Technical Note—An Integer Approach to Modular Design

This paper discusses the modular-design problem, as set up by David Evans, in which the module is made of several components: there exist E_i of the ith component in each module, and for every application j, D, modules will be needed to satisfy all component requirements. The problem is to design a module (i.e., choose Ē) such that the requirements are satisfied at a minimum cost of surplus components. Mathematically, the problem is: minimize_Ei,Dj ∑_i=1^i=me_iE_i ∑_j=1^j=nd_jD_j subject to E_iD_j ≧ R_ij; E_iD_j are positive integers and e_i, d_j, are constants. The conclusion of the paper is that the two procedures outlined by Evans and by A. Charnes and M. Kirby for the noninteger case cannot be used to find the integer solution. An integer branch-and-bound technique is proposed that has been shown to be useful in the solution of small problems and that has potential use in larger problems.