We address a multi-item capacitated lot-sizing problem with setup times that arises in real-world production planning contexts. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. The problem is NP-hard. We propose mixed integer programming heuristics based on a planning horizon decomposition strategy to find a feasible solution. The planning horizon is partitioned into several sub-horizons over which a freezing or a relaxation strategy is applied. Some experimental results showing the effectiveness of the approach on real-world instances are presented. A sensitivity analysis on the parameters of the heuristics is reported.
Mots-clés : lot-sizing, setup time, shortage cost, safety stock deficit, production planning, mixed integer programming, heuristic
@article{RO_2007__41_2_171_0,
author = {Absi, Nabil and Kedad-Sidhoum, Safia},
title = {MIP-based heuristics for multi-item capacitated lot-sizing problem with setup times and shortage costs},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {171--192},
publisher = {EDP-Sciences},
volume = {41},
number = {2},
year = {2007},
doi = {10.1051/ro:2007014},
mrnumber = {2341439},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro:2007014/}
}
TY - JOUR AU - Absi, Nabil AU - Kedad-Sidhoum, Safia TI - MIP-based heuristics for multi-item capacitated lot-sizing problem with setup times and shortage costs JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2007 SP - 171 EP - 192 VL - 41 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro:2007014/ DO - 10.1051/ro:2007014 LA - en ID - RO_2007__41_2_171_0 ER -
%0 Journal Article %A Absi, Nabil %A Kedad-Sidhoum, Safia %T MIP-based heuristics for multi-item capacitated lot-sizing problem with setup times and shortage costs %J RAIRO - Operations Research - Recherche Opérationnelle %D 2007 %P 171-192 %V 41 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro:2007014/ %R 10.1051/ro:2007014 %G en %F RO_2007__41_2_171_0
Absi, Nabil; Kedad-Sidhoum, Safia. MIP-based heuristics for multi-item capacitated lot-sizing problem with setup times and shortage costs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 2, pp. 171-192. doi : 10.1051/ro:2007014. http://www.numdam.org/articles/10.1051/ro:2007014/
[1] , Modélisation et résolution de problèmes de lot-sizing à capacité finie. Ph.D. thesis, Université Pierre et Marie Curie (Paris VI), (2005).
[2] and, Multi-item capacitated lot-sizing problem with setup times and shortage costs. Working paper, Available at http://www.optimization-online.org/DB_HTML/2005/09/1212.html, July 2005.
[3] , and, The single-item lot-sizing problem with immediate lost sales. Eur. J. Oper. Res. 147 (2003) 558-566. | Zbl
[4] and, bc-prod: A specialized branch-and-cut system for lot-sizing problems. Manage. Sci. 46 (2000) 724-738.
[5] and, Computational complexity of the capacitated lot size problem. Manage. Sci. 28 (1982) 1174-1186. | Zbl
[6] ,, and, Single item lot sizing problems. Eur. J. Oper. Res. 168 (2006) 1-16. | Zbl
[7] and, Analysis of relaxations for the multi-item capacitated lot-sizing problem. Ann. Oper. Res. 26 (1990) 29-72. | Zbl
[8] , Hybrid heuristics for planning lot setups and sizes. Comput. Ind. Eng. 44 (2003) 545-562.
[9] ,, and, Capacitated lot-sizing and scheduling by lagrangean relaxation. Eur. J. Oper. Res. 59 (1992) 444-458. | Zbl
[10] , An efficient implementation of the wagner-whitin algorithm for dynamic lot-sizing. J. Oper. Manage. 5 (1982) 229-235.
[11] , and, Deterministic production planning: algorithms and complexity. Manage. Sci. 26 (1980) 669-679. | Zbl
[12] , Chronological decomposition heuristic for scheduling: A divide and conquer method. AIChE Journal 48 (2002) 2995-2999.
[13] and, Plant location, set covering and economic lot sizes: An o(mn)-algorithm for structured problems, in optimierung bei graphentheoretischen and ganzzahligen probleme, edited by L. Collatz et al., Birkhauser Verlag, Basel (1977) 155-180. | Zbl
[14] , and, Facets and algorithms for capacitated lot-sizing. Math. Program. 45 (1989) 331-359. | Zbl
[15] CPLEX Callable Library. Ilog sa. http://www.ilog.com (2005).
[16] , and, The uncapacitated lot-sizing problem with sales and safety stocks. Math. Program. 89 (2001) 487-504. | Zbl
[17] LOTSIZELIB. http://www.core.ucl.ac.be:16080/wolsey/lotsizel.htm (1999).
[18] and, Mip-based heuristics for capacitated lotsizing problems. Inter. J. Prod. Econ. 85 (2003) 97-111.
[19] , Polyhedral Approaches to Capacitated Lot-Sizing Problems. Ph.D. thesis, Georgia Institute of Technology, USA (1999).
[20] , and, On the polyhedral structure of a multi-item production planning model with setup times. Math. Program. 94 (2003) 375-405. | Zbl
[21] and, Solving multi-item lot-sizing problems using strong cutting planes. Manage. Sci. 37 (1991) 53-67. | Zbl
[22] . Efficient, effective lot-sizing for multi-product, multi-stage production systems. Oper. Res. 41 (1993) 371-386. | Zbl
[23] and, A forward algorithm for the capacitated lot size model with stockouts. Oper. Res. 38 (1990) 474-486. | Zbl
[24] , Multilevel lot sizing with setup times and multiple constrained resources: Internally rolling schedules with lot-sizing windows. Oper. Res. 51 (2003) 487-502.
[25] and, The capacitated lot-sizing problem with linked lot sizes. Manage. Sci. 49 (2003) 1039-1054.
[26] , and, Capacitated lot-sizing with setup times. Manage. Sci. 35 (1989) 353-366.
[27] and, A general heuristic for production planning problems. INFORMS J. Comput. 16 (2004) 316-327.
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