Multicommodity network flow model of a human resource allocation problem considering time periods

This article addresses the problem of finding work assignments for employees within a given time horizon in a company using a multicommodity network flow model. The problem of human resource allocation is defined by the actual manpower demands of different periods which may vary during different periods. The investigation focuses on when workers should be called in-house and for how long to satisfy demands, while also complying with labour standards and regulations. Additional targets may also be set up, such as minimising the overall number of labour, as well as meeting “comfort” expectations, i.e. the most even working time should be realised for every worker within the event horizon. The paper describes how the multicommodity network flow model is constructed and the corresponding MILP mathematical programming model is formulated in a simple situation where there is only one position for the labour. Finally, the article explains how to construct the multicommodity network flow model and the MILP model for the general case, where there are multiple positions for the labour requiring various skills and competences per position within the periods.