A rolling-horizon approach for multi-period optimization

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. 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.

A rolling-horizon approach for multi-period optimization

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 modifications of our model. In this section you will find two strategies for implementing a rollinghorizon.

Discover content

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.

Implementing a Model with a Rolling Horizon

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. 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. The algorithm to implement the rolling horizon can be outlined asfollows.

• It requires just a single aggregation step and a singledisaggregation step.
• 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.
• We also provide a careful interpretation of the dynamic programming equations and illustrate our results by a simple numerical example.
• ArXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
• One is a simple strategy that will only work with certainrestrictions.
• 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.

About this article

Sorry, a shareable link is not currently available for this article. It is then sufficient to make the horizon sufficiently large so as tocover the whole time range of interest. ArXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Title:A rolling-horizon dynamic programming approach for collaborative caching

• In this paper, we develop a theoretical framework for the common business practice of rolling horizon decision making.
• With the facilitiesintroduced in the previous sections setting up such a model isrelatively easy.
• 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.
• In addition, we introduce conditions that guarantee the quality of the solutions.
• It is then sufficient to make the horizon sufficiently large so as tocover the whole time range of interest.
• We further demonstrate the applicability of the method to a variety of challenging optimization problems.

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. 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 rolling horizon approach to enable large scale optimization problems to be solved efficiently.