An improvement in possibilistic linear programming approach for imprecise production/transportation planning decisions

In many existing applications of possibilistic linear programming (PLP) model, the decision makers (DM) are asked to specify the positive ideal solution (PIS) and negative ideal solution (NIS) for defining the linear membership function proposed by Zimmermann. In practice, this is a real difficulty for an ordinary DM without possessing acute sense of arithmetic operation and adequate comprehension of PLP model. Furthermore, this task is obviously subjective and will influence the search route of the solution process via the linear membership functions. This study provides an objective method to specify appropriate PIS and NIS for defining efficient linear membership functions so as to rapidly approach a better compromise solution, and also presents a simple way for further improvement of the compromise solution to reach a satisfactory solution. The proposed approaches aim to facilitate the decision making process and promote computational efficiency as well as improve the compromise solution for the PLP method. Additionally, an integrated production/transportation planning decision (PTPD) problem is used to demonstrate the feasibility of applying the proposed methods to real industrial case. Not only the simplicity and objectivity in specifying PIS and NIS but also the computational efficiency, the results of this study show definite advantage of the proposed methods in solving PLP problem.