Association studies in populations relate genomic variation among individuals with medical condition. Key to these studies is the development of efficient and affordable genotyping techniques. Generic genotyping assays are independent of the target SNPs and offer great flexibility in the genotyping process. Efficient use of such assays calls for identifying sets of SNPs that can be interrogated in parallel under constraints imposed by the genotyping technology. In this paper, we study problems arising in the design of genotyping experiments using generic assays. Our problem formulation deals with two main factors that affect the genotyping cost: the number of assays used and the number of PCR reactions required for sample preparation. We prove that the resulting computational problems are hard, but provide approximate and heuristic solutions to these problems. Our algorithmic approach is based on recasting the multiplexing problems as partitioning and packing problems on a bipartite graph. We tested our algorithmic approaches on an extensive collection of synthetic data and on data that was simulated using real SNP sequences. Our results show that the algorithms achieve near-optimal designs in many cases and demonstrate the applicability of generic assays to SNP genotyping.