An updated two-step method for solving interval linear programming: A case study of the air quality management problem

Many real-world problems occur under uncertainty. In this paper, we consider interval linear programming (ILP) which can be used to tackle un certainties. Several methods have been proposed by researchers, such as the best and worst cases, Two-step method (TSM), improved TSM, ILP, improved ILP, three-step method, and robust two-step method. First, we define feasibility and optimality conditions in ILP models and review some solving methods shortly, and then show that some solutions of the TSM method are not feasible. Therefore, we propose an updated TSM method (namely, UTSM) by considering the feasibility and optimality conditions. In this paper, the UTSM method was applied to identify the reduction of aerosols by using two controllers with a minimized cost to demonstrate its application under uncertainty. Compared with other methods, the solutions obtained through ILP were presented as interval, which can provide intervals for the decision variables, objective function, and decision-makers. Therefore, the decision-makers can make the best decision based on the obtained solutionsthrough ILP, and then identify desired plans for aerosol-emission control under uncertainty.