Some classes of valid inequalities and convex hull characterizations for dynamic fixed-charge problems under nested constraints

Annals of Operations Research

Volumn 140, Issue 1, 2005, Pages 215-233

  Glover, Fred ^a   Sherali, Hanif D ^b  

^a UNIVERSITY OF COLORADO   (United States)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Capacitated lot sizing; Convex hull; Dynamic fixed charge problems; Reformulation linearization technique; Valid inequalities

Indexed keywords

EID: 28244433812     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1007/s10479-005-3972-6     Document Type: Article

References (39)

1. Atamturk, A. and J.C. Munoz. (2003). "A Study of the Lot-Sizing Polytope." Mathematical Programming (to appear).
2. Atamturk, A. and S. Kucukyavuz. (2003). "Lot-Sizing with Inventory Bounds and Fixed Costs: Polyhedral Study and Computation." Department of Industrial Engineering and Operations Research, University of California-Berkeley, CA 94720-1777.
3. Baharona, F. (1996). "Network Design Using Cut Inequalities." SIAM Journal of Optimization, 823-837.
4. Balas, E. (1979). "Disjunctive Programming "Annals of Discrete Mathematics 5, 3-51.
5. Balas, E. (1998). "Disjunctive Programming: Properties of the Convex Hull of Feasible Points." Discrete Applied Mathematics 80(1/2), 3-44.
6. Balas, E. and M.W. Padberg. (1976). "Set Partitioning: A Survey." SIAM Review 18, 710-760.
7. Barany, I., T.J. van Roy, and L.A. Wolsey. (1984a). "Uncapacitated Lot Sizing: The Convex Hull of Solutions." Mathematical Programming Study 22, 32-43.
8. Barany, I., T.J. van Roy, and L.A. Wolsey. (1984b). "Strong Formulations for Multi-Item Capacitated Lot-Sizing." Management Science 30, 1255-1261.
9. Cabot, A.V. and S.S. Erenguc. (1984). "Some Branch-and-Bound Procedures for Fixed-Cost Transportation Problems." Naval Research Logistics Quarterly 31, 145-154.
10. Cornuejols, G., L. Fisher, and G.L. Nemhauser. (1977). "Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms." Management Science 23, 789-810.
11. Crainic, T.G., A. Frangioni, and B. Gendron. (2001). "Bundle-based Relaxation Methods for Multicommodity Capacitated Fixed Charge Network Design." Discrete Applied Mathematics 112, 73-99.
12. Cruz, F.R.B., J. M. Smith, and G.R. Mateus. (1998). "Solving to Optimality the Uncapacitated Fixed-Charge Network Flow Problem." Computers and Operations Research 25(1), 67-81.
13. Glover, F. (1994). "Optimization by Ghost Image Processes in Neural Networks." Computers and Operations Research 21(8), 801-822.
14. Glover, F., D. Klingman, and N. Phillips. (1992). Network Models in Optimization and their Applications in Practice, John Wiley & Sons, New York, NY.
15. Hochbaum, D.S. and A. Segev. (1989). "Analysis of a Flow Problem with Fixed Charges." Networks 19, 291-312.
16. Kim, D. and P.M. Pardalos. (1999). A Solution Approach to the Fixed-Charge Network Flow Problem Using a Dynamic Slope Scaling Procedure." Operations Research Letters 24, 195-203.
17. Loparic, M., H. Marchand, and L.A. Wolsey. (2003). "Dynamic Knapsack Sets and Capacitated Lot-Sizing." Mathematical Programming Series B 95, 53-69.
18. Luna, H.P.L., N. Ziviani, and R.M.B. Cabral. (1987). "The Telephonic Switching Centre Network Problem: Formalization and Computational Experience." Discrete Applied Mathematics 18, 199-210.
19. Magnanti, T.L., P. Mireault, and R.T. Wong. (1986). "Tailoring Benders Decomposition for Uncapacitated Network Design." Mathematical Programming Study 26, 112-154.
20. Marchand, H. (1998). "A Polyhedral Study of the Mixed Knapsack Set and its Use to Solve Mixed Integer Programs." Ph.D. Thesis, CORE, Belgium.
21. Mirzan, A. (1985). "Lagrangian Relaxation for the Star-Star Concentrator Location Problem: Approximation Algorithm and Bounds." Networks 15, 1-20.
22. Nemhauser, G.L. and L.A. Wolsey. (1988). Integer and Combinatorial Optimization. John Wiley & Sons, Inc., New York, NY.
23. Nozick, L. (2001). "The Fixed Charge Facility Location Problem with Coverage Restrictions." Transportation Research E 37, 281-296.
24. Nozick, L. and M. Turnquist. (1998a). "Two-Echelon Inventory Allocation and Distribution Center Location Analysis." In Proceedings of Tristan III (Transportation Science Section of INFORMS), San Juan, Puerto Rico.
25. Nozick, L. and M. Turnquist. (1998b). "Integrating Inventory Impacts into a Fixed Charge Model for Locating Distribution Centers." Transportation Research Part E 31(3), 173-186.
26. Padberg, M.W., T.J. van Roy, and L.A. Wolsey. (1985). "Valid Linear Inequalities for Fixed Charge Problems." Operations Research 33(4), 842-861.
27. Pochet, Y. (1988). "Valid Inequalities and Separation for Capacitated Economic Lot Sizing." Operations Research Letters 7(3), 109-115.
28. Pochet, Y. and L.A. Wolsey. (1995). "Algorithms and Reformulations for Lot-Sizing Problems." In DIMACS Series in Discrete Mathematics and Theoretical Computer Science 20, 245-293.
29. Rothfarb, B., H. Frank, D.M. Rosembaun, and K. Steiglitz. (1970). "Optimal Design of Offshore Natural-Gas Pipeline Systems." Operations Research 18, 992-1020.
30. Sherali, H.D. and W.P. Adams. (1990). "A Hierarchy of Relaxations Between the Continuous and Convex Hull Representations for Zero-One Programming Problems." SIAM Journal on Discrete Mathematics 3(3), 411-430.
31. Sherali, H.D. and W.P. Adams. (1994). "A Hierarchy of Relaxations and Convex Hull Characterizations for Mixed-Integer Zero-One Programming Problems." Discrete Applied Mathematics 52, 83-106.
32. Sherali, H.D., W.P. Adams, and P.J. Driscoll. (1998). "Exploiting Special Structures in Constructing a Hierarchy of Relaxations for 0-1 Mixed Integer Problems." Operations Research 46(3), 396-405.
33. Sherali, H.D., Y. Lee, and W.P. Adams. (1995). "A Simultaneous Lifting Strategy for Identifying New Classes of Facets for the Boolean Quadric Polytope." Operations Research Letters 17(1), 19-26.
34. Sherali, H.D. and C.M. Shetty. (1980). Optimization with Disjunctive Constraints. Series in Economics and Mathematical Systems, Springer-Verlag, Berlin-Heidelberg-New York Vol. 181.
35. Stallaert, J. (2000). "Valid Inequalities and Separation for Capacitated Fixed Charge Flow Problems." Discrete Applied Mathematics 98, 265-274.
36. Suhl, U. (1985). "Solving Large Scale Mixed Integer Programs with Fixed-Charge Variables." Mathematical Programming 32, 165-182.
37. Sun, M., J.E. Aronson, P.G. McKeown, and D. Drinka. (1998). "A Tabu Search Heuristic Procedure for the Fixed Charge Transportation Problem." European Journal of Operational Research 106, 441-456.
38. Van Vyve, M. and F. Ortega. (2003). "Lot-sizing with Fixed Charges on Stocks: The Convex Hull." CORE DP 2003/14, Universite Catholique de Louvain, Louvainla-Neuve.
39. Wolsey, L.A. (1989). "Submodularity and Valid Inequalities in Capacitated Fixed Charge Networks." Operations Research Letters 8, 119-124.