Electrical power costs are the major operating expense for many power-intensive processes, such as air separation plants and cement plants. Since electricity markets became deregulated in the 1990s, prices have been subject to hourly as well as seasonal variations. These issues are likely to become more acute as renewable sources of energy like wind and solar are introduced for power generation and expected to grow not least due to the disaster at the Fukushima nuclear plant. From an industrial consumer's point of view, this has introduced a considerable amount of uncertainty and variability in its short-term operating expenses, which in turn affects the long-term strategic capacity planning.
Multi-period capacity planning for continuous multi-product plants has been widely studied in literature. Sahinidis et al. (1989) propose one of the first deterministic MILP models. Liu and Sahinidis (1996) extend the model to account for demand uncertainty. Iyer and Grossmann (1998) develop a bi-level decomposition strategy to deal with the large number of scenarios that result from uncertain demand. All these papers share the idea that in order to cover a time horizon of multiple years, the problem is divided into a number of time periods. A time period is typically several months or several years long. This implies that model parameters, such as prices, demands are assumed to be constant over one time period. However, if prices fluctuate on an hourly and seasonal basis, there is need for a more detailed scheduling model and representation of the process' feasible region.
In recent work (Mitra and Grossmann (2011)), we studied the operational problem of minimizing production costs under time-sensitive electricity prices. In this work, we integrate the operational problem with the long-term strategic capacity planning problem, which involves decisions on installing or upgrading equipment, or increasing storage capacity. The resulting full-space mixed-integer linear program (MILP) model for a single plant is computationally hard to solve due to the multi-scale nature of the problem. Hence, we propose a tailored bi-level decomposition algorithm, similar in spirit to the work by Iyer and Grossmann (1998) and You et al. (2010). The decomposition relies on solving an aggregated master problem in which design decisions are optimized, and subproblems in which operations are optimized for that design. Furthermore, to effectively deal with the multi-scale nature of the problem we represent a yearly operation by a subset of cyclic schedules. The proposed strategy allows us to solve the MILP problem to optimality within a reasonable amount of time and much faster than a full-space solution. We illustrate the performance of the proposed methodology for an air separation plant based on industrial data for different operating capacities.
Iyer, R.; Grossmann, I.E. (1998) A Bilevel Decomposition Algorithm for Long-Range Planning of Process Networks, Ind. Eng. Chem. Res.37, 474.
Liu, M. L.; Sahinidis, N. V. (1996) Optimization in process planning under uncertainty, Industrial & Engineering Chemistry Research35, 4154.
Mitra, S.; Grossmann, I.E. (2011) Optimal Production Planning under Time-sensitive Electricity Prices for Continuous Power-intensive Processes, to be submitted
Sahinidis, N.V.; Fornari, R.; Grossmann, I.E. (1989), Optimization model for long range Planning in the Chemical Industry, Comp. Chem. Eng.13, 1049-1063.
You, F.; Grossmann I.E.; Wassick, J. (2010), Multisite Capacity, Production and Distribution Planning with Reactor Modifications: MILP Model, Bilevel Decomposition Algorithm versus Lagrangean Decomposition Scheme, Ind. Eng. Chem. Res.,in press.