A polynomial algorithm for a lot-sizing problem with backlogging, outsourcing and limited inventory

Computers and Industrial Engineering

Volumn 64, Issue 1, 2013, Pages 200-210

  Chu, Chengbin ^a,b   Chu, Feng ^c   Zhong, Jinhong ^d   Yang, Shanlin ^d  

^a TONGJI UNIVERSITY   (China)

^b ECOLE CENTRALE PARIS   (France)

^c UNIVERSITÉ D EVRY VAL D ESSONNE   (France)

^d HEFEI UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Dynamic programming; Lot sizing; Polynomial algorithm; Production planning

Indexed keywords

COST FUNCTIONS; COSTS; OUTSOURCING; PLANNING; PRODUCTION CONTROL;

DYNAMIC LOT-SIZING MODEL; INVENTORY CAPACITY; LOT SIZING; LOT SIZING PROBLEMS; MINIMAL TOTAL COSTS; POLYNOMIAL ALGORITHM; PRODUCTION COST FUNCTIONS; PRODUCTION PLANNING;

DYNAMIC PROGRAMMING;

EID: 84869109657     PISSN: 03608352     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cie.2012.08.007     Document Type: Article

References (38)

1. Absi, N., Kedad-Sidhoum, S., & Dauzère-Pérès, S. (2011). Uncapacitated lot-sizing problem with production time windows, backlogs and lost sales. International Journal of Production Research, 49(9), 2551-2566.
2. Aggarwal, A., & Park, J. K. (1993). Improved algorithms for economic lot-size problems. Operations Research, 41(3), 549-571.
3. Aksen, D. (2007). Loss of customer goodwill in the uncapaciated lot-sizing problem. Computers & Operations Research, 34, 2805-2823. (Pubitemid 46188379)
4. Aksen, D., Altinkemer, K., & Chand, S. (2003). The single-item lot-sizing problem with immediate lost sales. European Journal of Operational Research, 147, 558-566.
5. Atamtürk, A., & Hochbaum, D. S. (2001). Capacity acquisition, subcontracting, and lot sizing. Management Science, 47(8), 1081-1100. (Pubitemid 34192807)
6. Atamtürk, A., & Kücükyavuz, S. (2005). Lot sizing with inventory bounds and fixed costs: Polyhedral study and computation. Operations Research, 53(4), 711-730. (Pubitemid 41344633)
7. Baker, K. R., Dixon, P., Magazine, M. J., & Silver, E. A. (1978). An algorithm for the dynamic lot-size problem with time-varying production capacity constraints. Management Science, 24(16), 1710-1720. (Pubitemid 9444885)
8. Bitran, G. R., & Yanasse, H. H. (1982). Computational complexity of the capacitated lot size problem. Management Science, 28(10), 1174-1186.
9. Blackburn, J. D., & Kunreuther, H. (1974). Planning horizon for the dynamic lot size model with backlogging. Management Science, 21(3), 1174-1186.
10. Chen, H. D., Hearn, D. W., & Lee, C. Y. (1994). A new dynamic programming algorithm for the single item capacitated dynamic lot size model. Journal of Global Optimization, 4, 285-300.
11. Chu, F., & Chu, C. (2007). Polynomial algorithms for single item lot sizing models with bounded inventory and backlogging or outsourcing. IEEE Transactions on Automation Science and Engineering, 4(2), 233-251.
12. Chung, C., & Lin, C. M. (1988). An O(T2) algorithm for the NI/G/NI/ND capacitated lot size problem. Management Science, 34, 420-426.
13. Federgruen, A., & Tzur, M. (1991). A simple forward algorithm to solve general dynamic lot sizing models with n periods in O(nlogn) orO(n) time. Management Science, 37(8), 909-925. (Pubitemid 23585668)
14. Feng, Y., Chen, S., Kumar, A., & Lin, B. (2011). Solving single-product economic lotsizing problem with non-increasing setup cost, constant capacity and convex inventory cost in O(NlogN) time. Computers & Operations Research, 38(8), 717-722.
15. Florian, M., & Klein, M. (1971). Deterministic production planning with concave costs and capacity constraints. Management Science, 18(1), 12-20.
16. Florian, M., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1980). Deterministic production planning: Algorithms and complexity. Management Science, 26(7), 669-679. (Pubitemid 11442296)
17. Ganas, L., & Papachristos, S. (2005). The single-product lot-sizing problem with constant parameters and backlogging: Exact results, a new solution, and all parameter stability regions. Operations Research, 53(1), 170-176. (Pubitemid 40320223)
18. Gutiérrez, J., Sedeno-Noda, A., Colebrook, M., & Sicilia, J. (2002). A new characterization for the dynamic lot size problem with bounded inventory. Computers & Operations Research, 30, 383-395. (Pubitemid 36650126)
19. Gutiérrez, J., Sedeno-Noda, A., Colebrook, M., & Sicilia, J. (2007). A polynomial algorithm for the production/ordering planning. Computers & Operations Research, 34, 934-937.
20. Gutiérrez, J., Sedeno-Noda, A., Colebrook, M., & Sicilia, J. (2008). An efficient approach for solving the lot-sizing problem with time-varying storage capacities. European Journal of Operational Research, 189, 682-693. (Pubitemid 351400544)
21. Janannathan, R., & Rao, M. R. (1973). A class of deterministic production planning problems. Management Science, 19, 1295-1300.
22. Lee, H. L., & Nahmias, S. (1993). Single-product, single-location models. In S. C. Graves, A. H. G. Rinnooy Kan, & P. H. Zipkin (Eds.). Handbooks in Operations Research and Management Science Logistics of Production and Inventory (Vol. 4, pp. 3-55).
23. Elsevier Science Publishers BV. Love, S. F. (1973). Bounded production and inventory models with piecewise concave costs. Management Science, 20(3), 313-318.
24. Lundin, R. E., & Morton, T. E. (1975). Planning horizon for the dynamic lot size model: Zabel versus protective procedure and computational results. Operations Research, 23(4), 711-734.
25. Morton, T. E. (1978). An improved algorithm for the stationary cost dynamic lot size model with backlogging. Management Science, 24(8), 869-873.
26. Sandbothe, R. A., & Thompson, G. L. (1990). A forward algorithm for the capacitated lot size model with stockouts. Operations Research, 38(3), 474-486.
27. Sandbothe, R. A., & Thompson, G. L. (1993). Decision horizons for the capacitated lot size model with inventory bounds and stockouts. Computers & Operations Research, 20(5), 455-465.
28. Shaw, D. X., & Wagelmans, A. (1998). An algorithm for single-item capacitated economic lot sizing with piecewise linear production costs and general holding costs. Management Science, 44, 831-838. (Pubitemid 128572653)
29. Swoveland, C. (1975). A deterministic multi-period production planning model with piecewise concave production and holding-backorder costs. Management Science, 21(9), 1007-1013.
30. Toczylowski, E. (1995). An O(T2) algorithm for the lot-sizing problem with limited inventory levels. Proceedings of the IEEE Symposium on Emerging Technologies & Factory Automation, 3, 78-85.
31. Van den Heuvel, W., Gutiérriez, J. M., & Hwang, H.-C. (2011). Note on ''An efficient approach for solving the lot-sizing problem with time-varying storage capacities''. European Journal of Operational Research, 213, 455-457.
32. Van den Heuvel, W., & Wagelmans, A. P. M. (2006). An efficient dynamic programming algorithm for a special case of the capacitated lot-sizing problem. Computers & Operations Research, 33(12), 3583-3599.
33. VanHoesel, C. P. M., & Wagelmans, A. P.M. (1996). AnO(T3) algorithmfor the economic lot-sizing problem with constant capacities. Management Science, 42, 142-150. (Pubitemid 126545091)
34. Van Hoesel, C. P. M., & Wagelmans, A. P. M. (2001). Fully polynomial approximation schems for single-item capacitated economic lot-sizing problems. Mathematics of Operations Research, 26(2), 339-357. (Pubitemid 34047219)
35. Veinott, A. F. (1964). Production planning with convex costs: A parametric study. Management Science, 10(3), 441-460.
36. Wagelmans, A. P. M., Van Hoesel, S., & Kolen, A. (1992). Economic lot-sizing: An O(nlogn) algorithm that runs in linear time in the wagner-whitin case. Operations Research, 40, 145-156.
37. Wagner, H. M., & Whitin, T. M. (1958). Dynamic version of the economic lot-size model. Management Science, 5(1), 89-96.
38. Zangwill, W. (1966). A deterministic multi-period production scheduling model with back-logging. Management Science, 13, 105-119.