Lastly, we introduce a new concept, the Value of the Rolling Horizon (VoRH) to measure the closeness of different rolling horizon schemes to a perfect foresight benchmark and provide some numerical tests on it using a stylized natural gas market. One simple approach is to use a scheduling model over the entire planning time horizon, which takes into account the production capacity of the plant. However, this approach results in problems of unrealistic size, which is often computationally intractable. The method is based on iteratively solving the integrated problem in a rolling time horizon mode. In every iteration of the solution procedure, the detailed scheduling requirements are imposed only for the current or several recent planning periods.
Dimitriadis et al. (1997) presented an RTN-based rolling horizon algorithm for medium-term scheduling of multipurpose plants. Sand et al. (2000) used a rolling horizon approach, in combination with a Lagrangian relaxation algorithm, for the solution of a two-level hierarchical planning and scheduling problem. Wu and Ierapetritou (2007) decomposed the planning time horizon into three stages with various durations.
Georghiou, Tsoukalas, & Wiesemann (2019) and Postek & Hertog (2016), provide frameworks for the handling of uncertain forward parameters. The rolling-horizon approach can often be considered as a variant of a relax-and-fix heuristic, as in Stadtler (2003), where it has been applied to a difficult variant of lot-sizing. This reduction involves a better exploitation of the existing power infrastructure. Peaks of power involve several disadvantages not only for the users, but also for the energy providers and for the grid.
- Hence, which approach to apply depends on the application, and some are solved more effectively by relax-and-fix, some others by rolling-horizon.
- Zhang et al. (2016) proposed a multi-objective optimisation approach to assess the trade-off between economics and environmental factors while scheduling energy tasks.
- Solutions obtained by the rolling-horizon approach depend on the decomposition in sub problems, but not on the formulation, provided that the same linking variables appear in the formulations.
- We distinguish between entrance aircraft delays and small random variations on the aircraft entry times in the TCA.
- Due to the formulation independency, the rolling-horizon approach is easier to analyze than relax-and-fix methods, since no formulation for the problem under consideration has to be specified.
Considering throughput, tardiness and waiting time, the flexible rolling horizon approach showed the best results, while the static one had the worst results. In Section 2, we define optimization problems with time structure, introduce decomposition methodologies and derive conditions under which solutions with provable solution quality can be obtained. In Section 3 we briefly demonstrate the applicability of our algorithm to lot-sizing problems.
Local cuts and two-period convex hull closures for big-bucket lot-sizing problems
In fact, energy decisions are often made under uncertainty with hedging of worst-case scenarios. With deterministic, perfect-foresight models, such things as costs and other parameters are assumed to be known with 100% certainty. As such, these models while instructive to serve as base cases, are less realistic than ones that allow for stochastic elements and/or some rolling horizon foresight, more in line with the way markets work. To have a better handle on the importance of allowing such flexibility to this extension of the Nash-Cournot paradigm, various endogenous probability/endogenous data schemes are considered in this paper. These learning algorithms are implemented as part of the rolling horizon methodology we propose wherein each player, after each roll can adjust their data (e.g., scenario probabilities, costs) to further their own ends.
Complementarity modeling in energy markets
Posteriorly, Zhang et al. (2013b) proposed an MILP formulation to manage the scheduling of energy and heat tasks within a smart building. This formulation considered the reduction of peaks by applying extra costs if electricity load from the power grid exceeds an established limit. In this section we provide some observations and counter-examples to more clearly differentiate between perfect foresight and rolling horizon MCPs with and without uncertainty. For time periods 2–4, demand is stochastic with the variance of demand increasing with time as Fig.
Energy Convers. Manage.
However, the method only generates feasible planning–scheduling decisions and the quality (optimality) of the solution cannot be ensured. As what we will show in this paper, production capacity information representing the scheduling problem can have great effect on the final solution’s quality. In the literature, Sung and Maravelias (2007) have proposed to derive the feasible production regions for scheduling problem through a computational geometry method, and then incorporate it into the rolling horizon planning model. rolling horizon approach The rolling horizon method has been proposed to address the integrated production planning and scheduling optimization problem. Since the method can generally result in small-scale optimization model and fast solution, it has been used in a number of applications in realistic industrial planning and scheduling problems. In this paper, it is first pointed out that the incorporation of valid production capacity information into the planning model can improve the solution quality in the rolling horizon solution framework.
An overview of the open issues in the area of modelling, control and optimisation of energy networks in terms of generation, storage and distribution can be found in Soroush and Chmielewski (2013). While these elements are not new in themselves, the combination of them is novel and leads to a more realistic perspective for modeling energy markets based on MCPs. Moreover, for such a new approach we have also introduced a new concept— the value of the rolling horizon or VoRH which is an attempt to measure how well the stochastic, rolling horizon MCP stacks up against a perfect foresight benchmark. In the subsections that follow, we describe in more detail the advantages of this modeling paradigm. The rolling-horizon approach has recently been applied to a large number of optimization problems. An excellent summary of rolling-horizon based solution approaches can be found in Chand, Hsu, & Sethi (2002).
This mathematical formulation determined the optimal schedule of tasks, considering both the availability and cost of electricity. For instance, Mohammadi et al. (2014) presented a scenario-based optimisation approach for the energy operation management taking into account uncertainties in the given energy generation, consumption and market price. In the same area, Zakariazadeh et al. (2014) proposed an MILP formulation to address the schedule of microgrids including the demand management, by introducing flexible energy consumption tasks. Production planning and scheduling belong to two of the most important decision making levels in the process industry.
Hytowitz and Hedman (2015) proposed a stochastic-based formulation to consider the uncertainty related to the generation of electricity through the use of photovoltaic panels under uncertain conditions. Moreover, Zhang et al. (2013a) presented a scenario-based MPC in order to minimise the energy consumption of a building, considering heat, ventilation and air conditioning systems. Menon et al. (2016) proposed a mathematical formulation based on the exploitation of an MPC in order to manage the optimal control strategy for the electricity and heat within a multi-building network. Naraharisetti et al. (2011) developed an MILP formulation for the optimal scheduling of microgrids connected to the power grid, in order to evaluate energy policies.
As the iterations proceed, planning decisions are updated with all the previous executed decisions fixed. The above idea is supported by the fact that planning decisions for far future could not be accurate enough due to the unpredicted future uncertainty. So it is reasonable to consider a relative rough model for far future planning periods in the aggregate planning model.
This negative environmental impact includes an increase in the pollution and the climate change. In this context, the European Union (EU) has set targets for 2020 regarding the climate change and sustainability. The EU’s renewable energy directive sets a target of 20% of energy from renewable sources by 2020, as well as a reduction by 20% in GHC emissions (considering 1990 as a baseline) and improving the https://business-accounting.net/ energy efficiency by 20% (European Commission, 2010). Some prior works focus on theoretical results for rolling-horizon heuristics, and deliver results which are taylored for specific problem classes. For example, Chand, Sethi, & Proth (1990) and Bylka & Sethi (1992) proved that the rolling-horizon approach delivers exact solutions for their version of a stationary non-discounted lot-sizing model.
We substantiate the findings with computational studies on the lot-sizing problem in production planning, as well as for large-scale real-world instances of the tail-assignment problem in aircraft management. It proves possible to solve large-scale realistic tail-assignment instances efficiently, leading to solutions that are at most a few percent away from a globally optimal solution. This work proposes a novel mathematical model to manage simultaneously energy and heat generation, purchases, sales, storage and tasks to minimise the cost of a microgrid by optimally adapting energy and heat generation and demand. The main novelty of this work is the combination of a rolling horizon approach and a stochastic formulation to optimally manage a microgrid under uncertainty. One of the main characteristics of this novel formulation is the flexibility in energy requirements, in terms of the starting time of energy consumptions. The energy requirements are limited by a time windows to perform a given energy consumption task, which can be delayed.
For the rolling-horizon approaches presented here, a theoretical analysis of the solution quality is possible, and huge tail-assignment instances can be solved. More recently, in Absi & van den Heuvel (2019) a worst case analysis of a relax-and-fix approach applied to an uncapacitated single-item lot-sizing problem is conducted. As the fixing of integer variables is in chronological order, the approach can be considered as a rolling-horizon heuristic. The theorems from Absi & van den Heuvel (2019) however are formulated specifically for the relax-and-fix heuristic, which enables to adapt continuous variables of periods with already fixed integer variables. This work addresses the coordinated management of electricity and heat generation, purchases, sales, storage and consumption within a microgrid. Several tasks have been scheduled, considering consumption profiles, time windows to execute the consumption, eventual interruptions, time-varying grid electricity prices and peak demand penalisations.
This formulation considered both real-time energy prices and priority to perform the considered energy consumptions. Zhang et al. (2016) proposed a multi-objective optimisation approach to assess the trade-off between economics and environmental factors while scheduling energy tasks. In the industrial area, Kato et al. (2011) developed an MILP formulation to reduce the energy consumption cost, considering both energy generation and storage in a demand-based framework. Also, Zondervan et al. (2010) presented a Mixed Integer Non-Linear Programming (MINLP) to reduce the operational cost for process industries.