A study into employee scheduling problem based on graph theory algorithms

Employee's scheduling problem is a very state-of-the-art problem that increases the efficiency and saves labor force effectively. This paper studies three scenarios that come close to the real situation of a specific factory: the first one considers only the requirements of the devices and the physical condition in the factory, based on which, the second takes the resting time of the employee into account, and the third one attempts to make the workers work off-peak in order to further increase the efficiency. To transform a real-life problem into a mathematic model, we map the condition of the factory into a graph where the devices are the nodes and the paths between the devices are the edges. To find the required minimum labor force, we use the Floyd's Algorithm to generate the complete graph and calculate the Hamiltonian cycle of it. To distribute the tasks evenly to every employee, in the first and the second scenarios, we equally separate the whole graph into several sub-graphs based on the minimum spanning tree, resulting in four and five sub-graphs respectively. However, for the third scenario, with the advantage of working off-peak, letting all the employees follow the Hamiltonian cycle is more efficient than letting each of them be responsible for each sub-graph. In this case, working off-peak requires the least labor force and provides the time to rest and eat for the workers. This model of employee scheduling problem can be utilized and expanded to many other fields including nursing patients in a hospital etc.