Sustainability in supplier selection and order allocation: combining integer variables with Markowitz portfolio theory

This research presents a decision support methodology for the multi-criteria supplier selection and order alloca-tion problem. The proposed approach supports purchasing managers in assembling mid-term supplier portfolios while making them aware of the trade-offs between the supplier sustainability, the purchasing costs, and the overall supply risk. First, we propose a multi-objective optimization model with three objectives: to maximize the supplier sustainability, to select the supplier portfolio with the lowest purchasing costs, and to minimize the supply risk. Our model extends existing mathematical approaches that follow the portfolio theory fathered by H. Markowitz by integrating the aspect ‘risk’ into the supplier selection problem. Secondly, since we allow for integer variables in our model—in contrast to the classical Markowitz portfolio theory—we use the ε-constraint method to visualize the efficient surface. The possibility of considering the non-dominated set of supplier port-folios is advantageous for purchasing managers as they gain a picture of the different optimal supplier portfoli-os and are able to analyze the trade-offs between the different purchasing goals before making a decision. Fi-nally, we illustrate the applicability of the proposed methodology in a real-world supplier selection and order allocation case from the automotive industry. In the example case, we identify 1,754 optimal supplier portfolios that may be assembled based on the eight available suppliers. Our analyses show that each optimal portfolio consists of two suppliers, with one specific supplier being included in each portfolio. Furthermore, four suppliers are not part of any optimal solution.