A Meta-Goal Programming Model with Lexicographic Achievement Function for Multi-Product Systems

Abstract

Goal programming approach is used for solving multi-objective optimization problems that balances the trade-off between conflicting goals. The meta-goal programming framework gives the decision maker the ability to add a new set of goals which are in some sense goals of the initial goals. Meta-GP model is formulated by adopting any of the alternative goal programming variants (i.e. weighted, lexicographic or minmax etc.) in its achievement function. The particular variant used in meta-GP depends on the structure of the problem being solved. In this paper we present a meta-goal programming model with lexicographic meta-achievement function and mixed-integer variables for the achievement of management’s goals in multi-product manufacturing systems. The formulated meta-goal programming model was illustrated with data collected from a multi-product company (Nigeria Breweries). With eight initial set of goals and three meta-goals, the results obtained using the LINGO optimization software showed that the meta-goal programming model with lexicographic meta-achievement function gives a more efficient solution when compared to that of a lexicographic GP model. The solution of the meta-goal programming model with lexicographic meta-achievement function was also checked for lexicographic redundancy and it was seen that the solution was not redundant. Hence the model was considered valid. A comparison of the solution of the meta-goal programming model with the lexicographic meta-achievement function with that of a meta-GP model with weighted meta-achievement function also showed that the former gives more satisfactory solution.