Numerous high-throughput genomics assays require the amplification of a large number of genomic loci of interest. Amplification is cost-effectively achieved using several short single-stranded DNA sequences called primers and polymerase enzyme in a reaction called multiplex polymerase chain reaction (MP-PCR). Amplification of each locus requires that two of the primers bind to the forward and reverse DNA strands flanking the locus. Since the efficiency of PCR amplification falls off exponentially as the length of the amplification product increases, an important practical requirement is that the distance between the binding sites of the two primers should not exceed a certain threshold. In this paper we study MP-PCR primer set selection with amplification length constraints from both theoretical and practical perspectives. Our contributions include an improved analysis of a simple yet effective greedy algorithm for the problem, and a comprehensive experimental study comparing our greedy algorithm with other published heuristics on both synthetic and genomic database test cases.