Robust Possibilistic Production Planning Under Budgeted Demand Uncertainty

The paper deals with a production planning problem, that is a version of the capacitated single-item lot sizing problem with backordering, under uncertain cumulative demands, modeled by fuzzy intervals centered around the cumulative demand nominal values. Their membership functions are regarded as possibility distributions for the values of the unknown cumulative demands. Furthermore, the budgeted uncertainty model is assumed, in which at most a specified number of cumulative demands can deviate from their nominal values at the same time. In order to choose a robust production plan that optimizes against plausible cumulative demand scenarios, under the model assumed, possibilistic criteria are adopted. Polynomial linear programming based methods for finding such robust production plans are proposed, showing in this way that the problem under consideration is not much computationally harder than its deterministic counterpart. Some results of computational tests are presented.