Satisfactory Efficient Linear Coordination Method forMulti-Objective Linear Programming Problems withConvex Polyhedral Preference Functions

At present, the most commonly used satisficing method for multi-objective linear programming (MOLP) is the goal programming (GP) based method but this method does 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. More flexible preferences such convex polyhedral preferences are preferred for many practical problems. In this research, a satisfactory effective linear coordination method for MOLP problems with convex polyhedral preference functions is proposed. The concept of the convex cone is used to formulate the convex polyhedral preference function and the existing lexicographic model of the 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.

In some situation, it is difficult for a decision maker to state a certain desirable level for each objective function. Applying fuzzy goal to capture the decision maker’s preferences has the advantage of allowing for vague aspirations, which can be considered as convex polyhedral preference functions. The satisfactory efficient linear coordination method can be applied to obtain an efficient solution, which is also close to the decision maker’s requirements.