Optimizing a bi-objective vendor-managed inventory of multi-product EPQ model for a green supply chain with stochastic constraints

In this paper, a bi-objective multi-product single-vendor single-buyer supply chain problem is studied under green vendor-managed inventory (VMI) policy based on the economic production quantity (EPQ) model. To bring the model closer to real-world supply chain, four constraints of model including backordering cost, number of orders, production budget and warehouse space are considered stochastic. In addition to holding, ordering and backordering costs of the VMI chain, the unused storage space cost is also added to the total cost of the chain. To observe environmental requirements and decrease the adverse effects of greenhouse gases emissions (GHGs) on the earth and human’s life, green supply chain is utilized to reduce the GHGs emissions through storage and transportation activities in the second objective function. Three multi-objective decision making methods namely, LP-metric, Goal attainment and multi-choice goal programming with utility function (MCGP-U) are implemented in different sizes to solve the presented model as well. Two multi-criteria decision making (MCDM) approach and statistical analysis are applied to compare the outcomes of three proposed solving methods. GAMS/BARON software is utilized to minimize the values of the objective functions. At the end, numerical examples are presented to represent the application of the mentioned methodology. To come up with more insights, sensitivity analysis is executed on the main parameters of proposed model.