitra G. (2000). A prototype decision support system for strategic planning under uncertainty. In: Irani Z., Love P.E.D. and Li H. (guest eds). Special Issue in Supporting Supply Chain Management through an IT/IS Infrastructure (Part II). Int J Phys Distrib Log Mngt 30: 640-660.
26. Maximal Software Incorporation (1996). MPL Modelling System Release 4.0. USA.
27. Lindo Systems Inc (1998). LINGO Modelling System Version 4.0. USA.
28. Ellison E.F.D. and Mitra G. (1982). UIMP: user interface for mathematical programming. ACM Trans Math Software 8: 229-255.
29. Fourer R., Gay D.M. and Kernighan B.W. (1993). AMPL: A Modelling Language for Mathematical Programming. Duxbury Press: Belmont, CA.
30. Bisschop J.J. and Roelofs M. (1999). AIMMS: The Language Reference. Paragon Decision Technology BV: Haarlem, The Netherlands.
31. Brooke A., Kendrick D. and Meeraus A. (1993). GAMS: A User's Guide, version 2.25. Boyd and Fraser Publishers: Danvers, MA.
32. Hürlimann T. (2002). Modelling languages: a new paradigm of programming. Volume on Modelling Languages and Applications. Ann Opns Res (in press).
33. Geoffrion A.M. (1992). Indexing in modelling languages for mathematical programming. Mngt Sci 38: 325-344.
34. Hürlimann T. (1993). LPL: a modelling language. Modelling tools for decision support. University of Fribourg Series in Computer Science Volume 2, University of Fribourg: Fribourg, Switzerland.
35. Fourer R. and Gay D.M. (1995). Expressing special structures in an algebraic modelling language for mathematical programming. ORSA J Comp 7: 166-190.
36. Zenios S. (1990). Integrating network optimisation capabilities into a high level modelling language. ACM Trans Math Software 16: 113-142.
37. Bradley G.H. and Clemence D.R. (1987). A type calculus for executable modelling languages. IMA J Math Mngt 1: 227-291.
38. Bisschop J.J. (1988). A functional description of an integrated modelling software for mathematical programming. 13th international Mathematical Programming Symposium. Tokyo
39. Williams H.P. (1999). Model Building in Mathematical Programming, 4th edition. Wiley: Chichester.
40. Kallrath J. and Wilson J.M. (1997). Business Optimisation in Mathematical Programming. MacMillan Press Ltd: Hound-mills, Basingstoke.
41. Mitra G., Lucas C., Moody S. and Hadjiconstantinou E. (1994). Tools for reformulating logical forms into zero-one mixed integer programs. Eur J Opl Res 72: 262-276.
42. Fourer R. (1998). Extending a general-purpose algebraic modelling language to combinatorial optimisation: a logic programming approach. In: Woodruff D.L. (ed). Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search: Interfaces in Computer Science and Operations Research. Kluwer Academic Publishers: Dordrecht, The Netherlands, pp 31-74.
43. Van Hentenryck P. (1999). The OPL Optimisation Programming Language. The MIT Press: Cambridge, MA.
44. Dincbas M. et al. (1988). The constraint logic programming language CHIE. Proceedings of the International Conference on Fifth Generation Computer Systems (FGCS'88). Tokyo, Japan, pp 693-702.
45. Colmerauer A. (1990). An introduction to Prolog III. Commun ACM 33: 69-90.
46. Wallace M., Novello S. and Schimpf J. (1997). ECLiPSe: a platform for constraint logic programming. ICL Sys J 12: 159-200.
47. Dantzig G.B. (1955). Linear programming under uncertainty. Mngt Sci 1: 197-206.
48. Dantzig G.B. and Madansky A. (1961). On the solution of two-stage linear programs under uncertainty. Proceedings of The Fourth Berkeley Symposium on Mathematical Statistics and Probability Volume 1: University of California Press: Berkeley, CA, pp 165-176.
49. Gassmann H.I. and Ireland A.M. (1996). On the formulation of stochastic linear programs using algebraic modelling languages. Ann Opns Res 64: 83-112.
50. Charnes A. and Cooper W.W. (1959). Chance-constrained programming. Mngt Sci 6: 73-79.
51. Geoffrion A.M. (1987). An introduction to structured modelling. Mngt Science 33: 547-588.
52. Gilmore P.C. and Gomory R.E. (1963). A linear programming approach to the cutting stock problem. Part II. Opns Res 11: 863-888.
53. Woolsey R.E.D. (1972). A candle to St. Jude, or four real world applications of integer programming. Interfaces 2: 20-27.
54. Infanger G. (1993). Planning Under Uncertainty. Solving Large-Scale Stochastic Linear Programs. Boyd and Fraser: Massachusetts.
55. Dempster M.A.H. and Thompson R.T. (1999). EVPI-based importance sampling solution procedures for multistage stochastic linear programs on parallel MIMD architectures. Ann Opns Res 90: 161-84.
56. Messina E. and Mitra G. (1997). Modelling and analysis of multistage stochastic programming problems: a software environment. Eur J Opl Res 101: 343-359.
57. Smith B.M., Brailsford S.C., Hubbard P.M. and Williams H.P. (1997). The progressive party problem: integer linear programming and constraint programming compared. Constraints Int J 1: 119-138.
58. Darby-Dowman K., Little J., Mitra G. and Zaffalon M. (1997). Constraint logic programming and integer programming approaches and their collaboration in solving an assignment scheduling problem. Constraints Int J 1: 245-264.
59. Darby-Dowman K. and Little J. (1998). Properties of some combinatorial optimisation problems and their effect on the performance of integer programming and constraint logic programming. INFORMS J Comput 10: 276-286.
60. Dantzig G.B. and Wolfe P. (1960). Decomposition principle for linear programs. Opns Res 8: 101-111.
61. McCarl B.A. (1998). Repairing misbehaving mathematical programming models: a poor man's guide. INFORMS Meeting in Monterey. Monterey, CA.
62. Brearley A.L., Mitra G. and Williams H.P. (1975). Analysis of mathematical programming problems prior to applying the simplex algorithm. Math Programming 8: 54-83.
63. Greenberg H.J. (1993). Enhancements of ANALYZE: a computer-assisted analysis system for linear programming. ACM Trans Math Software 19: 233-257.
64. Chinneck J.W. (1997). Feasibility and viability. In: Gal T. and Greenberg H.J. (eds). Recent Advances in Sensitivity Analysis and Parametric Programming. Kluwer Academic Publishers: Dordrecht, The Netherlands.
65. Chinneck J.W. (2001). Analyzing mathematical programs using Mprobe. Special Issue on Modeling Languages. Ann Opns Res 104: 33-48.
66. Sharda R. and Steiger D.M. (1996). Inductive model analysis systems: enhancing model analysis in decision support systems. Inform Sys Res 7: 328-341.
67. Codd E.F., Codd S.B. and Salley C.T. (1993). Providing OLAP (OnLine Analytical Processing) to User-Analyst: an IT Mandate. Codd & Associates. URL: http://www.salleurl.edu/~augc/codd2.pdf
68. Mitra G., Lucas C., Moody S. and Kristjanson B. (1995). Sets and indices in linear programming modelling and their integration with relational data models. Comput Optim Appl 4: 263-283.
69. Merrit J. (2000). The best B-schools. Special MBA Issue (October 2). Business Week.
70. Gass S.H., Hirshfeld D.S. and Wasil E.A. (2000). Model world: the spreadsheeting of OR/MS. Interfaces 30: 72-81.
71. Atamtürk A., Johnson E.L., Linderoth J.T. and Savelsbergh M.W.P. (2000). A relational modelling system for linear and integer programming. Opns Res 48: 846-857.
72. Valente P., Mitra G., Poojari C.A. and Kyriakis T. (2002). Software tools for Stochastic Programming: A Stochastic Programming Integrated Environment (SPInE). Technical Report TR/10/01, Brunel University: UK. Also to appear in: Wallace S.W and Ziemba W.T (eds). The Applications of Stochastic Programming. MPS-SIAM Series in Optimization.
73. Norman D.A. and Draper S.W. (eds) (1986). User Centered System Design: New Perspectives in Human Computer Interaction. Lawrence Erlbaum Associates: Hillsdale, NJ.
74. Steiger D. and Sharda R. (1993). LP modelling languages for personal computers: a comparison. In: Mitra G. and Maros I. (eds). Applied Mathematical Programming and Modelling. Ann Opns Res 43: 195-216.
75. ILOG Inc. (1999). ILOG OPL Studio User's Manual. URL: http://www.ilog.com.
76. Cohen M.D., Kelly C.B. and Medaglia A.L. (2001). Decision support with web-enabled software. Interfaces 31: 109-129.
77. Fourer R. and Goux J.P. (2001). Optimization as an Internet resource. Interfaces 31: 130-150.
78. NEOS Server for Optimization (2001). URL: http://www-neos.mcs.anl.gov//
79. OSP (2001). URL: http://www.osp-craft.com.