Invited ReviewRobustness in operational research and decision aiding: A multi-faceted issue
Introduction
In the field of operational research and decision aiding (OR-DA), robustness is increasingly present in the research published in the major scientific journals. It is also the focus of much less formal OR-DA research conducted by companies. The latter applied works are not well known in academic circles because even when such works are published, which is relatively rare, they tend to appear in journals that the scientific community judges “minor”, which means that most often it tends to be ignored.
In OR-DA, the multiple meanings accorded to the term “robust” are open to debate. This subject is discussed in detail in Newsletter (2002–2008) by the contributions of Aloulou et al. (No. 12), Dias (No. 13), Fernandez Barberis (No. 13), Pictet (No. 15), Rios Insua (No. 9), Rosenhead (No. 6), Roy (No. 6), Roy (No. 8), Ruggeri (No. 17), Sayin (No. 11), Sevaux and Sörensen (No. 10), Stewart (No. 18), Vincke (No. 8). This variety of viewpoints underscores the polysemic character of the notion of robustness. These multiple meanings are notably due to the fact that, depending on the situation, this notion can be related to, or integrated into, the notions of flexibility, stability, sensitivity and even equity.
In this article, I use the term robust as an adjective referring to a capacity for withstanding “vague approximations” and/or “zones of ignorance” in order to prevent undesirable impacts, notably the degradation of the properties to be maintained (see Roy, 2005). The research dealing with robustness seeks to insure this capacity as much as possible. Consequently, robustness is related to a process that responds to a concern: the need for a capacity for resistance or self-protection.
During a 2004 MCDA working group meeting, Philippe Vincke pointed out that, though the expression “robustness analysis” is frequently used, it seemed too restrictive. I proposed substituting the expression ”robustness concern”. Clearly, speaking of analysis infers that the scrutiny occurs a posteriori, as is the case with sensitivity analysis. Robustness, on the other hand, involves concerns that must be taken into account a priori, at the time that the problem is formulated (of course, this does not exclude the use of a sensitivity analysis to respond to such concerns, if necessary).
In the next section, I discuss these concerns in more detail, attempting to clarify the numerous reasons why these concerns exist. The reader who would wish real-world examples could, before approaching this section, read the ones presented in Section 4.2. As a means of examining the multiple facets of robustness concern more comprehensively, I explore the existing research about robustness, attempting to highlight what I see as the three different territories covered by these studies (Section 3). Two of these territories are clearly opposed; the third, transversal, includes those works that have certain features of the first territory and others of the second. In the fourth section, I refer to these territories to illustrate how responses to robustness concern could be even more varied than they currently are. In this perspective, I propose in Section 5 three new measures of robustness. In the last section, I identify several aspects of the robustness concern that should be examined more closely because they could lead to new avenues of research, which could in turn yield new and innovative responses.
Section snippets
Raisons d’être of robustness concern
From the perspective of decision aiding, in my opinion, it is the desire to take into account our own ignorance as much as possible that is the raison d’être for robustness concern. From this perspective, it is important to remember that the decisions for which decision aiding is performed will be:
- (1)
executed in a real-life context that may not correspond exactly to the model on which the decision aiding is based;
- (2)
judged in terms of a system of values that will appear to be pertinent (and not
Three territories for robustness concern
In order to draw attention (in the next section) to the multiple forms of the responses to robustness concern in the light of the raisons d’être described above, I believe it is useful to use the metaphor of three territories in which it is possible to situate the researches published until now on robustness. In this section, I will describe the characteristics of these three territories. The first two territories, called standard (S) and concrete (C), have characteristics that are in many
The diverse forms of responses that robustness concern can (or should) lead to
The forms of the potential responses are multiple, notably because it is possible to imagine both a large variety of theoretical problems that could lead to studies in territory S or M and an extremely diverse group of concrete contexts that could lead to studies in territory C or M.
Three measures of robustness
Inspired by the standard criteria recalled in Section 4.1d, I propose below three robustness measures that, in my opinion, are able to generate solutions that are quite relevant to a number of real-life contexts. To introduce these new robustness measures, I keep most of the notations used in Section 4.1d, but nonetheless modify the definition of , for reasons that will become understandable below.
In the following, is the value of the optimal solution in scenario s after the elimination
Facets and avenues of research to explore
Those responsible for making decisions, or more generally, for influencing the decision making process do not expect decision aiding to dictate their choices. They are looking for responses offering useful information that will help to restrict the scope of their deliberations and actions. Satisfying these expectations could involve proposing well-argued solutions or conclusions (e.g., of the type “if…, then…”), systems of rules or procedures that guarantee properties, such as flexibility,
Acknowledgements
Hassene Aissi and Daniel Vanderpooten provided feedback on a preliminary version of this article, and Mohamed Ali Aloulou and Eric Sanlaville examined the second draft and proposed a number of pertinent suggestions and critiques. Finally, I received from two reviewers very detailed and rich remarks and comments which have been taken into account. To all of them, I offer them my heartiest thanks. I would also like to thank Dominique François, who once again typed and proofread this manuscript,
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