This paper is motivated by the problem of fitting pipes of different d
iameters into a shipping container. Here we study the subproblem of fi
tting circles of different sizes into a rectangle since that problem i
s a central part of the larger problem. We formulate this situation as
a nonlinear mixed integer programming problem and develop a number of
heuristic procedures for (approximately) solving this problem. The he
uristics are based on a variety of solution building rules that emulat
e the process of packing a container. Some of these methods, including
a genetic algorithm, were based on a more structured design intended
to provide solutions which are 'stable' from a stowage viewpoint. Thes
e heuristics are described in detail and their relative performances a
re compared for a sample set of 66 randomly generated problems. Based
on this sample, the best performing heuristic methods were a quasi-ran
dom technique and a genetic algorithm of the 'stable' solution structu
re.