Lot-size scheduling of a single product on unrelated parallel machines
- 24 Downloads
We study a problem in which at least a given quantity of a single product has to be partitioned into lots, and lots have to be assigned to the unrelated parallel machines for processing so that the maximum machine completion time or the sum of machine completion times is minimized. Machine dependent lower and upper bounds on the lot size are given. The product can be continuously divisible or discrete. We derive optimal polynomial time algorithms for several special cases of the problem. For other cases we provide NP-hardness proofs and demonstrate existence of fully polynomial time approximation schemes.
KeywordsScheduling Parallel machines Lot-sizing Computational complexity Approximation
- 3.Borisovsky, P.A.: A genetic algorithm for one scheduling problem with changeovers. In: Proceedings of XIV Baikal International School-Seminar Optimization methods and their applications, vol. 4, pp. 166–173. Melentiev Energy Systems Institute SB RAS, Irkutsk (2008). (In Russian)Google Scholar
- 4.Chauhan, S.S., Eremeev, A.V., Romanova, A.A., Servakh, V.V.: Approximation of linear cost supply management problem with lower-bounded demands. In: Proceedings of Discrete Optimization Methods in Production and Logistics, DOM’2004, pp. 16–21. Nasledie Dialog-Sibir Pbs., Omsk (2004)Google Scholar
- 18.Shor, N.Z., Stecuk, P.I.: Piecewise concave problem of knapsack type. In: Mikhalevich, V.S. (ed.) Methods of Research of Extremal Problems, pp. 21–28. V.M. Glushkov Institute of Cybernetics N.A., Kiev (1994). (In Russian)Google Scholar