Lifting, superadditivity, mixed integer rounding and single node flow sets revisited

4OR

Volumn 1, Issue 3, 2003, Pages 173-207

  Louveaux, Quentin ^a   Wolsey, Laurence A ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Lifting; mixed integer rounding; single node flow sets

Indexed keywords

EID: 84891649175     PISSN: 16194500     EISSN: 16142411     Source Type: Journal    
DOI: 10.1007/s10288-003-0016-4     Document Type: Article

References (34)

1. Atamturk A (2001) Flow pack facets of the single node fixed-charge flow polytope. Operations Research Letters 29: 107-114.
2. AtamtürkA (2002) On the facets of single-constraint mixed-integer sets. Research Report Revised June, Department of Industrial and Operations Research, University of California at Berkeley.
3. Atamtürk A, Munoz (2002) A study of the lot-sizing polytope. Research Report BCOL. 02. 01, Department of Industrial and Operations Research, University of California at Berkeley.
4. AtamtürkA, Nemhauser GL, SavelsberghMWP(2001)Valid inequalities for problems with additive variable upper bounds. Mathematical Programming 91: 145-162.
5. Balas E (1975)Atime indexed formulation of non-preemptive single machine scheduling problems. Mathematical Programming 8: 146-164.
6. Ceria S, Cordier C, Marchand H, Wolsey LA (1998) Cutting planes for integer programs with general integer variables. Mathematical Programming 81: 201-214.
7. Crowder H, Johnson EL, Padberg MW (1963) Solving large scale zero-one linear programming problems. Operations Research 31: 803-834.
8. Goemans MX (1989) Valid inequalities and separation for mixed 0-1 constraints with variable upper bounds. Operations Research Letters 8: 315-322.
9. Gomory RE (1960) An algorithm for the mixed integer problem. Research Report RM-2597. The Rand Corporation.
10. Gu Z, Nemhauser GL, Savelsbergh MWP (1998) Lifted flow cover inequalities for 0-1 integer programs: Computation. INFORMS Journal of Computing 10: 427-437.
11. Gu Z, Nemhauser GL, Savelsbergh MWP (1999) Lifted flow cover inequalities for mixed 0-1 integer programs. Mathematical Programming 85: 439-468.
12. Gu Z, Nemhauser GL, Savelsbergh MWP (2000) Sequence independent lifting in mixed integer programing. Journal of Combinatorial Optimization 4: 109-129.
13. Hammer PL, Johnson EL, Peled UN (1975) Facets of regular 0-1 polytopes. Mathematical Programming 8: 179-206.
14. JeroslowRG(1979) An introduction to the theory of cutting planes. Annals of Discrete Mathematics 5: 71-95.
15. Johnson EL (1973) Cyclic groups, cutting planes and shortest paths. In: Hu TC, Robinson S (eds) Mathematical Programming. Academic Press, pp 185-211.
16. Marchand H, Wolsey LA (1999) The 0-1 knapsack problem with a single continous variable. Mathematical Programming 85: 15-33.
17. Marchand H, Wolsey LA(2001) Aggregation and mixed integer rounding to solve mips. Operations Research 49: 363-371.
18. Miller A, Nemhauser GL, Savelsbergh MWP (2003a) A multi-item production planning model with setup times: algorithms, reformulations, and polyhedral characterizations for a special case. Mathematical Programming B 95: 71-90.
19. Miller A, Nemhauser GL, Savelsbergh MWP (2003b) On the polyhedral structure of a multi-item production planning model with setup times. Mathematical Programming B 94: 375-406.
20. Nemhauser GL, Wolsey LA (1988) Integer and Combinatorial Optimization. Wiley, NewYork.
21. Nemhauser GL, Wolsey LA (1990) A recursive procedure for generating all cuts for 0-1 mixed integer programs. Mathematical Programming 46: 379-390.
22. OostenM(1996)Apolyhedral approach to grouping problems. PhD thesis, University of Maastricht.
23. Padberg M (1973) On the facial structure of set packing polyhedra. Mathematical Programming 5: 199-215.
24. Padberg MW, Van Roy TJ, Wolsey LA (1985) Valid inequalities for fixed charge problems. Mathematical Programming 33: 842-861.
25. Richard J-PP, de Farias IR, Nemhauser GL (2002a) Lifted inequalities for 0-1 mixed integer programming: Basic theory and algorithms. Research Report 2002, School of Industrial and Systems Engineering, Georgia Institute of Technology.
26. Richard J-PP, de Farias IR, Nemhauser GL (2002b) Lifted inequalities for 0-1 mixed integer programming: Superlinear lifting. Research Report 2002, School of Industrial and Systems Engineering, Georgia Institute of Technology.
27. Van Roy TJ, Wolsey LA (1986) Valid inequalities for mixed 0-1 programs. Discrete Applied Mathematics 14: 199-213.
28. Van Roy TJ, Wolsey LA (1987) Solving mixed 0-1 programs by automatic reformulation. Operations Research 35: 45-57.
29. Stallaert JIA (1997) The complementary class of generalized flow cover inequalities. Discrete Applied Mathematics 77: 73-80.
30. Wolsey LA (1975) Faces for linear inequalities in 0-1 variables. Mathematical Programming 8: 165-178.
31. Wolsey LA (1976) Facets and strong valid inequalities for integer programs. Operations Research 24: 367-372.
32. Wolsey LA (1977) Valid inequalities and superadditivity for 0-1 integer programs. Mathematics of Operations Research 2: 66-77.
33. Wolsey LA (1989) Submodularity and valid inequalities in capacitated fixed charge networks. Operations Research Letters 8: 119-124.
34. Wolsey LA (1990) Valid inequalities for mixed integer programs with generalised upper bound constraints. Discrete Applied Mathematics 25: 251-261.