Genetic algorithms are applied to the multiple products and multiple periods inventory lot-sizing problem with supplier selection under storage capacity. The objective of this research is to calculate the optimal inventory lot-sizing for each supplier and minimize the total inventory cost which includes joint purchase cost of the products transaction cost for the suppliers and holding cost for remaining inventory. It is assumed that demand of multiple products is known over a planning horizon. The problem is formulated as a mixed integer programming and is solved with genetic algorithms. Finally numerical example is provided to illustrate the solution procedure. The results determine what products to order in what quantities with which suppliers in which periods.

This paper presented the effectiveness of clustering data – the results from when the Fuzzy Kernel Compactness and Separation (FKCS) were proposed to compare with the performance of the Kernel Noise Clustering (KNC). The FKCS and KNC had largely been developed through basic steps of the Fuzzy Compactness and Separation (FCS) and Noise Clustering (NC) respectively. Ring data sets were used to test the effectiveness of clustering data between the FKCS and the KNC. In doing so the kernel function – the kernel gaussian function and the kernel polynomial function were used as testors. Along those processes noise data was added in order to test noise-resistant capacity of Fuzzy Kernel C-Mean (FKCM) FKCS and KNC. The results of the tests provided quite knowledgable understanding that when trying out with the ring datasets the FKCS with kernel gaussian function and kernel polynomial function could perform effectively clustering data. Moreover the KNC was even more robust and could work out better with noise data than the FKCM or the FKCS could.