An integrated stochastic EPQ model under quality and green policies: generalised cross decomposition under the separability approach

In this paper, a bi-objective multi-product constrained and integrated economic production quantity model is designed by considering the quality control and green production policies. The aforementioned model comes with stochastic constraints. Moreover, to create a kind of green approach policy, tax cost of greenhouse gas emissions and limitations are considered. The aim of this study is to optimise the total inventory cost and the total profit, while the stochastic constraints are satisfied. Due to the inconsistency of objectives, an Lp-metric function is utilised to integrate and achieve a single objective function. Therefore, the mathematical formulation of the problem is bi-objective stochastic mixed integer nonlinear programming large scale and hard to solve. Accordingly, generalised cross decomposition under the separability approach is utilised as an effective algorithm for global optimisation. Moreover, sensitivity analysis revealed that increasing the cost function weight versus decreasing the profit function weight leads to the change rate of the integrated-objective function becomes positive with a steep slope.

Automated summary

This study presents a bi-objective multi-product, quality control, and green production policy integrated production quantity model, aiming to optimize inventory costs and profits. The mathematical formulation involves a challenging problem of bi-objective stochastic mixed integer nonlinear programming, where generalised cross decomposition is applied for global optimization. Sensitivity analysis indicates an increase in cost function weight and a decrease in profit function weight lead to a steep increase in the integrated-objective function.