Violation analysis on two-step method for interval linear programming

In many real world problems, system parameters or model coefficients may be bounded between lower and upper bounds due to a variety of uncertainties. Over the past decades, intensive research efforts have focused on interval linear programming (ILP) to tackle such uncertainties. As one of the most popular methods for solving ILP problems, Two-Step Method (TSM, proposed by Huang et al. in 1995) allows uncertain information to be directly communicated into the optimization process and resulting solutions such that decision alternatives could be generated through the interpretation of interval solutions. However, part of optimum solution points obtained through TSM may go beyond the decision space in some cases. This phenomenon, referred to as solution violation, may mislead decision makers to unreasonable policies, plans, or strategies which play important roles in the social and economic development. Therefore, this study first investigates and identifies the essential cause for the solution violation of TSM. Following that, an improved solution method (namely, ITSM) is proposed to avoid resulting violation by introducing extra constraints in the solving process. A numeric example is then presented to demonstrate the effectiveness of ITSM in handling solution violation.