**3.2 Analytic hierarchy model**

*Operations Management - Emerging Trend in the Digital Era*

construction sustainability [23, 24].

**3.1 Functional resonance analysis method (FRAM)**

details about each step are provided below [26].

build a graphical representation of a FRAM model.

human functions (M), and of organizational functions (O).

**3. Materials and methods**

**Figure 3.**

*Documents by subject area.*

FRAM-AHP is proposed also in other two works. Both applied the hybrid to evaluate

FRAM methodology aims to analyze how the variability of one or more functions can be combined between them and how to prevent their resonance, which could lead to unwanted results [25]. For this purpose, FRAM method studies the system first under normal conditions, after FRAM analyzes the variability that cause to the event unwanted. The aim is obviously to be able to issue recommendations that prevent the repetition of the event. FRAM consists of four steps: 1) Identify system functions; 2) Characterize the potential variability of the functions; 4) Determine the dependencies among functions and 4) Monitor the variability. Some more

**Step#1 "Identification of the essential functions".** The present step aims to identify the functions or the specific action that are needed to carry out a specific task [27]. Each function is described using the six aspects (as shown in **Figure 4**): INPUT (I); OUTPUT (O); TIME (T); CONTROL (C); PRECONDITIONS (P) and RESOURCES (R). Functions can have links to each other. They can typically have multiple links and dependencies. From a practical point of view, to represent the variability it is possible to use the *FRAM Model Visualiser* (FMV). FMV allow to

**Step#2 "Identification of variability".** The present step identifies the variability of functions in order to understand how functions can become coupled and how this can lead to unexpected outcomes [28]. The FRAM assume that there are characteristic differences in the variability of technological functions (T), of

**Step#3 "Aggregation of variability and define functional resonance".** This step aims to analyze the variability of functions and how they interacted with each other [29]. The variability of a function depends on couplings among functions. It is not enough to evaluate the variability for the single function. It is necessary to

**4**

The main feature of Analytic Hierarchy Process (AHP) is to break down a decision-making problem in a hierarchy [31]. AHP uses a mathematical approach

#### **Figure 4.**

*FRAM hexagon: The six aspects used to characterize functions.*


#### **Table 1.**

*Example of aggregation of functions (output – input).*

based on matrix algebra to "measure" decisions [32]. AHP is characterized by three main phases as described below.

**Phase #1 "Define hierarchy".** The aim of the first step is to define the goal and the hierarchy of the decision problem. The decision maker or the experts team identifies a set of criteria for evaluating the *n* decision alternatives and assigns a percentage weight to each criterion; then assigns a score that is the impact of the criterion on the decision. The score of each decision alternative is the weighted average of the scores of each criterion on the decision by the weight assigned to each criterion. The top of hierarchy represents the goal of the decision problem. Lower levels represent criteria and sub-criteria in which the decision-making model is broken down. The bottom level represents all alternatives to evaluate in terms of the criteria [33].

**Phase #2 "Perform pairwise comparison and relative weight estimation".** After defining the hierarchy, the criteria are compared in pairs, the sub criteria and alternatives are compared in pairs by assigning a score of relative importance to the other. The sum of the weights must be 100%. Saaty suggested an increasing scale of values form 1 (*equal importance*) to 9 (*extreme importance*) when comparing two components [34]. The result of the comparison is the so-called *dominance coefficient* aij that represents the relative importance of the component on row (i) over the component on column (j), i.e., *a*ij *= w*i*/w*j*.* The pairwise comparisons can be represented in the form of a square matrix (n x n), symmetric and diagonal. The number of pairwise comparisons grows quadratically with the number of criteria and alternatives. The score of 1 represents equal importance of two components and 9 represents extreme importance of the component i over the component j. [35].

**Phase#3 "Perform consistency index".** Saaty (1990) proposed utilizing consistency index (CI) to verify the consistency of the comparison matrix [36]. The CI could then be calculated by: CI = (λmax − n)/n − 1. In general, if CI is less than 0.10, satisfaction of judgments may be derived. **Figure 5** shows a summary of the main steps and phases of the study.
