Evaluating strategic actions for a Greek publishing company

Abstract

The main objective of this paper is to structure a real world investment problem in the publishing sector as a multicriteria decision problem in order to support a large Greek publishing company in making its specific strategic decisions. As a first step of the proposed approach a set of twelve publishing products in the Greek market is identified. Afterwards the distinct set of incremental impacts as tangible results of these actions is determined by taking advantage of the system’s competitiveness, effectiveness and flexibility. Then a consistent family of nine criteria reflecting the company strategy is structured. Finally, the paper outlines the implementation of the ELECTRE II multicriteria method which is adapted to true evaluation criteria so as to rank order the strategic actions and to provide an adequate and efficient decision support.

Appendix: the ELECTRE II method

1.1 Building two outranking relations

The method ELECTRE II was initially presented by Roy and Bertier (see Roy and Bouyssou 1993; Figueira et al. 2005a; Siskos 2008). There are two embedded outranking relations to model the decision maker’s global preference: a strong outranking relation followed by a weak outranking relation. Both the strong and weak relations are built thanks to the definition of two concordance levels, $s^{1} > s^{2} ,\;{\text{where}}\;s^{1} ,s^{2} \; \in \;[0.5,\;1 - \min_{j \in F} p_{j} ]$. For each criterion are defined two veto thresholds $v_{j}^{i} ,\;\forall \;i = 1,2\;{\text{and}}\;j = 1,2, \ldots ,n$ where $v_{j}^{2} \ge v_{j}^{1}$. The first one $v_{j}^{1}$ (narrow) is for the strong outranking relation and the second one $v_{j}^{2}$ (greater than or equal to $v_{j}^{1}$) for the weak outranking relation.

The concordance and discordance conditions with the assertion “a outranks b” can be defined as follows:

$$ \begin{array}{ll}aS^{i} b \Leftrightarrow\quad \text{and}\quad C(a,b) = \mathop {\sum {p_{i*} \ge s^{i} } }\limits_{{i^{*} \{ i/g_{i} (a) \ge g_{i} (b)\} }} \quad{\text{and}}\quad C(a,b) \ge C(b,a),\;{\text{for}}\;i = 1,2\;{\text{and}} \\ \forall \;j \in F,\;g_{j} (b) - g_{j} (a) \le v_{j}^{i} ,\;{\text{for}}\;i = 1,2\end{array}$$

1.2 The ranking algorithm

Below we present the four steps of the ranking algorithm (Figueira et al. 2005b; Siskos 2008):

• 1. Partitioning the set A. First, let us consider the relation S ¹ over A. This relation may define on A one or several cycles. If all the actions belonging to each maximal cycle are grouped together into a single class, a partition on A will be obtained. Let $\overline{A}$ denote this partition. When each class of $\overline{A}$ is not singleton, the actions belonging to that class will be considered as one. For the purpose of comparison between elements of $\overline{A}$ a preference relation $\succ$ will be used.

• 2. Building a complete pre-order Z ₁ on $\overline{A}$. After obtaining $\overline{A}$, the procedure identifies a subset B ¹ of classes of $\overline{A}$ following the rule “no other is preferred to them” according to the relation $\succ$. After removing B ¹ from $\overline{A}$ and applying the same rule to $\overline{A} \backslash B^{1}$, a subset $B^{2}$ will be found. The procedure iterates in the same way till define the final partition on $\overline{A} ,\;\{ B^{1} ,B^{2} , \ldots \}$.

Now, on the basis of S ¹, we use the concordance level S ² to clear outranking of the actions inside the classes.

• 3. Determining a complete pre-order Z ₂ on $\overline{A}$. The procedure to obtain this pre-order is quite similar to the above one; only two modifications are needed:

  • a. Apply the rule “they are not preferred to any other” instead of “no other is preferred to them”; let $\{ B^{1'} ,B^{2'} , \ldots \}$ denote the partition thus obtained;

  • b. Define the rough version of the complete pre-order Z ₂ by putting it in the queue of this pre-order, and in an ex equo position all classes of B ¹’, then those of B ²’ and so forth.

• 4. Defining the partial pre-order Z. The partial pre-order Z is an intersection of Z ₁ and Z ₂, $Z = Z_{1} \cap Z_{2}$, and it is defined in the following way:

$$ aZb \Leftrightarrow aZ_{1} b\quad{\text{and}}\quad aZ_{2} b $$