We analyse the problem of executing periodic operations on a minimum number of identical processors under different constraints. The analysis is based on a reformulation of the problem in terms of graph colouring. It is shown that different constraints result in colouring problems that are defined on different classes of graphs, viz. interval graphs, circular-arc graphs and periodic-interval graphs. We discuss the colouring of such graphs in detail. Keywords: periodic assignment, graph colouring, interval graphs, circuJar-arc graphs, periodic-interval graphs.