A robust model for the lot-sizing problem with uncertain demands

We consider a lot-sizing problem with set-ups where the demands are uncertain, and propose a novel approach to evaluate the inventory costs. An interval uncertainty is assumed for the demands. Between two consecutive production periods, the adversary chooses to set the demand either to its higher value or to its lower value in order to maximize the inventory (holding or backlog) costs. A mixed-integer model is devised and a column-and-row generation algorithm is proposed. Computational tests based on random generated instances are conducted to evaluate the model, the decomposition algorithm, and compare the structure of the solutions from the robust model with those from the deterministic model.