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1. Introduction
The problem of police officers who work per shift in terms of ergonomics and efficiency has been widely discussed in the literature. There are different views about the mode that best suits police officers and it can be said that the generally accepted opinion has not been established yet. However, even when a particular police station chooses a particular mode, the problem of determining the specific working schedule of police officers, in accordance with the needs of the police station and preferences of policemen, still remains. Such schedules are usually done on a monthly basis by commanders of police stations, who consider this sort of administrative - nonpolice work difficult and time-consuming. In general, the problem of scheduling of employees in other industries is often taken as the optimization problem which resulted in the automation of specific schedule production. However, in practice, the police solve this problem without the help of the software in a manner that is known in the literature under the name of self-rostering (Silvestro and Silvestro, 2000).
In this paper, the problem of scheduling of police officers is viewed as the optimization problem in which police officers should determine the schedules that fully or partially satisfy the conditions relating to the: required number of officers per shift, rules of shift work, number of working hours of police officers, the monthly working standard, etc. For the observed problem, a mathematical model of goal programming has been formulated. Such a problem allows the formulation, in a situation where it is not possible to simultaneously satisfy all the needs of the police station and preferences of police officers, to depart from some requests. The paper consists of six sections. After the introductory section, in the second section, an overview of the literature on the issue of policemen scheduling and different ways of working in shifts, in terms of ergonomics and efficiency, will be given. The third part addresses the solving of police officers scheduling problem as an optimization problem. In the fourth section, the specific scheduling problem is described, as well as the mathematical model by which the problem is modeled. In the fifth part, the application of the formulated model is illustrated using the example of "real-life" police station. The last...