PurposeThe purpose of this paper is to further advance an existing supplier evaluation model for the purpose of identifying those supplier relations which predominantly threaten or worsen a company's performance. A defined basic set of parameters to determine complexity facilitates the identification of critical locations within a supply network (SN) under certain business conditions.Design/methodology/approachThis paper is based on a structured literature review in scientific periodicals in logistics/supply chain management between 2000 and 2009. Articles are analysed based on a structured framework and the identified complexity parameters are operationalised using quantitative and summable measures. The conceptual model is applied within a multiple case study in the Austrian agricultural industry.FindingsThis paper illustrates how complexity in SNs can be operationalised in a company‐specific configuration in order to achieve concrete managerial recommendations. Hence, the model allows evaluating SN‐partners based on selected parameters to determine the contribution of a single partner to the overall complexity.Research limitations/implicationsDue to the literature review executed and the case study approach chosen, the research may lack generalisability. Therefore, continued validation by means of implementing a greater amount of use cases in other companies and industries is advisable.Practical implicationsApplying the model, a company is able to determine tier‐1 to tier‐n suppliers which are predominantly affecting its business from a complexity perspective.Originality/valueUnlike typical current complexity evaluation approaches, the proposed model respects rapid and continuous applicability, profound conceptualisation and practical feasibility.