Solving Robust Production Planning Problem with Interval Budgeted Uncertainty in Cumulative Demands

In this paper, a production planning problem with inventory and backordering levels is discussed. It is assumed that cumulative demands in periods are uncertain and an interval uncertainty representation with continuous budget is used to model this uncertainty. The robust minmax criterion is applied to compute an optimal production plan. A row and column generation algorithm is constructed for solving the problem. Results of some computational tests are shown which demonstrate that the algorithm is efficient for the instances with up to 100 periods and returns solutions that are robust against the uncertainty in demands.