Late Acceptance Hill Climbing (LAHC) is a recent metaheuristic in the realm of local search based procedures. The basic idea is to delay the comparison between neighborhood solutions and to compare new candidate solutions to a solution having been current several steps ago. The LAHC was first presented at the PATAT 2008 conference and successfully tested for exam timetabling, the traveling salesman problem (TSP) and the magic square problem and the results seemed extraordinary. The purpose of this paper is to analyze the behavior of the method and to provide some extended understanding about its success and limitations. To do so, we investigate the method for a generalized version of the TSP, the traveling purchaser problem.