Lot sizing with inventory bounds and fixed costs: Polyhedral study and computation

Operations Research

Volumn 53, Issue 4, 2005, Pages 711-730

  Atamtürk, Alper ^a   Küçükyavuz, Simge ^a  

^a DEPARTMENT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH   (United States)

Author keywords

Computation; Facets; Lot sizing; Separation algorithms

Indexed keywords

FACETS; INVENTORY BOUNDS; LOT SIZING; SEPARATION ALGORITHMS;

ALGORITHMS; CALCULATIONS; COMPUTATIONAL METHODS; COSTS; LINEAR PROGRAMMING; MATHEMATICAL MODELS; PROBLEM SOLVING;

INVENTORY CONTROL;

EID: 25144467855     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.1050.0223     Document Type: Article

References (39)

1. Aggarwal, A., J. K. Park. 1993. Improved algorithms for economic lot size problems. Oper. Res. 41(3) 549-571.
2. Aghezzaf, E. H., L. A. Wolsey. 1994. Modelling piecewise linear concave costs in a tree partitioning problem. Discrete Appl. Math. 50 101-109.
3. Agra, A., M. Constantino. 1999. Lotsizing with backlogging and start-ups: The case of Wagner-Whitin costs. Oper. Res. Lett. 25 81-88.
4. Ahuja, R. K., T. L. Magnanti, J. B. Orlin. 1993. Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Englewood Cliffs, NJ, 107-108.
5. Atamtürk, A. 2001. Flow pack facets of the single node fixed-charge flow polytope. Oper. Res. Lett. 29 107-114.
6. Atamtürk, A., D. S. Hochbaum. 2001. Capacity acquisition, subcontracting, and lot sizing. Management Sci. 47 1081-1100.
7. Atamtürk, A., J. C. Muñoz. 2004. A study of the lot-sizing polytope. Math. Programming 99 43-65.
8. Bárány, I., T. van Roy, L. A. Wolsey. 1984. Incapacitated lot-sizing: The convex hull of solutions. Math. Programming Stud. 22 32-43.
9. Belvaux, G., L. A. Wolsey. 2000. bc-prod: A specialized branch-and-cut system for lot-sizing problems. Management Sci. 46 724-738.
10. Belvaux, G., L. A. Wolsey. 2001. Modelling practical lot-sizing problems as mixed-integer programs. Management Sci. 47(7) 993-1007.
11. Constantino, M. 1996. A cutting plane approach to capacitated lot-sizing with start-up costs. Math. Programming 75 353-376.
12. Constantino, M. 1998. Lower bounds in lot-sizing models: A polyhedral study. Math. Oper. Res. 23 101-118.
13. Federgruen, A., M. Tzur. 1991. A simple forward algorithm to solve general dynamic lot sizing models with n periods in O(n log n) or O(n) time. Management Sci. 37(2) 909-925.
14. Florian, M., M. Klein. 1980. Deterministic production planning with concave costs and capacity constraints. Management Sci. 26(7) 669-679.
15. Florian, M., J. K. Lenstra, H. G. Rinnooy Kan. 1971. Deterministic production planning: Algorithms and complexity. Management Sci. 18(1) 12-20.
16. Gu, Z., G. L. Nemhauser, M. W. P. Savelsbergh. 1999. Lifted flow cover inequalities for mixed 0-1 integer programs. Math. Programming 85 439-467.
17. Küçükyavuz, S. 2004. Polyhedral approaches to capacitated fixed-charge network flow problems. Ph.D. thesis, University of California at Berkeley, Berkeley, CA.
18. Leung, J. M. Y., T. L. Magnanti, R. Vachani. 1989. Facets and algorithms for capacitated lot sizing. Math. Programming 45 331-359.
19. Loparic, M., H. Marchand, L. A. Wolsey. 2003. Dynamic knapsack sets and capacitated lot-sizing. Math. Programming 95 53-69.
20. Loparic, M., Y. Pochet, L. A. Wolsey. 2001. The uncapacitated lot-sizing problem with sales and safety stocks. Math. Programming 89 487-504.
21. Love, S. F. 1973. Bounded production and inventory models with piece-wise concave costs. Management Sci. 20(3) 313-318.
22. Miller, A. J., G. L. Nemhauser, M. W. P. Savelsbergh. 2000. On the capacitated lot-sizing and continuous 0-1 knapsack polyhedra. Eur. J. Oper. Res. 125 298-315.
23. Nemhauser, G. L., L. A. Wolsey. 1988. Integer and Combinatorial Optimization. John Wiley and Sons, New York.
24. Ortega, F., L. A. Wolsey. 2000. A branch-and-cut algorithm for the single commodity uncapacitated fixed charge network flow problem. CORE discussion paper 2000/49, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.
25. Padberg, M. W., T. J. van Roy, L. A. Wolsey. 1985. Valid linear inequalities for fixed charge problems. Oper. Res. 33(4) 842-861.
26. Pochet, Y. 1988. Valid inequalities and separation for capacitated economic lot sizing. Oper. Res. Lett. 7(3) 109-115.
27. Pochet, Y., L. A. Wolsey. 1988. Lot-size models with backlogging: Strong reformulations and cutting planes. Math. Programming 40 317-335.
28. Pochet, Y., L. A. Wolsey. 1991. Solving multi-item lot-sizing problems using strong cutting planes. Management Sci. 37 53-67.
29. Pochet, Y., L. A. Wolsey. 1993. Lot-sizing with constant batches: Formulation and valid inequalities. Math. Oper. Res. 18(4) 767-785.
30. Pochet, Y., L. A. Wolsey. 1994. Polyhedra for lot-sizing with Wagner-Whitin costs. Math. Programming 67 297-323.
31. Stallaert, J. I. A. 1997. The complementary class of generalized flow cover inequalities. Discrete Appl. Math. 77 73-80.
32. 3) algorithm for the economic lot-sizing problem with constant capacities. Management Sci. 42(1) 142-150.
33. Van Roy, T. J., L. A. Wolsey. 1985. Valid inequalities and separation for uncapacitated fixed charge networks. Oper. Res. Lett. 4(3) 105-112.
34. van Vyve, M., F. Ortega. 2003. Lot-sizing with fixed charges on stocks: The convex hull. CORE discussion paper 2003/14, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.
35. Wagelmans, A., S. van Hoesel, A. Kolen. 1992. Economic lot sizing: An O(n log n) algorithm that runs in linear time in the Wagner-Whitin case. Oper. Res. 40 S145-S156.
36. Wagner, H. M., T. M. Whitin. 1958. Dynamic version of the economic lot size model. Management Sci. 5 89-96.
37. Wolsey, L. A. 1989. Submodularity and valid inequalities in capacitated fixed charge networks. Oper. Res. Lett. 8 119-124.
38. Wolsey, L. A. 1998. Integer Programming. John Wiley and Sons, New York.
39. Wolsey, L. A. 2002. Solving multi-item lot-sizing problems with an MIP solver using classification and reformulation. Management Sci. 48(12) 1587-1602.