(761b) A Multistage Stochastic Programming Approach to Long-Term Electricity Procurement for Large Industrial Consumers

Zhang, Q., Carnegie Mellon University
Pinto, J. M., Linde plc
Grossmann, I., Carnegie Mellon University
Due to the increasing volatility in electricity price, managing the procurement of electricity in power-intensive business has become a major challenge. Large industrial electricity consumers often enter into long-term bilateral contracts with favorable rates; however, such power contracts typically require the consumers to commit themselves to the amount that they are going to purchase months in advance. The vast majority of existing works on electricity procurement assume that the electricity demand is given, which implies that a separate production planning problem has already been solved, from which the electricity demand is determined. As shown in recent works on industrial demand side management (Zhang & Grossmann, 2016), this sequential approach is likely to be suboptimal.

In this work, we optimize long-term electricity procurement and production planning simultaneously, which poses two additional challenges: (1) how to account for time-sensitive electricity prices that change on an hourly basis while optimizing over a planning horizon that may span multiple months or years; (2) how to consider uncertainty in product demand, which can cause major disruptions in the production and electricity procurement plans. In order to solve this problem, we propose a multiscale multistage stochastic programming model in which a one-year planning horizon is divided into seasons, with each season represented by two characteristic weeks; also, each season corresponds to a stage at which the demand for that season is revealed. When applied to real-world industrial problems, the proposed approach results in model instances with tens of millions of variables and constraints. In order to solve these large-scale instances, we apply a decomposition algorithm based on the concept of progressive hedging.

We emphasize the importance of computing the value of stochastic solution (VSS) when evaluating the results of the model. The VSS was developed for two-stage stochastic programming and has rarely been applied to the multistage case. In this work, we apply the definition of VSS for multistage problems (VMSS) proposed by Escudero et al. (2007) and also extend it to define a VSS for applying a two-stage approximation of the problem (VTSS). When applied to an illustrative example, the results show that high VMSS can be achieved if the level of uncertainty is high, yet the VMSS are only marginally higher than the VTSS. Similar results have been observed when applying the proposed framework to an industrial air separation case.


Escudero, L. F., Garín, A., María, M., & Pérez, G. (2007). The value of the stochastic solution in multistage problems. Top, 15, 48–64.

Zhang, Q., & Grossmann, I. E. (2016). Enterprise-wide optimization for industrial demand side management: Fundamentals, advances, and perspectives. Chemical Engineering Research and Design, 116, 114–131.