Alternative Model Formulations

Abstract

The single step subproblems of the Customized Machine Tool model (see chapters 3 to 6) are formulated as mixed integer linear problems which can be solved with standard mathematical programming methods. The first subproblem, i.e., the Module Design subproblem, is a set covering problem. There exists an extensive literature on solution methods for such problems (for example, see Garfinkel and Nemhauser [1972], Bradley, Hax and Magnanti [1977], Winston [1994], Eppen et al. [1993] and Bertsimas and Tsitsiklis [1994]). Numerous sources are available on linear programs, formulation alternatives and solution algorithms. Jeroslow and Lowe [1984] show some subtleties of mixed-integer linear programming and develop effective modeling techniques. Despite of their combinatorial complexity, solving these subproblems to optimality is possible but the decisions based on these solutions may be suboptimal when solving the models sequentially. In order to find an optimal solution for all subproblems the models need to be combined into one master problem, the so called Customized Machine Tool model (CMTM), as stated before.