An Interval Programming Approach for Multi-period and Multi-product Aggregate Production Planning by Considering the Decision Maker's Preference

This paper presents an interval programming approach for solving a typical multi-period and multi-product aggregate production planning (MPMP-APP) problem. Firstly, a MPMP-APP model based on interval programming is developed, in which the decision maker's risk preference is taken into consideration. Next, to solve the MPMP-APP model based on interval numbers, the original uncertain objective function is replaced by two crisp objective functions which are equivalent to minimizing the interval value and the deviation of the uncertain objective function, respectively, and uncertain constraints are transformed into their corresponding crisp equivalents by using the possibility degree based on six possible relations between two intervals. And then, the linear weighted sum method is adopted to transform the above two-objective model into a single one which can be solved by LINGO software. Finally, an industrial example is used to illustrate the validity and flexibility of the proposed method. It is expected that this study can provide a useful reference for decision makers to make a rational production plan in uncertain environment.