Decision process

A decision is not an instantaneous phenomenon, but rather impact point resulting from a certain number of steps, namely, the impact point of a process.

Those steps (or highpoints) are defined by the time of a decision process which marks a break with respect to the previous period. Breaks are typically the arrival of a new information, an important event, or even the modification of the decision problem itself.

In this process, there is a progressive elaboration of options, which are fragments of decision.

Participants, stakeholders, decision-maker

An individual (group) is a participant to a decision process if, through his/her value system, he/she influences (directly or indirectly) the outcome of the decision process.

For a group of individuals to be identified as a single participant to the decision process, the value system and informational system of the members of this group should be, if not identical, sufficiently close.

The set of participants to a decision process usually evolve over time (emergence/disappearance of participants).

Decision aid / support

Definition (Decision Aid): Models to help a participant of a decision process to elaborate pieces of answers to questions he/she faces. It should increase the consistency between the evolution of the process and this participant objectives and value system.

Example

Example: A dairy collects on a daily basis the milk produced in several farms, and wants to do so in an efficicent manner.

Taken litteraly, the problem is a Traveling Salesman Problem, with the set of options being hamiltonian circuits. This model is a caricature representation, usually solved with combinatorial solutions.

Note: The model is too simplitic as:

• Farms production varies and is not known in advance.
• Transportation time is variable (weather, trafic,…), timing for cows milking is subject to “time windows”.
• There exists 3 Trucks → the problem changes in its nature,
• A single criterion? risk of uncollected milk, …

The model can not be considered out of the context.

Building a decision model can contribute to modifying the formulation of the initial problem:

• Installation of a second dairy
• Policy for bying/renting trucks
• Subcontracting milk collection

Load balancing problem: Cover the load using a minimum staf

Problem data:

• $t = 1, 2, …, T$ periods
• $C_{t}$ = load for period $t$, $t = 1, 2, …, T$
• $h = 1, 2, …, H$ working hours types
• $a_{ht} = \begin{cases}1& \text{if working hours type h covers period t}\ 0 & \text{ otherwise}\end{cases}$

Decision variables: x_{h}, h = 1, .., H is the number of persons employed using working hours type h.

Optimization model: $\begin{align} Minimize & \sum_{h=1}^{H} x_{h}\\ s.t. & \begin{cases} \sum_{h=1}^{H} x_{h} \geq C_{t} \forall t\\ x_{h}\geq 0, \forall h \end{cases} \end{align}$

Note: There can be additional constraints such as:

Work load curve ? Usually rules like type of airplane × destination × time

Alternatives, problem stat

The alternatives are typically the possible options (hamiltonian path for traveling salesman problem for instance).

Types of alternatives:

Decision problem statements:

• Choice of the best alternative
• Rank from the best to the worst (ranking can be complete or partial)
• Rank from the best to the worst (ranking can be complete or partial)

Note: More decision problem statements