3.1. Model Basis
The algorithm presented here assumes that a set of companies and its characteristics (size, industry, age, etc.) are available. The objective is to define an algorithm that maximizes the position of a company compared with its competitors in terms of ITIL implementation. The selection of processes to implement depends on the strategic needs of the company and the degree of implementation of every ITIL process compared to the competitors. The algorithm selects the process that maximizes the benefits of ITIL implementation in front of its competitors.
Let
Ωe be the set of available companies from which characteristics are known and stored. Usually this set of data is taken from a great poll:
Let
E be any company included in the dataset:
Let
Ωne be the complementary set of
Ωe, that is the set constituted by companies that have not been included in the data set:
It will be noted by
Esel any company included in this last data set:
Let us denote by
Ωp the set of the
pITIL processes that can be implemented out of the available data:
Let
pITIL be the number of ITIL processes that can be implemented, so:
Let pi any of the pITIL potential processes that can be implemented and di the assessment of pi process in a particular company, E:
The possible value of
di are:
where
Cm(
Pi) is a Boolean function that indicates if the
pi process satisfies an implementation degree of
cm. The possible values for the degrees are in the interval [1..
M], so 1 represents the worst option and
M represents the best option. That is:
For example, the c1 condition could mean that the process is not implemented, neither will it be in the long term; in that case C1(pi) = True would indicate that pi is not implemented, neither will it be implemented in the long term in company E; in such case di(E) = 1.
It should be noticed that {1...M} represents the values given to the different degrees of implementation that a pi process may have in company E.
Let
Ωv be the set of the
v parameters that define the characteristics of every company, which are identified by {
v1,
v2, …,
vv}. Such parameters could be the type of activity, the age, the number of employees, the geographical area where it operates, etc.,
Following this, let us define the domain of each parameter that belongs to
Ωv:
where
nk represents the number of possible values for the parameter
vk.Next, let us define every
v functions {
V1,
V2, …,
Vv} which assign a value
vij to the parameter
vi for the company
E:
In such case, the
v vector of parameters which define the characteristics of a company are given by:
Next,
si1j is defined as the average of the assessment of the
pi process for the companies that satisfy
v1 =
v1k:
In a general way, the average of the assessment of the
pi process for all companies which satisfy
vj =
vjk can be denoted by
sijk:
Or, expressed in a more formal way:
This means that the average of the assessments
di for the
pi process for every company
ee whose parameter
Vj satisfies
Vj(
ee) =
vjk. The ordinality of the set of companies that satisfy such condition is given by:
At this point, it is possible to show the algorithm that allows any company to decide which process should be first implemented.
Let us define
Esel as any company not included in the set
:
3.2. Criteria for Establishing the Sequence
In order to decide which process should be first implemented, it is necessary to define a parameter containing information about the implementation of an ITIL process in other companies with similar characteristics. To define it, and taking in consideration the definitions presented in previous paragraphs, the next parameters are needed; where
Sijk is referred to the set of available set of companies in the database and
Di is specifically referred to the company
Esel:
In this expression, M represents the maximum value that the implementation of an ITIL process pi can take. This M value represents a complete implementation of the pi process or a very short-term implementation.
It can be seen how Sijk represents, for a specific pi process, the distance between the maximum value M and the average of the values of implementation for that particular process in companies with the same characteristics vjk as Esel. It can be also seen how Di represents the distance between the maximum value M from the response of the company Esel.
It is necessary to define an indicator or parameter to help us to decide the best process to be implemented next. This indicator should take high values when the relative position (in terms of implementation of a process) is better than the reference companies denoted by V(Esel). This indicator should also take low values when the company is in a worse position than similar companies with characteristics V(Esel).
Let
r be the indicator “relative position” defined as follows:
This indicator can be particularized for a particular process
pi and for all companies with the same characteristics
V(
Esel):
where
ri represents the value of the
r indicator for the company
Esel and for the process
pi.
This expression calculates ri from the S2 value for each group of companies that satisfy the condition of having the same characteristics as Esel: Low values of Di indicate that the process pi is implemented or it will be soon in the company Esel; on the other hand, high values of Di indicate that process is not implemented, neither will it be in the short term. At the same time, high values for Sijtj address that the pi process is not implemented in the companies with the same characteristics , while low values show this process is implemented in companies with same characteristics, but it is not in Esel.
As a consequence, if the pi process is implemented in similar companies but it is not in the company Esel (that is, Esel position is worse than competitors), this leads to a really small value for r, compared to the maximum value it could take; it can be also shown that if a company has the process pi implemented but similar companies do not (that is, the relative position of Esel is better than competitors), then r will take a high value. Thus we can conclude that parameter r is a measurement of the relative position of a company for a specific process pi compared to similar companies. Anyway, the value of r goes from 0 to 1.
Thus, we can formalize
ri as the relative positioning indicator and
Ri as the function to evaluate
ri:
Thus, Ri represents the function that evaluates the relative positioning ri if a company ex for the process pi compared to similar companies.
Once this indicator is defined, it is possible to define the selection criteria for the first process to be implemented:
This expression means that the best process and the one that should be first implemented, that is, the one that will most improve the rank of the company (in terms of ITIL implementation) compared to the competitors, is the one with the lowest value for rp, that is, the one that has the lowest relative positioning.
The criteria shown previously needs a small correction: Due to the fact that relative positioning
r has taken into account the situation of the process in the company itself, every process that is already implemented should be excluded; that is, the processes with
Di = 0. This obliges the exclusion of every process that has been already implemented and review only processes with
Di ≠ 0.
Thus, if we select iteratively the Popt process (of course, on every iteration this process will be different as Popt process has already been implemented in the previous iteration and so, dismissed as selectable), we get a sequence of processes to implement that optimizes the degree of implementation compared to the competitors, for the criteria defined (age, size, etc.).