Dynamic green supplier selection and order allocation with quantity discounts and varying supplier availability

•Green and traditional criteria for supplier selection were split into two sets.•A bi-objective optimization model with quantity discounts was formulated.•The model allows the available suppliers to vary from period to period.•The model uses a combination of three tools: AHP, fuzzy TOPSIS and optimization.•The numerical results recommend ranking the suppliers only once for all periods.

This paper aims to solve a multi-period green supplier selection and order allocation problem with all-unit quantity discounts, in which the availability of suppliers differs from one period to another. The proposed approach involves three stages. In the first stage, decision makers use fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) to assign two preference weights to every potential supplier based on the supplier's performance in two sets of criteria considered separately: traditional and green. In the second stage, top management uses the analytic hierarchy process to assign an importance weight to each of the two sets of criteria based on the organization's strategy. The outputs of the first and second stages serve as inputs for a single-product bi-objective integer linear programming model with deterministic demand that takes into account all-unit quantity discounts and a varying number of suppliers in each period of the planning horizon. We implement the proposed mathematical model in MATLAB R2014a software using the weighted comprehensive criterion method and the branch-and-cut algorithm. Statistical analysis helps determine the most suitable ranking approach for suppliers when their availability changes in each period. This paper presents a numerical comparison between two settings: the first considers all-unit quantity discounts, and the second does not. Moreover, a time study shows that the proposed bi-objective integer linear programming model has an exponential computation time.