The Science and Art of Formulating Linear Programs

Abstract

This paper describes the philosophy underlying the development of an intelligentsystem to assist in the formulation of large linear programs. The LPFORM system allowsusers to state their problem using a graphical rather than an algebraic representation.A major objective of the system is to automate the bookkeeping involved in thedevelopment of large systems. It has expertise related to the structure of many of thecommon forms of linear programs (e.g. transportation, product-mix and blendingproblems) and of how these prototypes may be combined into more complex systems.Our approach involves characterizing the common forms of LP problems according towhether they are transformations in place, time or form. We show how LPFORM usesknowledge about the structure and meaning of linear programs to construct a correcttableau. Using the symbolic capabilities of artificial intelligence languages, we canmanipulate and analyze some properties of the LP prior to actually generating a matrix.