5.2.4.1. Goal Constraints

The total number of shifts assigned to each staff by their seniority should be as equal as possible. *Goal 1:* Constraints for Shift Supervisors

$$\sum\_{i=1}^{4} t\_i \, \ast \, \, X\_{ijk} - d\_{1jk}^+ + d\_{1jk}^- = \, 1 \ast 0.06432254 \mathfrak{j} = 1, 2, 3, \dots, mk = 1, 2, \dots, n \tag{33}$$

*Goal 2:* Constraints for Foremen

$$\sum\_{i=5}^{16} t\_i \, \* \, X\_{ijk} - d\_{2jk}^+ + d\_{2jk}^- = \, 3 \ast 0.026957512 \, j = 1, 2, 3, \dots, mk = 1, 2, \dots, n \tag{34}$$

*Goal 3:* Constraints for Experts

$$\sum\_{i=17}^{40} t\_i \, \ast X\_{i\bar{j}k} - d\_{3\bar{j}k}^{+} + d\_{3\bar{j}k}^{-} = \, 6 \ast 0.022802299 \, j = 1, 2, 3, \dots, mk = 1, 2, \dots, n \tag{35}$$

*Goal 4:* Constraints for Assistants

$$\sum\_{i=41}^{80} t\_i \, \ast X\_{ijk} - d\_{4jk}^+ + d\_{4jk}^- = 10 \ast 0.016094762j = 1,2,3,\dots,mk = 1,2,\dots,n \tag{36}$$

5.2.4.2. Objective Function

$$\min Z = \sum\_{j=1}^{30} \sum\_{k=1}^{3} d\_{1jk}^{-} + d\_{1jk}^{+} + d\_{2jk}^{-} + d\_{2jk}^{+} + d\_{3jk}^{-} + d\_{3jk}^{+} + d\_{4jk}^{-} + d\_{4jk}^{+} \tag{37}$$

5.2.5. Analysis of The Result

All goals have the same weight. Solving of the model is used with the features computer which processor "Intel (R) Core (TM) i7-2800 CPU@2.00 GH", 16 GB of memory and Windows 10 operating system. The proposed model, ILOG CPLEX Studio IDE is written in the program and is solved with the CPLEX solvent. The proposed schedule is created after running the ILOG CPLEX Studio IDE Solver at a reasonable time.

The complete assignment results can be seen in Figure 6. In order to examine the results in detail, the amount of deviation or not, if any, was calculated. The results show that a 1.56% positive deviation was observed from the second goal. A 0.48% negative deviation was observed to the fourth goal. There was no deviation from the first and third goals. As can be seen here, the deviation rates are very low, and the model has yielded positive and efficient results.

The model of this study increases the balanced assignments of the workers and that the program needs to adapt these workers on shift scheduling. Thus, it will increase the satisfaction of workers in terms of considering their shift schedule. As it seen from the Table 4, workloads of the personnel are unstable and irregular when the schedules are done in the manual. It has been determined that staff assignments are made by ignoring the hard and soft constraints.

In the Table 5, the workloads of each personnel can be seen after scheduling is done with a mathematical model. All hard constraints are satisfied and many of the soft constraints are satisfied. Worker's preferences are not ignored.

**Figure 6.** The final schedule.


**Table 4.** Workloads of each personnel with manual scheduling.

**Table 5.** Workloads of each personnel after scheduling is done with mathematical model.


Computational results are given in Table 6. When the results are examined, the ratio of the demands that are met before the work is done and the rates after the work are done are different from each other. According to gathering results, fair scheduling requests were met, and fairness was provided from shift schedules. The preferences mentioned in the study constitute the entire hard and soft constraints. In the previous manual scheduling, 4 of 10 constraints, some hard, some soft, were not available. After the solution of the proposed mathematical model, all hard and weak constraints were met. 24 of the total 80 employees work 22 days and 56 of them work 23 days in a month for proposed scheduling mathematical model.

**Table 6.** Computational result.


This scheduling study, together with shift scheduling issues, has made very high contributions to reducing costs. In order to express the contributions of this work in decreasing costs, it is more appropriate to first explain the calculation over the capacity of the plant. We can say that if the power plant runs at 100% capacity, installed capacity of the power plant is 1000 MW. According to this, the monthly capacity can be calculated as 720 hours (24 hours × 30 days). 1 MW electricity is selling by 17.1 Kuru¸s (One Turkish Lira (༲) is equal to 100 Turkish Kuru¸s) from the Energy Market Inspection Agency (EPDK, Ankara, Turkey). This value is the wholesale electricity sales price for 2018 in Turkey. We can find the monthly 100% total generation capacity of the NGCCPP as 720.000 MW (1000 MW × 24 Hours × 30 Days).

There are some shutdown problems of the power plant also included, which arise from doing shift scheduling manually. When the shift scheduling is done manually, on average 53 hours were lost because of SSP. Due to the faults from shift scheduling, 53 hours shutdown caused 90.630.000 ༲ expenses to the NGCCPP (53 Hours × 1000 MW × 17,1 Kr¸s × 100). After the proposed schedule was applied in six months in the power plant, some results were gathered and calculated from the engineering department. According to this, 53 hours loss has been decreased to 4 hours loss after the proposed model of shift scheduling was done. After our implementation of the new schedule, only 4 hours shutdown were seen in the NGCCPP because of the faults from shift scheduling errors. 4 hours shutdown cause 6.840.000 ༲ expenses to the NGCCPP (4 Hours × 1000 MW × 17,1 Kr¸s × 100). According to this calculations, 83.790.000 ༲ total profit (90.630.000 ༲ – 6.840.000 ༲) is gathering from proposed model of shift scheduling. For this reason, this article differs from other studies in the literature in the context of giving the results of application.
