Contributed Session Wed.2.MA 004

Wednesday, 13:15 - 14:45 h, Room: MA 004

Cluster 20: Robust optimization [...]

Applications of robust optimization IV


Chair: Pierre-Louis Lancelot Poirion



Wednesday, 13:15 - 13:40 h, Room: MA 004, Talk 1

Jorge Vera
Improving consistency of tactical and operational planning using robust optimization

Coauthors: Pamela Alvarez, Sergio Maturana


This work is motivated by a problem in the forest industry, in which tactical planning is carried out using an optimization model and then short term decisions are taken. It is expected that operational decisions be consistent with tactical plans, but that is not usually the case as the process is subject to various uncertainty, especially those originating in the natural variation of the forest. The "rolling horizon'' approach is used in practice as an attempt to reduce inconsistencies, but we propose that using a robust optimization tactical planning model should increase the chances of consistency with the short term. The question, however, is how much robustness do we need, as being robust is expensive, and whether structural characteristics of the problem can be used to anticipate these factors. We provide some specific estimates, like probabilities of consistency, and results on the relations as well as computational results based on an industrial case. We also show how to dynamically adjust the degree of robustness of the planning process in such a way to approach an "optimal'' policy. These results should be relevant also in other problems where consistency is desirable.



Wednesday, 13:45 - 14:10 h, Room: MA 004, Talk 2

Florian Bruns
Robust load planning of trains in intermodal transportation

Coauthors: Marc Goerigk, Sigrid Knust, Anita Schöbel


In this paper the problem of robust load planning for trains in intermodal
container terminals is studied. The objective is to assign load units (container,
swap bodies and trailer) to wagons of a train such that the utilization of the
train is maximized, and setup and transportation costs in the terminal are minimized.
However, in real-world applications many of the parameters needed for the
model are not known exactly.
In our paper we enhance the load planning problem by taking the most important
uncertainties into account. Based on a mixed-integer linear programming
formulation developed in Bruns and Knust (2010) we are able to formulate
robust counterparts and show how these may be solved
within a reasonable runtime.
Our results indicate that it might be worth to study the robust counterparts
even of large and complicated mixed-integer programs.



Wednesday, 14:15 - 14:40 h, Room: MA 004, Talk 3

Pierre-Louis Lancelot Poirion
Robust optimal sizing of an hybrid energy stand-alone system

Coauthors: Alain Billionnet, Marie-Christine Costa


The development of renewable energy brought new complex combinatorial optimization problems as the one studied here: the conception of an autonomous hybrid energy system. The study is made considering a finite time horizon divided into periods where an energy demand has to be fulfilled. An auxiliary fuel generator guarantees to meet the demand in every case but its use induces important costs. The aim is to determine the optimal number of photovoltaic panels, wind turbines and batteries while minimizing the total cost of investment and use. We first propose a mixed integer linear model for the problem without uncertainty. However, the stochastic behavior of both solar and wind energy and of the demand needs to be taken into account for a robust solution: here, we only consider the variation of the demands. We focus on an approach where we assume that the total variation of the demands is bounded. The problem is modeled as a two stage optimization program where the decision variables are integer while the recourse problem is a quadratic continuous program. We show that it can be linearized, which allows us to solve the global robust problem with a constraint generation algorithm.


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