Abstract: A multi-objective, multi-period and multi-product aggregate production planning (APP) problem with uncertain demand and uncertain parameters, such as operating cost, production capacity and so on, is studied. An interval goal programming model is developed through introducing interval numbers to represent uncertainties in the APP problem, in which two objectives are taken into consideration, one to minimize the total production cost and the other to maximize machine utilization rate. To solve the uncertain model, the theory of interval programming and the possibility definition based on interval ordinal relation are adopted to transform the uncertain model into its equivalent crisp one, and Lingo software is used to solve the model. The approach overcomes the deficiency of traditional uncertain optimization methods in obtaining precise probability distributions and fuzzy membership functions. In addition, the approach is able to interactively analyze impacts of different confidence levels on the objective function according to the decision maker's preference. Theoretical basis is provided for decision makers to make a rational production plan in uncertain environment. Finally, an industrial example is used to illustrate the validity and flexibility of the proposed method.

Key words: parameter uncertainty, production planning, interval number, goal programming