INTERACTIVE, SEMI-AUTOMATED, LAGRANGEAN RELAXATION AND DECOMPOSITION MODELING SYSTEM FOR LINEAR AND MIXED INTEGER PROGRAMMING

THIS PROJECT ADDRESSES METHODS TO PROVIDE PRACTITIONERS OF MATHEMATICAL PROGRAMMING WITH READY ACCESS TO THE ADVANCED LINEAR PROGRAMMING (LP) TOOLS OF LAGRANGEAN RELAXATION (LR) AND LAGRANGEAN DECOMPOSITION (LD). THESE TOOLS ARE USED PRIMARILY TO SOLVE MIXED INTEGER PROGRAMS (MIP). THESE PROGRAMS ARISE NATURALLY IN THE SOLUTION OF PROBLEMS THAT OCCUR IN MYRIAD INDUSTRIAL SETTINGS, SUCH AS PROCESS INDUSTRIES, MANUFACTURING, FINANCE, GOVERNMENT, TRANSPORTATION, AND UTILITIES. CURRENT APPLICATION OF STATE-OF-THE-ART TECHNIQUES TO THE SOLUTION OF THESE PROBLEMS IS CLEARLY HELD BACK BY A LACK OF MODELING TOOLS. THE PROJECT INITIATES WORK WHICH COMBINES ONE OF THE BEST MODELING TOOLS--GAMS--WITH THE CAPABILITIES OF LR AND LD TO PROVIDE AN ADVANCED MODELING SYSTEM THAT WILL FACILITATE THE SOLUTION OF LARGE, COMPLEX PROBLEMS. THE SYSTEM WILL INTERACTIVELY PROVIDE THE NON-EXPERT USER WITH FULL ACCESS TO THE POWER OF MODERN MATHEMATICAL PROGRAMMING TECHNIQUES FOR USE IN SOLVING PROBLEMS WITHIN THEIR OWN FIELDS OF EXPLORATION.