In energy-intensive industries, the traditional strategy is to schedule the production first. From the production schedule, the demand for energy is predicted and an optimization of the energy-supply cost is performed. The academic approach is to combine all the production and energy-cost related constraints into a single monolithic problem. In contrast, in this work a different approach is proposed. The energy-cost optimization problem is solved using Multiparametric Programming (mp), separately from the scheduling problem. Based on the solution from the mp-MILP (Mixed Integer Linear Programming) problem, several production scheduling problems with sensitivity information from the mp-MILP solution embedded can be solved in parallel in order to find the system-optimal solution. The approach is tested on realistic data instances of a stainless-steel process and obtains the optimal solution. However, the computational performance is strongly limited to very small instances due to limitations of the mp-MILP solvers.
Efficient frameworks for scheduling of energy-intensive industries are important enablers for the industrial implementation of the demand-side management concept (DSM). DSM enables enterprises to cut their energy cost as well as to support the grid in dealing with fluctuating availability of energy. In this work, we present an improvement of the energy-aware production scheduling strategy reported in Hadera et al.,(1) which is based upon a continuous-time scheduling formulation. The improvement concerns the modeling of the coupling between the scheduling problem and the computation of the energy bill. The resulting optimization problem is solved by the heuristic bilevel decomposition from Hadera et al.(2) Numerical studies showed that although the proposed formulation and heuristic decomposition does not guarantee to obtain the global minimum it does provide good quality solutions within reasonable solution times. The new energy-awareness formulation reduces the number of binary variables and constraints and results in shorter solution times.