Cluster analysis involves the problem of optimal partitioning of a given set of entities into a pre-assigned number of mutually exclusive and exhaustive clusters. Here the problem is formulated in two different ways with the distance function (a) of minimizing the within groups sums of squares and (b) minimizing the maximum distance within groups. These lead to different kinds of linear and non-linear (0–1) integer programming problems. Computational difficulties are discussed and efficient algorithms are provided for some special cases.