Modeling a stochastic multi-objective, multi-site, multi-mode, and multi-item supplier selection and order allocation problem

Supplier selection and order allocation are important issues in supply chain management. Several features differentiate this research from other studies. The two-echelon supply chain network studied in this research comprises of suppliers and production centers. The supply chain model is a multi-site, multi-mode, and multi-item model which incorporates multiple sites for production centers, multiple transportation modes, and multiple purchased items from suppliers. In this model, demand, delivery delay, and percentage of defective items are deemed stochastic parameters. It is assumed that these uncertain parameters have normal distributions with known means and standard deviations. The most significant contribution of this research is incorporating uncertainty with two indicators of mean and standard deviation into a multi-objective model for the supplier selection and order allocation problem. To deal with stochastic demand, the chance constraint approach is applied. The multi-objective optimization model aims to minimize purchasing cost, delivery delay, and defective items. To solve this model, first, a mixed-integer formulation is established to address the order allocation problem. Then, after using the epsilon constraint method, the Torabi-Hassini approach is used to transform the multi-objective model into an equivalent single-objective model. Real data from poultry and dairy industries are used to evaluate the model performance. Sensitivity analysis shows that the most improvements in the objective functions occur when the means and standard deviations of delivery delay and percentage of defective items for suppliers and transportation modes are decreased simultaneously.