Supplier selection and order allocation with green criteria: An MCDM and multi-objective optimization approach

Green and traditional criteria for supplier selection were split into two sets.Two bi-objective and one multi-objective optimization models were proposed.The models use a combination of three tools: AHP, Fuzzy TOPSIS and optimization.The results show that the proposed approach is more flexible than the existing ones. This research provides a decision-making tool to solve a multi-period green supplier selection and order allocation problem. The tool contains three integrated components. First, fuzzy TOPSIS (technique for order of preference by similarity to ideal solution) is used to assign two preference weights to each potential supplier according to two sets of criteria taken separately: traditional and green. Second, top management uses an analytic hierarchy process (AHP) to assign a global importance weight to each of the two sets of criteria based on the strategy of the company and independently of the potential suppliers. Third, for each supplier, the preference weight obtained from fuzzy TOPSIS regarding the traditional criteria is then multiplied by the global importance weight of the set of traditional criteria. The same is done for the green criteria. The two combined preference weights obtained for each supplier are then used in addition to total cost to select the best suppliers and to allocate orders using multi-period bi-objective and multi-objective optimization. The mathematical models are solved using the weighted comprehensive criterion method and the branch-and-cut algorithm. The approach of this research has a major advantage: it provides top management with flexibility in giving more or less importance weight to green or traditional criteria regardless of the number of criteria in each category through the use of AHP, which reduces the effect of the number of criteria on the preference weight of the suppliers. Contrary to the case in which each supplier is evaluated on the basis of all criteria at the same time, the proposed approach would not necessarily result in a supplier with poor green performance being ranked among the best for a situation in which the number of green criteria is smaller than the number of traditional criteria. In this case, the final ranking would mainly depend on the global weight of the green criteria set given by the top management using AHP as well as on the ranking of the supplier in terms of green criteria obtained from fuzzy TOPSIS. Extensive numerical experiments are conducted in which the bi-objective and multi-objective models are compared and the effect of the separation between green and traditional criteria is investigated. The results show that the two optimization approaches provide very close solutions, which leads to a preference for the bi-objective approach because of its lower computation time. Moreover, the results confirm the flexibility of the proposed approach and show that combining all criteria in one set is a special case. Finally, a time study is performed, which shows that the bi-objective integer linear programming model has a polynomial computation time.