Bi-objective inventory allocation planning problem with supplier selection and carbon trading under uncertainty

Concern is growing that business enterprises focus primarily on their economic activities while disregarding the adverse environmental and social effects of these activities. To contribute to the literature on this matter, this study investigates a novel bi-objective inventory allocation planning problem with supplier selection and carbon trading across multiple periods under uncertainty. The concepts of a carbon credit price and a carbon cap are proposed to demonstrate the effect of carbon emissions costs on inventory allocation network costs. Demands of manufacturers, transport price, and defect rate of materials that should be rejected are set as random variables. We combine normalized normal constraint method, differential evolution algorithm, and uncertainty simulation to deal with the complex model. One representative case shows the effectiveness and practicability of this model and proposed method. The Pareto frontier is generated by solving the bi-objective model. We extend the results of numerical examples in large scale problems, and compare the solution method results with exact solutions. The environmental objective across the inventory allocation network varies with changes of the carbon cap and the carbon credit price.