Abstract
This research presents a linear solution method for multi-product and multi-period aggregate production planning (APP) with fuzzy goals. Two main objectives of aggregate production planning: the maximization of profit and the minimization of changes of workforce level are defined by fuzzy goals. Fuzzy goals are quantified by concave polyhedral membership functions, which are directly gotten from the decision maker or from linear approximation of continuous concave membership functions. Forecasted demands are also considered to be fuzzy. Trapezoidal membership functions are used to represent them. Linear coordination method, which has been shown its advantages in formulating convex polyhedral penalty functions, is applied to transform a multiple objective APP problem with fuzzy goals and demands to the crisp optimization problem using only linear equations by converse consideration on the maximization problem of concave polyhedral membership functions as the minimization problem of convex polyhedral penalty functions. The efficient linear coordination model is proposed in this research. A satisfactory efficient solution, which is also close to the decision maker's requirements, can be obtained. This model can be easily solved by the existing linear programming solvers. The proposed model is more appropriate than non-fuzzy formulations in terms of reflecting a realistic problem. Moreover, preference information from the decision maker can be clearly exhibited using concave polyhedral membership functions, which have not been used in existing APP problems. Finally, a numerical example is illustrated and briefly discussed.
