JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Computational Study of Cutting Planes for a Lot-Sizing Problem in Branch-and-Cut Algorithm
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Computational Study of Cutting Planes for a Lot-Sizing Problem in Branch-and-Cut Algorithm
Chung, Kwanghun;
  PDF(new window)
 Abstract
In this paper, we evaluate the strength of three families of cutting planes for a lot-sizing problem. Lot-sizing problem is very basic MIP model for production planning and many strong valid inequalities have been developed for a variety of relaxations in the literature. To use three families of cutting planes in Branch-and-Cut framework, we develop separation algorithms for each cut and implement them in CPLEX. Then, we perform computational study to compare the effectiveness of three cuts for randomly generated instances of the lot-sizing problem.
 Keywords
Mixed-Integer Programming (MIP);Branch-and-Cut;Lot-Sizing Problem;Separation;
 Language
English
 Cited by
 References
1.
Balas, E. and M. Perregaard, "A precise correspondence between lift-and-project cuts, simple disjunctive cuts, and mixed-integer gomory cuts for 0-1 programming," Mathematical Programming, Vol.94(2003), pp.221-245. crossref(new window)

2.
Balas, E., S. Ceria, and G. Cornuejols, "A lift-and-project cutting plane algorithm for mixed 0-1 Programs," Mathematical Programming, Vol.58(1993), pp.295-324. crossref(new window)

3.
Balas, E., S. Ceria, G. Cornuejols, and R.N. Natraj, "Gomory cuts revisited," Operations Research Letters, Vol.19(1996), pp.1-9. crossref(new window)

4.
Barany, I., T.J. Van Roy, and L.A. Wolsey, "Uncapacitated lot-sizing:The convex hull of solutions," Mathematical Programming, Vol.22(1984), pp.32-43.

5.
Bixby, R. and E. Rothberg, "Progress in computational mixed integer programming-a look back from the other side of the tipping point," Annals of Operations Research, Vol. 149(2007), pp.37-41. crossref(new window)

6.
Danna, E., E. Rothberg, and C. Le Pape, "Exploring relaxation induced neighborhoods to improve MIP Solutions," Mathematical Programming, Vol.102(2005), pp.71-90. crossref(new window)

7.
Gomory, R.E., "An algorithm for the mixed integer program," Technical report RM-2597, The RAND Corporation, 1960.

8.
Gu, Z., G.L. Nemhauser, and M.W.P. Savelsbergh, "Lifted cover inequalities for 0-1 integer programs:Computation," INFORMS Journal on Computing, Vol.10(1998), pp.427-437. crossref(new window)

9.
Marchand, H. and L.A. Wolsey, "Aggregation and mixed integer rounding to solve MIPs," Operations Research, Vol.49(1998), pp.363-371.

10.
Marchand, H. and L.A. Wolsey, "The 0-1 knapsack problem with a single continuous variable," Mathematical Programming, Vol.85 (1999), pp.15-33. crossref(new window)