A simple augmented ∈-constraint (SAUGMECON) method is put forward to generate all non-dominated solutions of multi-objective integer programming (MOIP) problems. The SAUGMECON method is a variant of the augmented ∈-constraint (AUGMECON) method proposed in 2009 and improved in 2013 by Mavrotas et al. However, with the SAUGMECON method, all non-dominated solutions can be found much more efficiently thanks to our innovations to algorithm acceleration. These innovative acceleration mechanisms include: (1) an extension to the acceleration algorithm with early exit and (2) an addition of an acceleration algorithm with bouncing steps. The same numerical example in Lokman and Köksalan (2012) is used to illustrate workings of the method. Then comparisons of computational performance among the method proposed by Özlen and Azizoǧlu (2009), Özlen et al. (2012), the method developed by Lokman and Köksalan (2012) and the SAUGMECON method are made by solving randomly generated general MOIP problem instances as well as special MOIP problem instances such as the MOKP and MOSP problem instances presented in Table 4 in Lokman and Köksalan (2012). The experimental results show that the SAUGMECON method performs the best among these methods. More importantly, the advantage of the SAUGMECON method over the method proposed by Lokman and Köksalan (2012) turns out to be increasingly more prominent as the number of objectives increases.