Summary: We consider the heuristic of Sequential Location and Allocation (SLA) which is commonly used to solve location problems. Our focus is on planar and network median and center problems. We first prove that for \(p\)-median and \(p\)-center problems, the SLA heuristic can generate solutions with values as high as for the corresponding 1-median or 1-center problem in the worst case scenario. We then consider combining repeated applications of SLA with statistical estimation of the globally optimal solution using the Weibull distribution. We present computational experience for several different types of problems, and compare the statistical method to bounding procedures suggested in the literature. For large problems with many SLA equilibrium points, our computational results suggest that statistical estimation provides a good estimate of the globally optimal solution.