Generating a supply chain plan includes accessing data describing a supply chain network having buffers. Each buffer is operable to store items and is associated with a corresponding time variable. The supply chain network is constrained by a constraint. A linear programming problem is generated for the supply chain network. The linear programming problem is approximated by discretizing the time variables of the buffers to yield discretized time variables and by relaxing the constraint to yield a relaxed constraint. An optimized supply chain plan is calculated for the approximated linear programming problem. The optimized supply chain plan describes a quantity of items at each buffer for at least one time value of the corresponding time variable. The optimized supply chain plan is adjusted to satisfy the constraint.