**1. Introduction**

Personnel efficiency and productivity is one of the basic objectives of many companies and organizations. While trying to find all the existing elements that can affect efficiency and productivity, personnel scheduling is an important problem that must be attentively steered. Personnel scheduling problems can be even more complicated by shifts in plans for industries in which shift personnel work seven days a week, and specific personnel have to work non-routine working hours. Some service providers must continuously operate, such as power plants, hospitals, and security and safety-related units while serving mostly the common good, and scheduling problems such as the above are further complicated.

Electricity generation in power plants and maintenance or repair work require complex structured, specialized, and labor-intensive activities. When considering the high impact and indispensability of electrical energy in daily human life, the process of assigning suitable employees to such specialized work and improving the performance of these employees comes to the fore with the impact on society, in addition to the economic value added. Power plants are continuous generation facilities with the main purpose of achieving uninterrupted, reliable, efficient, economical, and environmentally-friendly energy generation called sustainable energy supply, therefore, it is an indispensable requirement to manage the generation, manpower, material, and maintenance processes within this system by operating the plants in accordance with the operating rules in the direction of this five-legged comprehensive target. In other words, maximizing employee performance related to personnel managemen<sup>t</sup> through balanced work distribution, appointment of the appropriate employees for the appropriate jobs, etc. has critical importance in terms of sustainable energy supply. With today's constantly developing technology, power plants are operated by shift personnel from a main control center or supervisory control and data acquisition (SCADA) system, which distributes control to the power plant (DCS) remotely. Throughout the world, as in Turkey, although not with the SCADA system currently, personnel-operated power plants are still existing. Compared to advanced technology, the number of shift personnel working in these old plants is naturally higher than that of modern plants, and the probability of operator errors from shift personnel is higher than that of SCADA. Put differently, shift personnel may experience faulty operations due to fatigue, lack of concentration, experience, fair working order, and thus lack of motivation in these power plants. As a result, long-term failures and thus millions of kWh of energy and income loss may occur. In addition, a negative social impact may occur due to the lack of sustainable energy supply. From this point of view, it can be said that personnel scheduling models used for fair and appropriate assignments have critical importance in electricity generation facilities.

In spite of the various models proposed and resolved in SSPs, shift scheduling studies involving personnel in power plants or other related areas are still insufficient. Previous works on SSPs have mainly focused on factory or security personnel, health personnel (i.e., doctors and nurses), teachers, and police officers. For this reason, this study is a new application of models for shift scheduling problems (SSPs) and will be relevant to solving SSPs.

When the distribution of resources used in electricity generation in the world is examined, it is seen that the most widely-used resource for electricity generation is coal, after which natural gas is the second most common resource. When we look at the resources with the largest share of electrical energy generation in the countries with the largest economies, coal is predominantly used in the United States, China, India, and Germany, natural gas in Russia, nuclear energy in France, and renewable energy resources in Canada. Natural gas is the number one resource to generate electricity in Turkey, and this has not changed in the last 10 years. Over the last 10 years in Turkey, power was generated on average of 40% due to natural gas, and the share of this resource in Turkey's energy mix was 35.17% as at of the end of 2018. According to these data, natural gas is the most widely used resource in electricity generation in Turkey [1]. Although there is no resource availability in Turkey for natural gas, NGCCPPs are the most widely used power plants, because these large-scale facilities have important advantages such as having high capacities, low setup times, low installation costs, low environmental impacts, short run times, high yields, ease of operation and maintenance, and long economic lifespans, compared to other fossil-fueled-based power plants. The high share of natural gas in Turkey's total electricity generation with the above-mentioned advantages of the NGCCPPs and the importance of the personnel scheduling in the power plants are taken into consideration together, and the objective of the study is to schedule the shift personnel fairly and according to their capabilities in the large-scale NGCCPP in Turkey.

NGCCPPs consist of generation blocks, and each combined cycle generation block includes two gas turbines, two compressors, two gas turbine generators, two waste heat boilers, two condenser units, one steam turbine and one steam turbine generator. In addition to these, dry-type or sea water-cooled wet type cooling towers, water treatment plant, switchgear, and control and control systems are located in the plant.

Generation blocks operate independently of each other in NGCCPPs. However, blocks use some facilities that are in common. Electricity generation in these plants is carried out in two different stages, as shown in Figure 1. The natural gas is mixed with air and it is been burned in gas turbines. Burned gas turns the gas turbine on the same shaft as a generator and generates electricity in the first stage. Simultaneously, the hot gases generated from this combustion are sent to the waste heat boiler, and steam is generated by this heat. Steam reaching the required pressure and temperature is sent to the steam turbine and the turbine is rotated to generate the second stage electricity by the generator means located on the same shaft as the steam turbine. Steam from the steam turbine is condensed in the condensers with the cooling water from the cooling towers and converted into water. The condensation water, which accumulates in the lower part of the condensers, is sent to the waste heat boilers for reheating. Steam produced in the boiler is sent to the steam turbine and the cycle is completed. There are three different pressure levels (low, medium, high pressure) in the boilers, which is produced by steam force in order to keep the efficiency at maximum level. Thus, the hot gases in the boilers are utilized as much as possible [2].

**Figure 1.** Schematic representation of the working principle of the combined cycle power plant.

Turbines are the most important of the systems mentioned in NGCCPPs. This is, as the basic reasons explain, that electricity is produced in gas-turbine steam turbines. If the turbines are deactivated, the corresponding block disables the unit (each gas turbine is called a unit) and the system stops. On the other hand, some NGCCPPs have by-pass lines, and the hot gas from an accidental gas turbine, which is formed in the waste heat boilers of the steam turbine, can be directly discharged to the atmosphere by means of a by-pass chute and only electricity generation can be continued in gas turbines (single operation). In addition, these systems are structurally more complex than other systems in the plant.

When previous studies were examined, SSP with this size (30 days for 80 personnel) within the energy sector has not been studied before. The problem of the scheduling of worker's shift known as SSP can be complicated, especially in the case of multiple shifts and multiple employees with many employees and skills, due to the sophisticated constraints and solution alternatives. Preparing the schedules of staffs manually is thus infertile and time consuming. Therefore, a methodical approximation for initiating a useful schedule is required within a short period of time. Currently, the scheduling of the operation of the shifts of the NGCCPP is carried out manually. This paper deals with the formulation of a model for the shift scheduling problem for NGCCPP employees working with newly defined constraints that define the structure of the industry, organizational policies, and shift schedules, and the requirements that determine the daily preferences of workers. The model seeks to produce the most appropriate monthly shift plan that maximizes employees' job satisfaction. In this way, stoppages caused by operator error are reduced from 53 hours to 4 hours, and both financial gain is achieved, and the target of sustainable energy supply is reached at this power plant. Furthermore, with this study which provides multi-objective scheduling on the basis of the capabilities of a large group of 80 employees working in NGCCPP for the first time in the literature, a shortcoming in the SSP literature is eliminated.

The paper is shaped as follows: After a brief introduction, the next section gives a literature overview around the problems of shift scheduling. The next section gives information about the perspectives and applications of the study. The last section gives related discussions of the computational results and the conclusion of the study.

### **2. Shift Scheduling Problem (SSP)**

Coordination of workload plans and assignment of personnel and staff planning and personnel scheduling in order to meet the demand for resources that change with time. These problems occur in service industries, such as police officers, call center operators, hospital nurses, transportation personnel (aircraft crews, bus drivers) and so on. It is a very important topic for personnel scheduling. These environments are often prolonged and unsteady, and personnel needs undulate over time. Schedules typically include equipment requirements, trade union rules, etc. It is the subject of various restrictions dictated by inherent features of personnel scheduling problems. The problems that arise tend to be combinatorically difficult. For personnel scheduling problems, Baker proposed one of the first classification methods [3]. In the study of Baker [3] and Pinedo [4] SSP is a brand of the personnel scheduling problem. Personnel scheduling problem's structure can be divided into several categories. General solution method is with integer programming. This method contains a large class of personnel scheduling problem solutions. Besides, there is a specific category of integer programming problems, namely cyclical personnel problems. This problem can be used in terms of class and a combinatorial viewpoint. Apart from these, crew and operator scheduling problems have a different model structure. In the personnel scheduling problem, there are assignment models. In spite of the fact that every assignment mold belongs to a financial reason, it is a reason why the cost is relatively easy. A cycle structure is thinking of a beforehand. With annotative adjustments, the cycle can be a single day, another week or a few weeks. Part of the previous episode is limited to a loop.

In general, the SSP deals with the assignments of employees to each shift determining the number and criteria. Each shift is getting shaped to specific start and finish times. The number and placement of moats time or the long and the short lengths of the shifts are limiting with legal and business rules. The main goal of scheduling shifts is to optimize employee allocations. Besides, it also helps to minimize the total cost. This requires that each shift be precisely assigned to personnel, qualified by several constraints that must be satisfied. SSP is key to ensuring that services continuously operate without any timeframes in specific service sectors, as well as hospitals, police stations, seizure centers, railway stations and airports [5].

One of the main difficulties of shift scheduling concerns with requirements and limitations of existing personnel while a work pattern of each shifts depending on the number of certain regulations. This planning is getting more difficult when multiple shifts and break or idle times and/or lots of skilled and variable shifts are involved, where every shift needs a combination of these to fulfill the request for that shift. When highly skilled employees can accomplish many different activities during the same shift, the problem becomes more difficult. The shift programming problem's mathematical models are formulated to solve, subject to several constraints such as one shift per day, number of permits per day, shift order, gap between shifts, rest day after day and night shifts, consecutive days, and working consecutive night regulations, fixed hours for shifts, restricted working hours, number of workers based on skill or skill, etc. Restrictions taken into account in the SSP may include the ordering or preference of consecutive shifts or preferred shifts to be followed, forbidden shift sequences, constraints on demand, and minimum rest periods between shift changes. For this reason, various SSP variations can be found depending on the restrictions applied. A type of SSP is the Day-off SSP (D-SSP) that focuses on determining the most suitable rest days for an employee's planning horizon. This problem is that the cost of closed molds on different days is different and the goal is to minimize the

total labor cost. In this study, model formulation is considered preferences of the workers presented through its objective function and constraints.

In this paper, the SSP is formulated as Analytic Network Process (ANP) and Goal Programming (GP) model for personnel of power plant, referred to as the SSP-ANP-GP model. However, the recommended goal programming model is different from other models for scheduling shift personnel described above because of the different goals. The objective of the SSP-ANP-GP model is to maximize the personnel's needs, which is determined with four goals in the proposed model.

Mathematical programming models for the SSP can be solved using precise algorithms, intuitive approaches, and top-level information. Our model gives an optimal solution, but in the case of large-scale problems, it is hard to apply in terms of operation time and complexity. Because of that reason, metaheuristics and intuitive approaches are more hopeful options for these situations. It is much better in big-size problems when an intuitive, optimization is sufficient as a solution and has optimal solutions in reasonable time. Approximate optimization algorithm frameworks are meta-analyses that can be defined as a primary strategy or a general algorithmic framework that can be applied to a variety of problems with only a few changes. They are commonly used when they are confronted with a complex problem that cannot be resolved by certain algorithms [6]. The SSP-ANP-GP model of our paper is solved using the integer linear programming algorithm of IBM ILOG optimization tool (IBM, Armonk, New York, NY, USA), which employs the heuristics and exact approaches.

In our paper, a different SSP approach is used for the literature review in shift scheduling studies apart from other studies. It shows that our SSP application area is different from other data and application areas. The energy sector is a new sector for the SSP problems. According to the results of the investigated papers, shift scheduling studies are done for the main production or service personnel. In other words, there is a gap in scheduling of people working in auxiliary and complementary processes in the energy sector for personnel scheduling literature.

On the other hand, these processes may directly affect the quality levels of output of production and service systems, customer satisfaction levels, even sectoral positions of enterprises and social welfare level. The most important examples of this are continuous production systems such as electricity generation, petrochemical and cement production, telecommunication, and health services. However, personnel performing auxiliary and complementary processes may be partly or entirely engaged in the same work with the shift team directly involved in the main processes. The most important example in this situation is the power generation plants. Personnel operating and maintaining these facilities, especially those with electrical and electronic origins, can be operated as both shift and maintenance personnel. This provides significant advantages in terms of productivity, quality, uninterrupted production, and costs in terms of the establishment that owns the plant. Because of that reason, shift scheduling studies are very important in the energy sector, and above all, in power generation facilities.
