Efficient linear combination method for multi-objective problems with convex polyhedral preference functions

At present, the most commonly used method for multiobjective linear programming (MOLP) is goal programming (GP) based methods but these methods do not always generate efficient solutions. Recently, an efficient GP-based method, which is called reference goal programming (RGP), has been proposed. However, it is limited to only a certain target point preference, which is too rigid. The more flexible preferences are preferred in many practical problems. In this research, an effective linear combination method for MOLP problems with convex polyhedral preference functions is proposed. The concept of the convex cone is used to formulate convex polyhedral preference functions and the existing reference point method (RPM) is integrated to ensure the efficiency of the solution of the problem. The formulated model can be solved by existing linear programming solvers and can find the satisfactory efficient solution. The convex polyhedral function enriches the existing preferences for efficient methods and increases the flexibility in designing preferences for decision makers. For some situations, it is difficult for the decision maker to state the certain aspiration level for each objective function. Fuzzy goals, which can be considered as convex polyhedral preference functions, can be used to represent aspiration levels with respect to linguistic terms.