A cross entropy-Lagrangean hybrid algorithm for the multi-item capacitated lot-sizing problem with setup times

Computers and Operations Research

Volumn 36, Issue 2, 2009, Pages 530-548

  Caserta, M ^a   Rico, E Quiñonez ^b  

^a UNIVERSITY OF HAMBURG   (Germany)

^b SCHOOL OF ENGINEERING AND SCIENCES   (Mexico)

Author keywords

Capacitated lot sizing; Cross entropy; Lagrangean heuristics; Metaheuristics; Production

Indexed keywords

CIRCUIT THEORY;

CAPACITATED LOT SIZING; COMPUTATIONAL TIME; CROSS ENTROPY; FINITE PLANNING HORIZONS; GLOBAL OPTIMIZER; HYBRID ALGORITHM; LAGRANGEAN HEURISTICS; LAGRANGEAN RELAXATION; LIMITED RESOURCES; META HEURISTIC; METAHEURISTICS; MULTI-ITEM; OPTIMAL PARAMETERS; ORIGINAL PROBLEM; PRODUCTION; RESPONSE SURFACE METHODOLOGIES; SET-UP TIMES; SOLUTION QUALITY;

HEURISTIC PROGRAMMING;

EID: 52049111930     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2007.10.014     Document Type: Article

References (33)

1. Aras OA. A heuristic solution procedure for a singlefacility multiitem dynamic lot sizing and sequencing problem. PhD thesis, Syracuse University; 1981.
2. Trigeiro W.W., Thomas J.L., and McCain J.O. Capacitated lot sizing with setups. Manage Sci 35 (1989) 141-161
3. Nemhauser G.L., and Wolsey L.A. Integer and combinatorial optimization. Wiley-interscience series in discrete mathematics and optimization (1999), Wiley, New York
4. Dzielinski M., and Gomory R. Optimal programming of lot-sizing inventory and labor allocation. Manage Sci 11 (1965) 874-890
5. Eppen G., and Martin R. Solving multi-item capacitated lot sizing problems using variables redefinition. Oper Res 35 6 (1987) 832-848
6. Pochet Y., and Wolsey L.A. Polyhedra for lot sizing with Wagner-Within costs. Math Program 67 (1994) 297-323
7. Constantino M. A cutting plane approach to capacitated lot-sizing with start-up costs. Math Program 75 (1996) 353-376
8. Miller AJ, Nemhauser GL, Savelsberg MW. Solving multi-item capacitated lot-sizing problems with setup times by branch and cut. Core dp 2000/39, Université Catholique de Louvain, Louvain-la-Neuve, Belgium; 2000.
9. Pochet Y. Valid inequalities and separation for capacitated economic lot sizing. Oper Res Lett 7 (1988) 109-116
10. Miller A.J., Nemhauser G.L., and Savelsbergh M.W.P. On the capacitated lot sizing and continuous 0-1 knapsack polyhedra. Eur J Oper Res 125 (2000) 298-315
11. Miller AJ, Nemhauser GL, Savelsbergh MWP. A multi-item production planning model with setup times: algorithms, reformulations, and polyhedral characterizations for a special case. Core dp 2001/6, Université Catholique de Louvain, Louvain-la-Neuve, Belgium; 2001.
12. Miller A.J., Nemhauser G.L., and Savelsbergh M.W.P. On the polyhedral structure of a multi-item production planning model with setup times. Math Program Ser B 94 (2003) 375-405
13. Loparic M., Marchand H., and Wolsey L. Dynamic knapsack sets and capacitated lot sizing. Math Program 95 1 (2003) 53-69
14. Magnanti T., and Sastry T. Facets and reformulations for solving production planning with changeover costs. Oper Res 50 4 (2002) 708-719
15. Diaby M., Bahl H.C., Karwan M., and Zionts S. A Lagrangean relaxation approach for very large scale capacitated lot sizing. Manage Sci 38 (1992) 1329-1340
16. Tempelmeier H., and Derstoff M. A Lagrangean-based heuristic for dynamic multilevel multi-item constrained lot sizing with setups. Manage Sci 42 (1996) 738-757
17. Katok E., Lewis H., and Harrison T. Lot-sizing in general assembly systems with setups costs, setup times, and multiple constrained resources. Manage Sci 44 (1998) 859-877
18. Hindi K.S., Fleszar K., and Charalambous C. An effective heuristic for the CLSP with set-up times. J Oper Res Soc 54 (2003) 490-498
19. Sambasivan M., and Schmidt C.P. A heuristic procedure for solving multi-plant, multi-item, multi-period capacitated lot sizing problems. Asia-Pacific J Oper Res 19 (2002) 87-105
20. Gopalakrishnan M., Ding K., Bourjolly J., and Mohan S. A Tabu-search heuristic for the capacitated lot-sizing problem with set-up carryover. Manage Sci 47 6 (2001) 851-863
21. Caserta M, Quiñonez Rico E, Márquez Uribe A. A cross entropy algorithm for the knapsack problem with setups. Comput Oper Res 2007; 35(1): 241-52.
22. De Boer P., Kroese D.P., Mannor S., and Rubinstein R.Y. A tutorial on the cross-entropy method. Ann Oper Res 134 1 (2005) 19-67
23. Rubinstein R.Y. Cross-entropy and rare events for maximal cut and partition problems. ACM Trans Model Comput Simul 12 1 (2002) 27-53
24. Aggarwal A, Park JK. Improved algorithms for economic lot sizing problems. Oper Res 1993; 549-71.
25. Wolsey L.A. Progress with single-item lot sizing. Eur J Oper Res 86 (1995) 395-401
26. Karimi B., Fatemi Ghomi S.M.T., and Wilson J.M. The capacitated lot sizing problem: a review of models and algorithms. Omega 31 (2003) 365-378
27. Brahimi N., Dauzere-Peres S., Najid N.M., and Nordli A. Single item lot sizing problems. Eur J Oper Res 168 (2006) 1-16
28. Wagelmans A., Hoesel S.V., and Kolen A. Economic lot sizing: an O (n log n) that runs in linear time in the Wagner within case. Oper Res 40 1 (1992) 145-156
29. Federgruen A., and Tzur M. A simple forward algorithm to solve general dynamic lot sizing models with n periods in O (n log n) or O (n) time. Manage Sci 37 (1991) 909-925
30. Van Hoesel S., Kuik R., Salomon M., and Van Vassenhove L.N. The single item discrete lot sizing and scheduling problem: optimization by linear and dynamic programming. Discrete Math 48 (1994) 289-303
31. Held M., and Karp R.M. The traveling salesman problem and minimum spanning tree: part II. Math Program 1 (1971) 6-25
32. Lougee-Heimer R. The common optimization interface for operations research. IBM J Res Develop 47 1 (2003) 57-66
33. Box G., and Wilson K. On the experimental attainment of optimum conditions. J R Stat Soc, Ser B 13 (1951) 1-45