**3. Related Works**

According to the observations on personnel scheduling, most studies focused on creating appropriate shift schedules or work programs for workers, considering a deterministic workload. The research process of this paper started with an investigation of the review articles [7,8]. After that point, the cited paper was investigated, which were given in the review articles. The whole reference list was checked and completed in related articles. Search phrase combinations were stated: Workforce scheduling, personnel scheduling and staffing.

Personnel scheduling literature showed a variety of investigation methodologies that brought together a specific analytical approach with a solution or evaluation technique. A number of studies, mathematical programming categories such as goal programming, linear programming, dynamic programming, and integer programming or optimization were classified as intuitive. Queuing, constraint programming and simulation were other categories for solution technique.

In general, scheduling has an important role in the production and service sector [9]. Most popular studies are done in the shift scheduling area. Shift scheduling is a widely studied area, which is a process that plays an important role in manufacturing and service industries. SSPs can be very complicated, especially in the case of multiple shifts with a large number of employees due to multiple constraints and skill-based works. Shift scheduling problem is a complex NP-hard integer programming problem. There are some examples about large-scale scheduling problems in the literature. As a literature observation, the SSP study in the energy sector has not been encountered in previous studies before. The SSP can be complex, especially in the case of several shifts, with many employees and skills, due to complex constraints and solution alternatives. Especially in most of the shift scheduling studies, the application results were not given. At this point, our study reveals its difference from other studies. Considering all of these, it is thought that shift scheduling studies on energy facilities are a new area waiting to be explored.

In Figure 2, a general literature overview is shown. Those studies are the most related studies to this paper. As is shown in Figure 2, solution methods and objectives/criteria are investigated. Generally; heuristic methods [10–24], integer programming [25–38] and goal programming [39–49] are the most used techniques for solving SSP. Within the scope of all the studies in Figure 2, some studies which were thought to be most similar to the model structure of our study were selected and explained in detail below.

Aickelin et. al. [10] have studied a heuristic technique which is called Improved Squeaky Wheel Optimization (ISWO) for scheduling problems of the drivers in their work. This method develops the main Squeaky Wheel Optimization (SWO) method.

Aickelin et al. [11] developed a solution to two different staff scheduling problems by discussing and analyzing a heuristic method. The new model improves the effectiveness and execution speed. The results are presented on two different areas of staff scheduling. These are: Bus and train driver shift schedules and nurse shift schedules.

Yunes et. al. [13] have dealt with the issue of shift scheduling for a firm using hybrid algorithms and integer programming methods in their work. In this article, the general team managemen<sup>t</sup> problem has been discussed, which derives from the daily operation of an urban transit bus company serving the public area. They divided the problem into two distinct subproblems: Shift scheduling and crew rostering. They studied each of these problems using constraint logic programming and mathematical programming approaches. Moreover, hybrid column generation algorithms are developed for solving problems, with combining constraint logic programming methods and mathematical programming.

Akjiratikarl et al. [14], the problem of scheduling home caregivers was solved by the Particle-based Swarm Optimization (PSO), the meta-intuitive technique for population. The proposed methodology is applied, tested and compared with existing solutions on various real problem examples. With these aspects of the study revealed, it showed the difference between the others.

Abbink et. al. [24] have successfully implemented a complex SSP model in their work. The authors described the corresponding analysis methods for scheduling the personnel. The authors have developed an alternative heuristic model that satisfies personnel. New schedules produced according to the alternative production model have reduced personnel costs.

In Alfares [27]'s study, a four day-off scheduling problem for three weeks were resolved. A mathematical model of this problem has been formulated and solved efficiently by setting a limit on the workforce dimension.

Trilling et al. [28] have studied the SSP of the nurses at the hospital in their work. Their study focuses two methods to solve the staff scheduling problem based on constraint and integer programming. Maximization of the fairness of the schedule is the main objective. They tested two techniques in order to be compared.


**Figure 2.** Literature Overview.

Lezaun et al. [29] studied the shift scheduling of railroad drivers. They presented a practical study on how to provide a more equitable annual work allocation for Metro Bilbao. The proposed model is solved as a series of four types of integer programming problems. The main benefit of this paper is to combine part-time allocation with a workload unevenly distributed on the days of the week and a planning time frame divided into five periods of three different types.

In Alfares [32]'s paper, the Information Technology help desk operators described personnel shift schedules for a large petrochemical company. The aim of the author was to reduce the cost of labor by setting the best staff level and employee weekly tour schedules needed to cover the changing workload during the 24-hour work period. An integer programming model has been formulated and solved to determine tour scheduling assignments. Selected tour scheduling offers better service at a lower cost and for fewer employees.

In another study Lezaun et al. [33], presented a case study commissioned by the Spanish railway carrier for the annual rostering of shift schedules for the station personnel. A mixed rostering process

was used in their research. These problems were resolved using the computer software LINGO package. The model of the study was similar to our model structure.

Corominas et al. [34] aimed at eliminating the issue of production planning by making shift schedules of production workers in their work. They proposed a mixed-integer linear program model. The model helped to solve the problem of scheduling the production and the working hours of an expert team which runs in a multi-product process.

Bard et al. [35] investigated the tour scheduling problem in the United States Postal Service for their work. The study suggested a model to tour scheduling problem for decreasing the size of the personnel scheduling, targeted with several scenarios with integer linear programing. The whole mathematical model included not only full-time but also part-time workers, in addition the specific constraints described by the union contract. They solved the problem faster and in a more cost-efficient way.

Corominas et al. [36] have studied problems such as labor balancing and regulation, using a mixed integer programming model in their work. Their study presented the scheduling problem of annual working hours for any employee, where weekly working hours belong to a pre-set finite set and day-off weeks are the same for all employees. The problem is modeled and solved as a mixed integer linear program.

Ba ˘g et al. [39] investigated the SSP of nurses using a 0–1 goal programming and analytic network process in their work. The analytical networking process (ANP) was used to determine the weights of the goal program. The model was implemented in a state hospital.

Hung-Tso et al. [40] investigated the problem of staff scheduling with the goal programming technique in their work. A linear goal programming model is proposed, and three managemen<sup>t</sup> goals are considered simultaneously for generating a roster.

Li et al. [41], Kassa and Tizazu [42], Louly [43], Labadi et al. [44] and Todovic et al. [45] studied shift scheduling by using goal programming method and intuitive methods together.

Shuib and Kamarudin [46], studied an SSP of the workers at the largest power plant in Malaysia. Their study aimed to define the basic criteria and conditions of the shift planning problem at the power plant in order to formulate the goal programming model for the shift programming problem, which optimized the daytime preferences of the workers and determined the optimal scheduling for the model-based workers. The study focused on three legs which were shift scheduling, day-off scheduling, and scheduling with demands. The study involved scheduling 43 personnel in a specific department of the power plant for 28 days where personnel work in three shifts (morning, evening, and night shifts) and with day-offs.

Ernst et al. [50] conducted a bibliographic study that contributed significantly to the literature on personnel SSPs in their work. They do not review the software packages in their work. Rather, they review scheduling problems in specific areas of application and the models and algorithms reported in the literature for the solutions. They also search for commonly used methods to solve staff problems.

Azaies and Al-Sharif [51] have solved the SSPs of the nurses by using a 0–1 goal programming method in their studies. This study is an example of an NP-hard integer programming problem. The model of the study is similar to our model structure. The constructed model calculates as well as some of the policies proposed in the literature regarding both the hospital targets and the preferences of the nurses. Hospital objectives include providing uninterrupted service with unnecessary nursing skills and staff size and avoiding additional costs for unnecessary overtime.

Topalo ˘glu [52] studied the problem of shift scheduling health-care personnel with goal programming method. The author suggested a goal programming (GP) model that includes both hard and soft constraints for a monthly planning period. Hard constraints must be strictly observed but may be violated if soft constraints are required. The relative significance values of soft constraints were calculated by the analytic hierarchy process (AHP) used as deviation coefficients from the soft constraints in the objective function. Their models were tested in the emergency room of a large local

university hospital. The main results of the study are that realistic problems can be solved quickly, and the schedules created have very high qualifications according to the schedules prepared manually.

In Alfares [53]'s study, a simulation approach was presented for workers' permission schedules when daily labor demands were random variables. The author created a simulation model and stated that the proposed approach is a case study application. The model stated that the employees had a limited number of jobs, included variable workload, and that employees had policy restrictions on the selection of work programs. The shift scheduling model also offered an alternative for leave days, reducing average production times for maintenance work orders by 25% without increasing the number of employees or cost.

Alfieri et al. [54] have defined an intuitive procedure with an intuitive branch-price algorithm based on a dynamic programming algorithm to find a suitable solution for pricing. They tested the results on the timetable of train lines.

Chu [55] solved the SSP of airport staff using the goal programming technique in his work. Chu proposed an integrated crew duty assignment for the luggage department staff at Hong Kong International Airport. The results could be adopted as a good crew schedule. The result showed that it was both feasible and the model satisfied various work conditions and minimized idle shifts.

In Thompson and Pullman's [56] study, the SSP of the staff were solved. The study focused on workforce schedules breaks or reliefs of the workers.

Sinreich and Jabali [57] used a linear programming model and simulation tools to solve the SSP in their work. In their study, they used a linear optimization model (S-model) and a heuristic iterative simulation-based algorithm (SWSSA) for scheduling the resources' work shifts, one resource at a time. Their algorithm was tested using data that was gathered from emergency departments of five general hospital. By using this model, they were able to achieve a reduction in patient's "length of stay" minutes.

The other paper of Al-Yakoob and Sherali [58] concerns the issue of assigning employees to a range of work centers, taking into account the preferences expressed for specific shifts, days and business centers by using a heuristic method. Computational results have shown that the proposed approach can facilitate the creation of good quality scheduling even for large-scale problematic cases at a reasonable time. De Matta and Peters [59] used branch and price; Tsai and Li [60] used genetic algorithm and Lezaun et al. [61] used binary programming for solving scheduling problems.

Rönnberg and Larsson [62] studied the problem of appointing nurses shift scheduling in the Swedish healthcare sector. The authors present a pilot study that aims to determine if it is possible to create an optimization tool that presents a program that is automatically available based on the charts recommended by nurses. The study was conducted in a typical Swedish nursing ward, where we developed a mathematical model and presented timetables. The results of this study are highly encouraging and sugges<sup>t</sup> ongoing studies. Zolfaghari et al. [63] used genetic algorithm and Alsheddy and Tsang [64] used linear programming for solving scheduling problem.

Fırat and Hurkens [65] performed personnel shift schedules with mixed integer programming. The authors assigned technicians to tasks with multi-level skills requirements. The study deals with the scheduling of complex tasks with a non-homogeneous resource set. They created programs by repetitively applying a flexible matching model that selects the tasks to be processed and which creates technician groups assigned to task combinations. The underlying mixed integer programming model is capable of reviewing technician-task distributions and performs very well, especially in the case of rare skills. Asensio-Cuesta et al. [66] used genetic algorithm for solving scheduling problem.
