Solving a stochastic lot-sizing problem with a modified sample approximation approach

We consider an optimization problem arising in the context of industrial production planning, namely the single-item capacitated lot-sizing problem. We focus on the case where the customer demand to be satisfied by the production plan is subject to uncertainty and model the resulting stochastic optimization problem as a joint chance-constraint program. We propose a new extension of the previously published sample approximation method to solve this difficult optimization problem. The main advantage of the proposed extension is that it does not require the introduction of additional binary variables in the mixed-integer linear programming formulation. We then present some preliminary computational results on small-size instances of the problem showing that the proposed approach leads to significantly reduced computation times as compared to the previously published sample approximation method.