Computer assisted modelling of linear, integer and separable programming problems

Abstract

For mathematical programming (MP) to have greater impact upon the decision making process, MP software systems must offer suitable support in terms of model communication and modelling techniques . In this paper modelling techniques that allow logical restrictions to be modelled in integer programming terms are described and their implications discussed. In addition it is demonstrated that many classes of non-linearities which are not variable separable may be reformulated in piecewise linear form. It is shown that analysis of bounds is necessary in the following three important contexts: model reduction, formulation of logical restrictions as 0-1 mixed integer programs and reformulation of nonlinear programs as variable separable programs, It is observed that as well as incorporating an interface between the modeller and the optimiser there is a need to make available to the modeller software facilities which support the modelling techniques described here.