A two-stage modeling and solution framework for multisite midterm planning under demand uncertainty

A two-stage, stochastic programming approach is proposed for incorporating demand uncertainty in multisite midterm supply-chain planning problems. In this bilevel decision-making framework, the production decisions are made `here-and-now' prior to the resolution of uncertainty, while the supply-chain decisions are postponed in a `wait-and-see' mode. The challenge associated with the expectation evaluation of the inner optimization problem is resolved by obtaining its closed-form solution using linear programming (LP) duality. At the expense of imposing the normality assumption for the stochastic product demands, the evaluation of the expected second-stage costs is achieved by analytical integration yielding an equivalent convex mixed-integer nonlinear problem (MINLP). Computational requirements for the proposed methodology are shown to be much smaller than those for Monte Carlo sampling. In addition, the cost savings achieved by modeling uncertainty at the planning stage are quantified on the basis of a rolling horizon simulation study.