38 Flexibility and Robustness in Scheduling
iii) Choice of a method for repetitive applications
– Management support method for restocking a store: does the method protect against out of stock risks that could result from a failure to respect of delivery lead times by suppliers? Is it adapted for possible evolutions of purchase agreements?
– Method controlling budget distribution between members in a group: knowing that the size and composition of beneficiary groups can greatly change over time and space, will the method retained be considered fair in all cases where it will be applied?
– Adjustment method for a model dedicated to emphasizing the way in which different factors contribute to global client satisfaction during consecutive surveys:
how can we avoid the results depending on final retained values (chosen in a relatively arbitrary manner in certain intervals) for different technical parameters involved in the model?
2.1.3. Plan of the chapter
In the next section, I will examine where, for a decision aiding problem (DAP),
“vague approximations” and “zones of ignorance” come from, for which the need for protection leads to the search for robustness. These vague approximations and zones of ignorance are closely linked to the way that the decision aiding problem is formulated (DAPF). They can also depend (although generally less so) on the processing procedure applied to this formulation in the decision aiding process. This leads me to introduce the general concept of version. In section 2.3, I will specify the meaning I give to several currently used terms (procedure and method notably) in order to clarify their links with the concern for robustness. In section 2.4, I will focus on the way to take robustness into consideration: what must be robust? How can we formalize robustness? In what form can vague approximations and zones of ignorance be taken into account? Unfortunately, many questions raised here will remain unanswered. A brief conclusion will complete this chapter.
2.2. Where do “vague approximations” and “zones of ignorance” come from? –
Robustness in Operations Research and Decision Aiding 39
studied, the way it is formulated and the process mode applied. Nevertheless, I think it is possible to see them whatever they are as frailty points connected to sources of inaccurate determination, uncertainty or arbitrariness (see [ROY 89]). The vague approximations and zones of ignorance that must be resisted actually come from such sources. They can, it seems, be classified into three categories (even though the line separating these categories is not perfectly well defined, they affect sides of the DAPF which I think it is important to distinguish):
– SourceS· α: vague, uncertain, unknown, and even undetermined character of factual data, objective descriptions of phenomena and purely technical procedural aspects in relation to the form in which they must occur during the aiding process in the present situation.
This source may, for example, affect frailty points such as: processing times, due dates, process cost, failure probabilities, probability distributions chosen for modeling a random factor, discrimination thresholds, values given to the parameters playing a mostly technical role in a model or procedure, techniques used to adjust a model intended to represent complex phenomena, etc.
– SourceS·β: implementation conditions of the decision that must be taken; these conditions can be influenced by the future state of the environment:
- during implementation if the decision is punctual (i.e., taken all at once);
- by consecutive environmental steps if the decision is sequential.
This source may, for example, affect frailty points such as: what will have happened (during implementation), labor and/or raw material cost, interest rates, consumption patterns, boundaries of what is acceptable (social and environmental standards among others) or the presence or absence of disrupting events (unavailable personnel or equipment, opposition of some stakeholders, climatic incidents, etc.).
– SourceS·γ: eminently subjective character of different aspects (not dealing with sourcesS· α and S · β) dealing with feasibility, relative interest and process modes of the different potential actions, especially the fuzzy, unstable and possibly incoherent and/or incomplete character of value systems which are supposed to prevail in the decision aiding process.
This source may, for example, affect frailty points such as the role devoted to certain criteria (notably on the basis of values allocated to substitution rates, weight, veto thresholds, etc.), the level required to validate a majority or set a cut-off threshold, the mode of appreciation for limits marking the feasibility or boundary between categories, the way to code a qualitative dimension by means of an interval
40 Flexibility and Robustness in Scheduling
scale, the way to apprehend attitude toward risk, the place reserved for certain actors (notably future generations).
2.2.2. DAP formulation: the concept of version
The expression DAP formulation must be taken in a very general sense. It obviously includes the model, insofar as there is modeling (see section 2.3.3 below), but in a broader sense, everything that was in question and has finally been retained to contain and consequently formulate the problem, including the problematic (the way in which decision aiding was conceived, see [ROY 96], Chapter 6), the properties to preserve and, in general, the undesirable impacts from which we want to be protected.
When we start being concerned about robustness in OR-DA, it is necessary in my opinion to start by identifying in DAPF what I have called frailty points connected to each of the three types of sourcesS· α, S · β, S · γ. Relative to each of these frailty points, we should then explain the different options which deserve to be considered within this formulation in order to take inaccurate determination, uncertainty and arbitrariness margins into consideration from these sources. The selection of a specific option for each of the identified frailty points defines what I proposed (see [ROY 02, ROY 07]) to call a version of DAPF. If it is carried out without precautions, this selection can very well lead to combinations lacking in coherence or plausibility. Let ˆV be the set of versions V corresponding to combinations of options deemed (possibly from very subjective bases) to be of interest ( ˆV cannot be discrete).
From this definition, two versions of ˆV can notably differ by:
1) The values assigned to certain factual data or technical parameters characterizing events, phenomena, etc.: this is the case in particular with vague approximations and zones of ignorance fromS.α; when in the DAPF, this source is the most significant, the word version becomes synonymous with instance or datasets.
2) The way that we describe the future universe in which the decision must be executed: this is the case in particular with vague approximations and zones of ignorance fromS.β; when in the DAPF, this source is the most significant, the word version becomes synonymous with scenario.
3) The way in which ambiguities, uncertainties and the multiplicity of value systems are taken into consideration: with vague approximations and zones of ignorance fromS.γ this is particularly the case for; when in the DAPF, this source is the most significant, the word version becomes synonymous with interpretation or mode of appreciation.
Robustness in Operations Research and Decision Aiding 41
I think it is useful to emphasize that the way in which ˆV versions distinguish themselves does not generally come from only one of the three sources. The search for robustness must rely on what comes from each source in order to arrive at an appropriate design (see section 2.4.3) of the set ˆV . However, the processing procedure of these versions in a perspective of decision aiding can also be affected (in certain cases, we could also say “infected”) by sourcesS·α, S ·β, S ·γ as will be emphasized in the next section.