MILP reformulation of the multi-echelon stochastic inventory system with uncertain demands

It is shown that by reformulating the three-stage multiechelon inventory system with specific exact linearizations, larger problems can be solved directly with mixed-integer linear programming (MILP) without decomposition. The new formulation is significantly smaller in the number of continuous variables and constraints. An MILP underestimation of the problem can be solved as part of a sequential piecewise approximation scheme to solve the problem within a desired optimality gap.