**5. Case Study**

This study was carried out on a large-scale shift scheduling optimization with the sustainability of the electricity generation of a NGCCPP for 80 workers at their place of destination directly acting considering programming model for 30 days in Turkey. The application area and the magnitude of the problem have been realized by the combination of the methods mentioned for the first time in the literature. The implementation steps of the work are given in Figure 3. Our study was conducted with four levels. The First Level was getting shaped in the name of the data collection and model development. The second stage was generated as ANP calculations and analysis of the result. The third level was generated as a model computation and analysis step. The fourth level was the validation and verification of the model. In the first level, all data were taken from the technical managemen<sup>t</sup> and human resource department of the power plant.

**Figure 3.** Schematic representation of the study.

In this study, scheduling focuses on three steps. These are demand modeling, scheduling of shifts, and scheduling of the days-off. This paper deals with SSP of the personnel who are in working for generation of the electricity to the power plant. The goal programming method is used for its advantages in many shifts and many employees of many workers.

### *5.1. Determining the Workers' Skill Weights with Analytic Network Process (ANP)*

Analytic Network Process includes decision-maker's judgments value. It can also provide a decision-making process included in the model. Besides significant tangible or intangible factors to be correct, the decision must be examined. ANP gives solution that can accommodate within the complex structure and this method is capable of easy calculation. As mentioned in the first phase of the work, there are a number of situations that stop electricity production if it is checked and not intervened at the required times. The ability of each worker working in the natural gas combined cycle line to intervene in these situations is different. As it seen in Figure 4, ANP steps are applied in order. Schematic representation of the network structure can be seen in Figure 5.

**Figure 4.** Schematic representation of the analytic network process (ANP) steps.

There are nine criteria of the skills of the workers. Each criterion is determined with the expert of the power plant. The network structure was established based on the internal and external dependencies among the criteria in the hierarchical structure. According to these nine criteria, each personnel's skill weight is determined. These criteria are given in Table 1.

**Table 1.** Criteria about personnel skills (C1, C2, . . . , C9).


Consistency ratios (CR) of the binary comparison matrix prepared with the central experts were found to be less than 0.10. This means that the matrices were consistent. Three types of super matrix calculations are made in ANP. These are the unweighted supermatrix, weighted supermatrix and limit supermatrix. On a lean quilt; matrices obtained as a result of initial effects. The relative weight vectors obtained from the ANP charts are placed on the columns and rows of this matrix.

**Figure 5.** Schematic representation of the network structure.

After transferring the data to the super decisions 3.0 package program, the weighted sequence of the alternatives is reached by obtaining the non-weighted super matrix, the weighted super matrix and the limit super matrix, respectively. Limit super matrix of the ANP calculations is given in Appendix A as Figures A1–A3.

After all calculations, each worker's score is determined with the help of the nine criteria. In Table 2, ANP weights of each worker are given.


**Table 2.** ANP Weights (*ti*) of the workers (P1, P2, P3, . . . P80).

In this model, a seniority-based calculation was made in order to incorporate the skill basics into the model, and a separate mean value was calculated for each level of seniority level. In calculating these average values, the number of seniorities (4 different levels) and the individual weight values (obtained in ANP calculations) were used. Therefore, the weights are included in the model. According to this, the average values for the shift supervisor, foreman, expert and assistant are given in Table 3 respectively.

**Table 3.** Seniority-based ANP weights (*ti*) of the workers.


The values which are observed in Table 3 will be used in the goal constraints.

### *5.2. Proposed Goal Programming Model*

Satisfying every goal specified by the decision-makers may not always be possible to completely provide. Therefore, goal programming is often referred to as a sequence of procedure in which the multiple goals are satisfied in their priority order [71]. The shift scheduling model will also attempt to satisfy several goals like establishing fairness among personnel. Because of that reason, a unique goal programming model is an excellent approach to solve this problem.
