In 1981, Borsik and Doboš studied in depth the problem of how to merge, by means of a function, a collection (not necessarily finite) of distance spaces in order to obtain a single one as a result [J. Borsik, J. Doboš, On a product of metric spaces, Math. Slovaca 31 (1981) 193-205]. Later on, Herburt and Moszyńska studied the same problem for the case of normed linear spaces, inspired by the fact that every norm induces in a natural way a distance on a linear space, and analyzed the relationship between the both aforenamed problems [I. Herburt, M. Moszyńska, On metric products, Colloq. Math. 62 (1991) 121-133]. More recently, Romaguera and Schellekens introduced a mathematical approach, based on the notions of asymmetric distance and asymmetric normed linear space, which is suitable for the complexity analysis of programs and algorithms in Computer Science [S. Romaguera, M. Schellekens, Quasi-metric properties of complexity spaces, Topology Appl. 98 (1999) 311-322]. In this paper, motivated by the importance of the information fusion techniques in Artificial Intelligence and by the utility of asymmetric distances and asymmetric norms in Computer Science, we study the Herburt and Moszyńska problem for asymmetric normed linear spaces. In particular we give a general description of how to combine a collection (not necessarily finite) of asymmetric normed linear spaces in order to obtain a single one as output and, in addition, we clear up the relationship between this problem and its analogous of combining asymmetric distance spaces which has been already explored by Mayor and Valero [G. Mayor, O. Valero, Aggregation of asymmetric distances in computer science, Inform. Sci. 180 (2010) 803-812]. Furthermore, it is shown that the asymmetric norms employed, in the spirit of Romaguera and Schellekens, in complexity analysis can be retrieved as a particular case of the developed theory. The last fact opens the possibility of applying a wide range of properties from the general aggregation theory in Artificial Intelligence to the complexity analysis of programs and algorithms in Computer Science.