The continuous multiple-modular design problem

In this article we extend our previous work on the continuous single-module design problem to the multiple-module case. It is assumed that there is a fixed cost associated with each additional module used. The Kuhn–Tucker conditions characterize local optima among which there is a global optimum. Modules are associated with partitions and a special class, guillotine partitions, are characterized. Branch-and-bound, partial enumeration, and heuristic procedures for finding optimum or good guillotine partitions are discussed and illustrated with examples.