Chapter 2
Robustness in Operations Research and Decision Aiding
It is always advisable to perceive clearly our ignorance.
(Charles Darwin)
36 Flexibility and Robustness in Scheduling
2.1.1. Robust in OR-DA with meaning?
As I see it, robust is a term that is generally used in the sense of 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.
“Vague approximations” can refer to a way of modeling, the restrictive character of certain hypotheses, mode of value allocation to data and/or parameters, etc.
“Zones of ignorance” may deal with the complexity of certain phenomena and of value systems but mostly the future: trends, contingencies, behavior of others, etc.
Here are a few examples to illustrate this meaning of the term “robust” in scheduling. In Chapter 1, a solution is said to be robust if its “performance is rather insensitive to data uncertainties and disturbances”. In this context, insensitivity to data uncertainty means resisting to this uncertainty1. The uncertainty in question can for example refer to the way of modeling which processes certain data as insignificant or not influenced by contingencies, a Gaussian hypothesis simplifying the mode of consideration of a random phenomenon or the approximate character of values attributed to data (processing time, due date, etc.).
In some maintenance studies, scheduling must be conceived to guarantee deadlines are respected even though the jobs to be done are not well known (resistance to a certain form of ignorance). Job-shop scheduling may have to be chosen for its capacity to face an order book that is only partially known or with unknown reactions to delays that the end customer may encounter because of contingencies. Climate conditions, as well as work-related accidents or social upheavals, are sources of ignorance that project management may have to consider.
Two comments seem necessary to specify the meaning of what was just discussed:
1) Even though the borderline between vague approximations and zones of ignorance is far from being well defined, all vague approximations do not come from a zone of ignorance and all zones of ignorance do not lead to vague approximations.
1. The term “uncertainty” imperfectly covers all forms of vague approximations and zones of ignorance that need to be resisted. This is the case in particular of vague approximations resulting from simplifications or ill determinations. This is also the case for zones of ignorance coming from certain forms of imperfect knowledge relative to the complexity of phenomena or value systems.
Robustness in Operations Research and Decision Aiding 37
2) Resistance can have the following meanings: protecting from, adapting to, being rather insensitive to, remaining stable, settling a certain form of equity, etc.
We will now examine the reasons resulting in the need to resist these vague approximations and zones of ignorance in OR-DA.
2.1.2. Why the concern for robustness?
In OR-DA, the capacity for resistance qualified by robustness is required in order to be protected from undesirable impacts, impacts that should be apprehended taking into account these vague approximations and/or zones of ignorance that need to be resisted. The nature of these impacts, along with the (very often subjective) way of assessing their undesirable character, are contingent to the context involved. The concerns motivating the search for robustness are extremely diversified for these reasons. I will settle for illustrating them through a series of examples in this chapter:
i) Exceptional character decisions
– Layout of a large linear infrastructure (very high speed train line, highway, high-tension line, etc.): throughout the execution (five years or more), what reactions will it generate? Once this is finished, what standards will it be judged by? Will the size be adapted to traffic?
– Construction of a sanitation or waterworks system: knowing that implementing such activities, as with the evolution of consumption patterns, can only be defined in large variation ranges, will the designed system be able to fulfill population requirements in the planned horizon without needing adjustments leading to prohibitive costs?
– Updating of equipment: considering the evolution of technology and environmental standards, when should the decision be made to update?
ii) Sequential character decisions
– Plan designed to be implemented in stages: how will the contexts in future stages be affected by the decisions taken at this present stage? Do they allow for possible evolutions of these contexts by keeping the range of adaptations and reactions open?
– Scheduling flight personnel in an airline company: how can we handle unexpected unavailability of teams (unforeseen absences, immobilization during a mission, etc.) in acceptable economic conditions and with no planning disruptions for agents?
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? –