@article{oai:edo.repo.nii.ac.jp:00000666, author = {ザン ピン and Ping Zhan}, journal = {江戸川大学紀要, Bulletin of Edogawa University}, month = {Mar}, note = {P(論文), Lot-sizing problems have been extensively researched for more than half century.There are relative small number of papers on lot-sizing models with outsourcing, despite its important applications in operations research. Recently several papers related to out-sourcing models are published.When there is no bound on production capacity, linear algorithm( totally square) is possible. Period varying capacitated lot-sizing model is known as NP-hard even outsourcing is not allowed. In this manuscript, we treat these two extreme cases, we give a efficient algorithm for former case, and propose a pseudo-polynomial scheme for period varying production capacities.}, title = {Algorithms for unbounded and varied capacitated lot-sizing problems with outsourcing}, volume = {26}, year = {2016} }