Constrained production schedule optimization of output-normalized expenditures under uncertainty in shift duration and energy price forecasts

Variability in day-ahead energy prices offers the potential for reductions in energy expenditures through flexible load planning in which production is shifted to periods of low predicted energy prices. In this paper we present a means of optimizing a production run for the following day and week given basic constraints on the start and end times of production shifts as well as the total production within a specified time frame (planning horizon). The general problem is a difficult, non-convex optimization problem over stochastic variables that can only be solved in its original form by global optimization and Monte Carlo simulation techniques. However, reasonable approximations to the original problems render it more tractable. By linearizing the energy price forecasts and the plant consumption profile, as well as discretizing the stochastic variables involved, we can reduce the planning problem to a mixed integer quadratic programming (MIQP) problem, with the customary linear bounds.