Exact methods for single-item capacitated lot sizing problem with alternative machines and piece-wise linear production costs

International Journal of Production Economics

Volumn 119, Issue 2, 2009, Pages 367-379

  Akbalik, Ayşe ^a   Penz, Bernard ^b  

^a CEA LETI   (France)

^b LABORATOIRE G SCOP   (France)

Author keywords

Alternative machines; Dynamic programming; Mixed integer linear programming; Single item capacitated lot sizing problem; Step wise production costs

Indexed keywords

ALTERNATIVE MACHINES; CAPACITATED LOT SIZING PROBLEM; CAPACITATED VEHICLES; COMPUTATIONAL TIME; COST STRUCTURE; DISTRIBUTION CENTERS; DYNAMIC PROGRAMMING ALGORITHM; DYNAMIC PROGRAMS; EXACT METHODS; FINISHED GOODS; FINISHED PRODUCTS; LOWER AND UPPER BOUNDS; MILP FORMULATION; MIXED INTEGER LINEAR PROGRAMMING; NP-HARD; OPTIMAL PRODUCTION; PIECEWISE LINEAR; PRODUCTION COST; SINGLE-ITEM CAPACITATED LOT SIZING PROBLEM; STEP-WISE PRODUCTION COSTS; STORAGE SPACES; SUPPLY CHAIN STRUCTURES; VALID INEQUALITY;

COMPUTATIONAL COMPLEXITY; COSTS; DISTRIBUTION OF GOODS; DYNAMIC PROGRAMMING; LINEAR PROGRAMMING; LINEARIZATION; OPTIMIZATION; PLANNING; PRODUCTION CONTROL; SUPPLY CHAINS; SYSTEMS ENGINEERING;

INTEGER PROGRAMMING;

EID: 67349282740     PISSN: 09255273     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijpe.2009.03.010     Document Type: Article

References (18)

1. Akbalik, A., Pochet, Y., 2009. Valid inequalities for the single-item capacitated lot sizing problem with step-wise costs. European Journal of Operational Research 198, 412-434.
2. Belvaux G., and Wolsey L. Modelling practical lot-sizing problems as mixed integer programs. Management Science 47 7 (2001) 993-1007
3. Brahimi N., Dauzère-Pérès S., Najid N.M., and Nordli A. Single item lot sizing problems. European Journal of Operational Research 168 1 (2006) 1-16
4. Chan L.M.A., Muriel A., Shen Z.-J., and Simchi-Levi D. On the effectiveness of zero-inventory-ordering policies for the economic lot-sizing model with a class of piecewise linear cost structures. Operations Research 50 6 (2002) 1058-1067
5. Diaby M., and Martel A. Dynamic lot sizing for multi-echelon distribution systems with purchasing and transportation price discounts. Operations Research 41 1 (1993) 48-59
6. Erengüç S.S., Simpson N.C., and Vakharia A.J. Integrated production/distribution planning in supply chains: An invited review. European Journal of Operational Research 115 (1999) 219-236
7. Florian M., Lenstra J.K., and Rinnooy Kan A.H.G. Deterministic production planning: Algorithms and complexity. Management Science 26 7 (1980) 669-679
8. Garey M.R., and Johnson D.S. Computers and Intractability: A Guide to the Theory of NP-Completeness (1979), Freeman, New York
9. Geunes J., and Pardalos P.M. Network optimization in supply chain management and financial engineering: An annotated bibliography. Networks 42 2 (2003) 66-84
10. Jans, R., 2006. Solving lotsizing problems on parallel identical machines using symmetry breaking constraints. Technical Report #ERS-2006-051-LIS, Erasmus Research Institute of Management.
11. Jans R., and Degraeve Z. Modeling industrial lot sizing problems: A review. International Journal of Production Research 46 6 (2008) 1619-1643
12. Li C.-L., Hsu V.N., and Xiao W.-Q. Dynamic lot sizing with batch ordering and truckload discounts. Operations Research 52 4 (2004) 639-654
13. Lippman S.A. Optimal inventory policy with multiple set-up costs. Management Science 16 1 (1969) 118-138
14. Pochet Y., and Wolsey L.A. Production Planning by Mixed Integer Programming (2006), Springer, Berlin
15. Pochet Y., and Wolsey L.A. Lot-sizing with constant batches: Formulation and valid inequalities. Mathematics of Operations Research 18 4 (1993) 767-785
16. Sarmiento A.M., and Nagi R. A review of integrated analysis of production-distribution systems. IIE Transactions 31 (1999) 1061-1074
17. Shaw D.X., and Wagelmans A.P.M. An algorithm for single-item capacitated economic lot sizing with piecewise linear production costs and general holding costs. Management Science 44 6 (1998) 831-838
18. Swoveland C. A deterministic multi-period production planning model with piecewise concave production and holding-backorder costs. Management Science 21 9 (1975) 1007-1013