Algorithm for the random personnel assignment problem

The article presents the problem of random personnel assignment, which occurs in a real-world company. A mathematical model for this issue has been formulated. Subsequently, a priority algorithm for solving the random personnel allocation problem has been proposed. Finally, an example illustrating the algorithm’s operation is presented.1. INTRODUCTION
The problem of assigning personnel to workstations is an important issue related to work organization. The criterion for evaluating this assignment is, for example, achieving maximum personnel efficiency or filling all workstations while taking into account the qualifications and skills of employees.
Ensuring the staffing of workstations is particularly important in a certain company where there are specific requirements regarding the allocation of employees to positions. In this company, there is a need for random assignment of employees to service stations. This is due to the fact that potential customers should not know by whom they will be served. Such random allocation of employees will reduce the potential risk of corrupt behavior.
No considerations regarding random personnel assignment were found in the literature. However, the general assignment problem [4] is considered, which boils down to assigning members of one group of objects (e.g., employees) to members of another group (e.g., tasks, workstations). A special case is the classic personnel assignment problem [2]. The problem is described as a bipartite graph. The disjoint parts of the graph, between which there are no internal connections, constitute a set containing nodes representing employees and a set containing nodes representing workstations. There are arcs with assigned weights between personnel and workstations. The weights of the connections between employees and workstations determine the productivity (efficiency) of an employee when performing tasks at a given workstation. In the classic problem, the number of workstations is equal to the number of assigned employees, and each employee is connected to each workstation. Each employee is assigned to one workstation (performs one task). Exactly one employee is assigned to each workstation (task). The sought solution is a set of assignments (arcs connecting employees to workstations) for which work efficiency, measured as the sum of the weights of the selected connections, is maximized. (…)

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