Solving a class of stochastic mixed-integer programs with branch and price

Mathematical Programming

Volumn 108, Issue 2-3, 2006, Pages 395-418

  Silva, Eduardo F ^a   Wood, R Kevin ^b  

^a Marinha do Brasil   (Brazil)

^b NAVAL POSTGRADUATE SCHOOL   (United States)

Author keywords

Branch and price; Column generation; Stochastic mixed integer program

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; PROBLEM SOLVING; RANDOM PROCESSES; STATISTICAL METHODS;

BRANCH AND PRICE; COLUMN GENERATION; STOCHASTIC MIXED-INTEGER PROGRAM;

INTEGER PROGRAMMING;

EID: 33745712306     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-006-0716-6     Document Type: Article

References (61)

1. Ahmed, S., Sahinidis, N.V.:. An approximation scheme for stochastic integer programs arising in capacity expansion. Oper. Res. 51, 461-471 (2003)
2. Ahuja, R. K., Magnanti, T.L., Orlin. J.B.: Network Flows. Prentice Hall, Englewood Cliffs, NJ, 1993
3. Appleget, J. A., Wood, R.K.: Explicit-constraint branching for solving mixed-integer programs. M. Laguna, J.L. Gonzalez-Velarde, (eds), Computing Tools for Modeling, Optimization and Simulation, Kluwer Academic Publishers, Boston, MA, 243-261 2000
4. Appelgren, L.H.: A column generation algorithm for a ship scheduling problem. Transp. Sci. 3, 53-68 (1969)
5. Barcelo, J., Casanova, J.: A heuristic lagrangean algorithm for the capacitated plant location problem. Eur. J. Oper. Res. 15, 212-226 (1984)
6. Barnhart, C., Hane, C.A., Vance, P.H.: Using branch-and-price-and-cut to solve origin-destination integer multicommodity flow problems. Oper. Res. 48, 318-326 (2000)
7. Barnhart, C., Johnson, E.L., Nemhauser, G.L., Savelsbergh, M.W.P., Vance, P.H.: Branch-and-price: Column generation for solving huge integer programs. Oper. Res. 46, 316-329 (1998)
8. Beale, E.M.L: On minimizing a convex function subject to linear inequalities. J. R. Stat. Soc. 17B, 173-184(1955)
9. Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4, 238-252 (1962)
10. Bertsimas, D.J.: A vehicle routing problem with stochastic demand. Oper. Res. 40, 574-585 (1992)
11. Birge, J.R., Louveaux, E: Introduction to Stochastic Programming. Springer-Verlag, New York, (1997)
12. Brown, G.G., Graves, G.: Real-time dispatch of petroleum tank trucks. Manage. Sci. 27, 19-32 (1981)
13. Brown, G.G., Graves, G., Honczarenko, M.: Design and operation of a multicommodity production/distribution system using primal goal decomposition. Manage. Sci. 33, 1469-1480 (1987)
14. Butchers, E.R., Day, PR., Goldie, A.P., Miller, S., Meyer, J.A., Ryan, D.M., Scott, A.C., Wallace, C.A.: Optimized crew scheduling at Air New Zealand. Interfaces 31, 30-56 (2001)
15. Butler, J.C., Dyer, J.S.: Optimizing natural gas flows with linear programming and scenarios. Dec. Sci. 30, 563-580 (1999)
16. Camm J.D., Chorman, T.E., Dill, F.A., Evans, J.R., Sweeney, D.J., Wegryn, G.W.: Blending OR/MS, judgment, and GIS: Restructuring P&G's supply chain. Interfaces 27, 128-142 (1997)
17. Carøe, C.C., Tind, J.: L-shaped decomposition of two-stage stochastic programs with integer recourse. Math. Program. 83, 451-464 (1998)
18. Chen, Z.-L., Li, S., Tirapati, D.: A scenario-based stochastic programming approach for technology and capacity planning. Comput. Oper. Res. 29, 781-806 (2002)
19. Chu P.C., Beasley, J.E.: A genetic algorithm for the generalized assignment problem. Comput. Oper. Res. 24, 17-23 (1997)
20. COIN. 2004. http://www.coin-or.org (accessed July 2004)
21. Damodaran, P., Wilhelm, W.E.: Branch-and-price methods for prescribing profitable upgrades of hightechnology products with stochastic demands. Dec. Sci. 35, 55-82 (2004)
22. Dantzig, G.B., Wolfe, P.: The decomposition principle for linear programs. Oper. Res. 8, 101-111 (1960)
23. Day, P.R., Ryan, D.M.: Flight attendant rostering for short-haul airline operations. Oper. Res. 45, 649-661 (1997)
24. Desrochers, M., Desrosiers, J., Solomon, M.: 1992. A new optimization algorithm for the vehicle routing problem with time windows. Oper. Res. 40, 342-354.
25. Desrochers, M., Solomon, P.M.: A column generation approach to the urban transit crew scheduling problem. Transp. Sci. 23, 1-13 (1989)
26. Desrosiers, J., Dumas, Y., Solomon, M.M., Soumis, F.: Time constrained routing and scheduling. (M.O. Ball, T.L. Magnanti, C.L. Monma and G.L. Nemhauser (eds), Handbooks in Operations Research and Management Science, Vol. 8, Network Routing, Elsevier, Amsterdam, 35-140 (1995)
27. Du Merle, O., Villeneuve, D., Desrosiers, J., Hansen, P.: Stabilized column generation. Discrete Math. 194, 229-237 (1999)
28. Ehrgott, M., Ryan, D.M.: Constructing robust crew schedules with bicriteria optimization. Journal of Multicriteria Decision Analysis 11, 139-150 (2002)
29. Ford, L.R., Fulkerson, D.R.: A suggested computation for the maximal multicommodity network flows. Manage. Sci. 5, 97-101 (1958)
30. Gilmore, P.C., Gomory, R.E.: A linear programming approach to the cutting stock problem. Oper. Res. 9,849-859(1961)
31. Girard, A., Sansó, B.: Multicommodity flow models, failure propagation, and reliable loss network design. IEEE/ACM Transactions on Networking 6, 82-93 (1998)
32. ILOG 2002.ILOG CPLEX 8.0 Reference Manual
33. Johnson, E.L.: Modeling and strong linear programs for mixed integer programming. S.W. Wallace (ed), Algorithms and Model Formulations in Mathematical Programming, Springer-Verlag, 1-43 (1989)
34. Kleywegt A.J., Shapiro, A., Homem-de-Mello, T.: The sample average approximation method for stochastic discrete optimization. SIAM J. Optim. 12, 479-502 (2002)
35. Laporte, G., Louveaux, F.V.: The integer L-shaped method for stochastic integer programs with complete resource. Oper. Res. Lett. 13, 133-142 (1993)
36. Laporte, G., Louveaux, F.V., Van Hamme, L.: Exact solution to a location problem with stochastic demands. Transp. Sci. 28, 95-103 (1994)
37. Linderoth, J., Wright, S.J.: Decomposition algorithms for stochastic programming on a computational grid. Optimization Technical Report 02-07, Computer Sciences Department, University of WisconsinMadison (2002)
38. Lorena, L.A.N., Senne, E.L.F.: A column generation approach to capacitated p-median problems. Comput. Oper. Res. 31, 863-876 (2004)
39. Lougee-Heimer, R.: The Common optimization interface for operations research: Promoting open-source software in the operations research community. IBM J. Res. Dev. 47, 57-66 (2003)
40. Louveaux, F.V., Peelers, D.: A dual-based procedure for a stochastic facility location. Oper. Res. 40, 564-573 (1992)
41. Lübbecke, M.E., Desrosiers, J.: Selected topics in column generation. Les Cahiers de GERAD G-2002-64, Group for research in decision analysis, montreal, Canada. http://www.optimizationonline.org/DB_FILE/2002/12/ 580.pdf (accessed July 2004)
42. Lulli, G., Sen, S.: A branch-and-price algorithm for multi-stage stochastic integer programming with application to stochastic batch-size problems. Manage. Sci. 50, 786-796 (2004)
43. Mak, W.-K., Morton, D.P., Wood, R.K.: Monte Carlo bounding techniques for determining solution quality in stochastic programs. Oper. Res. Lett. 24, 47-56 (1999)
44. Papagiannaki, K., Moon, S., Fraleigh, C., Thiran, P., Diot, C.: Measurement and analysis of single-hop delay on an IP backbone network. IEEE Journal on Selected Areas in Communications 21, 908-921 (2003)
45. Ralphs, T.K., Ladanyi, L.: CO1N/BCP User's Manual, http://www-124.ibm. com/developerworks/opensource/coin/presentations/bcp- man.pdf (accessed July 2004) (2001)
46. Ribeiro C.C., Soumis, F.: A column generation approach to the multiple-depot vehicle scheduling problem. Oper. Res. 42, 41-52 (1994)
47. Rockafellar, R.T., Wets, R.J.-B.: Stochastic convex programming: relatively complete recourse and induced feasibility. SIAM J. Control Optimization 14, 547-589 (1976)
48. Ryan, D.M., Foster, B.A.: An integer programming approach to scheduling. A. Wren, (ed), Computer Scheduling of Public Transport, Urban Passenger Vehicle and Crew Scheduling. North Holland, Amsterdam, 269-280 (1981)
49. Savelsbergh, M.W.P.: A branch-and-price algorithm for the generalized assignment problem. Oper. Res. 45, 831-841 (1997)
50. 2 algorithm for large scale stochastic integer programming: Set convexification. Stochastic Programming E-Print Series, (http://dochost.rz.hu-berlin.de/speps) (2000)
51. Shiina, T., Birge, J.R.: Stochastic unit commitment problem. Int. Trans. Oper. Res. 11, 19-32 (2004)
52. Silva, E.F.: Improving branch-and-price algorithms and applying them to stochastic programs. PhD Dissertation, Naval Postgraduate School, Monterey, CA (2004)
53. Singh, K., Philpott, A., Wood, R.K.: Column generation for design of survivable networks. Working paper, Dept. of Engineering Science, University of Auckland, Auckland, New Zealand (2005)
54. Spoerl, D., Wood, R.K.: A stochastic generalized assignment problem. INFORMS Annual Meeting, Atlanta, GA, 19-22 October (2003)
55. Teo, C-P., Shu, J.: Warehouse-retailer network design problem. Oper. Res. 52, 396-408 (2004)
56. Vance, P.H., Barnhart, C., Johnson, E.L., Nemhauser, G.L.: Airline crew scheduling: A new formulation and decomposition algorithm. Oper. Res. 45, 188-200 (1997)
57. Walkup, D.W., Wets, R.J.-B.: Stochastic programs with recourse. SIAM J. Appl. Math. 15, 1299- 1314 (1967)
58. Weingartner, H.M., Ness, D.N.: Methods for the multidimensional 0/1 knapsack problem. Oper. Res. 15, 83-103 (1967)
59. Wets, R.J.-B. 1966. Programming under uncertainty: the complete problem. Zeitschrift für Wahr-scheinlichkeitstheorie und Verwandte Gebiete 4, 316-339 (1996)
60. Wolsey, L.A.: Integer Programming. John Wiley& Sons, New York, 1998
61. Zhou, J., Liu, B.: New stochastic models for capacitated location-allocation problem. Computers and Industrial Engineering 45, 111-125 (2003)