Group decision making with multiple criteria is the most popular method for ranking a set of alternatives. In this regard, all alternatives are compared based on a common criteria set. Meanwhile, decision makers sometimes encounter special situations, for example, having to select from among a set of alternatives without a set of criteria or with a set of criteria that are grouped/related to various alternatives. Thus, it may be impossible to select from among a set of alternatives using typical methods. Hence, in this study, a new, modified VIKOR method is proposed to address the lean tool selection problems in manufacturing systems. In this study, a model was developed to help practitioners improve their ability to solve problems when the possible solutions have their own individual criteria. In fact the modified VIKOR method can be applied to rank alternatives in threefold: alternatives with common criteria, without common criteria, with integrated common, and uncommon criteria. This paper offers numerical examples of the model, using a case study to illustrate an application of the proposed model and properly assess the validity of this new method. The results demonstrate the usefulness and effectiveness of the modified new method. The model covers the lack existing in the current literature to assess effectiveness of applying lean tools.