A Mathematical-Computer Language for Linear Programming Problems

Abstract

This paper describes the development of a compiler which permits the translation of linear programming problems from a mathematical statement of the problem to a GAMS statement. The GAMS statement can then be read by the computer and the linear programming problem can be solved. Thus it is demonstrated that it is feasible to develop a computer language which will permit one to use mathematical symbols to direct the computer to solve a class of linear programming problems.The paper provides a small example linear programming transportation problem and shows how the problem may be input to the computer in a mathematical formatting language and then translated (i) into a mathematical statement and (ii) into a GAMS statement. Then a description is given of the lexical analyzer generator and the parser generator that were used to develop the math to GAMS translator.The present version of the translator can handle only a very restricted set of problems. Thus the paper closes with a description of the work which will be required to enable the translator to handle a much wider class of programming problems.