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One is a simple strategy that will only work with certainrestrictions. It requires just a single aggregation step and a singledisaggregation step. This strategy, however, requires that aggregation anddisaggregation steps be performed between every two subsequent SOLVEstatements.

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In both cases, the horizon-based solution obtained from a previous solvewill not be accurate when you move the planning interval. Thus, youshould follow a generic strategy which adds an additional disaggregationand aggregation step to every iteration. In this section you will find two strategies for implementing a rollinghorizon.

• In both cases, the horizon-based solution obtained from a previous solvewill not be accurate when you move the planning interval.
• This section outlines the steps that are required toimplement a model with a rolling horizon, without going into detailregarding the contents of the underlying model.
• It requires just a single aggregation step and a singledisaggregation step.
• For this non-standard optimization problem with optimal stopping decisions, we develop a dynamic programming formulation.
• The term rolling horizon is used to indicate that a time-dependentmodel is solved repeatedly, and in which the planning interval is movedforward in time during each solution step.
• Various generalizations are shown to be captured by straightforward modifications of our model.

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Mathematical optimization problems including a time dimension abound. For example, logistics, process optimization and production planning tasks must often be optimized for a range of time periods. Usually, these problems incorporating time structure are very large and cannot be solved to global optimality by modern solvers within a reasonable period of time. This approach aims to solve the problem periodically, including additional information from proximately following periods.

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• The main idea of our approach is that the usefulness of rolling horizon methods is, to a great extent, implied by the fact that forecasting the future is a costly activity.
• This strategy, however, requires that aggregation anddisaggregation steps be performed between every two subsequent SOLVEstatements.
• Usually, these problems incorporating time structure are very large and cannot be solved to global optimality by modern solvers within a reasonable period of time.
• It is then sufficient to make the horizon sufficiently large so as tocover the whole time range of interest.
• The algorithm to implement the rolling horizon can be outlined asfollows.

A rolling-horizon approach for multi-period optimization

The term rolling horizon is used to indicate that a time-dependentmodel is solved repeatedly, and in which the planning interval is movedforward in time during each solution step. With the facilitiesintroduced in the previous sections setting up such a model isrelatively easy. This section outlines the steps that are required toimplement a model with a rolling horizon, without going into detailregarding the contents of the underlying model.

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In this paper, we develop a theoretical framework for the common business practice of rolling horizon decision making. The main idea of our approach is that the usefulness of rolling horizon methods is, to a great extent, implied by the fact that forecasting the future is a costly activity. For this non-standard optimization problem with optimal stopping decisions, we develop a dynamic programming formulation. We also provide a careful interpretation of the dynamic programming equations and illustrate our results by a simple numerical example. Various generalizations are shown to be captured by straightforward rolling horizon approach modifications of our model.

The algorithm to implement the rolling horizon can be outlined asfollows. It is then sufficient to make the horizon sufficiently large so as tocover the whole time range of interest. Sorry, a shareable link is not currently available for this article.

In this paper, we first investigate several drawbacks of this approach and develop an algorithm that compensates for these drawbacks both theoretically and practically. As a result, the rolling horizon decomposition methodology is adjusted to enable large scale optimization problems to be solved efficiently. In addition, we introduce conditions that guarantee the quality of the solutions. We further demonstrate the applicability of the method to a variety of challenging optimization problems. 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 optimum solution.