The generation of synthetic populations through simulation methods is an important research topic and has a key application in agent-based modeling of transport and land use. The next step in this research area is the generation of complete synthetic households; this research area requires some way to associate synthetic persons with household positions. This work formulated the person to the position matching problem as a bipartite graph matching and tested two models for determining match utility with data from the 2000 Swiss census. The functions tested were both multinomial logit models, one based on the household size attribute and the other on household type. Synthetic persons were matched into the head position of real households, and then the remaining population was used to run a second match with a separately calibrated version of the size choice model for the spouse position. This method is a long list-based approach that keeps the original marginal consistent. Results show that the size choice model returns the best results for head and spouse positions, although both models provide a good match quality as measured by the distributions of individual attributes in real and matched populations as well as the distributions of unique attribute combinations. Possible extensions include matching to other household positions and evaluating the performance of these synthetic households in modeling applications.