Preprocessing techniques and column generation algorithms for stochastically efficient demand

We construct a discrete–time, multi–period replenishment plan that integrates the inventory, production and distribution functions and that satisfies the conditions of a very demanding cycle service level. The corresponding optimization problem takes the form of a very complex mixed–integer stochastic program. We develop a new enumerative algorithm that identifies the stochastically efficient demand trajectories at an authorized level of stockout, and derive three algorithmic preprocessing techniques used to discriminate the above trajectories. The application of the enumerative and preprocessing algorithmic approaches transforms the stochastic program into a disjunctive integer program solved through a column generation that reduces the risk of a bottleneck in the distribution resources of the supply chain. Computational results evaluate the efficiency of the algorithmic developments proposed in this paper, and attest the quality and robustness of the solution method. The solution methodology is validated on a real–life problem.