Vehicle capability is one of the factors that constrain the set of transportation options available for personal transportation. The capacity for carrying passengers and cargo is of particular interest when energy consumption is considered, because the use of more efficient vehicles may be limited for trips with higher load requirements. This paper presents a method for considering trip capacity requirements when the available vehicles are assigned to the trips on a household activity schedule. A constraint-based vehicle assignment model that uses the trip data from the 2001 National Household Travel Survey as an example is introduced. Initial results from the analysis of these data show that by optimally assigning existing vehicles to trips, the average value of potential fuel savings ranges from 5% to 23%, depending on the size and vehicle type composition of the household fleet. Households with more vehicles in the fleet and a more diverse range of vehicles to choose from are able to achieve greater fuel savings than those with more homogeneous fleets. Considering the extent to which household vehicle assignment decisions were already consistent with the minimization of fuel consumption, in 2001 actual household vehicle assignment was, on average, only slightly better than random.