This project is concerned with the design of a new Reformulation-Linearization Technique (RLT) and the development of its application to various classes of problems arising in production, location-allocation, economics, and various engineering and systems design and operational contexts. At the heart of this methodology is a procedure developed under a previous National Science Foundation project for generating tight, higher dimensional, linear programming representations for linear and polynomial zero-one mixed-integer programming problems. The basic RLT procedure possesses a considerable degree flexibility that can be exploited to develop effective algorithmic variants. Various transformations and implementation schemes will be investigated in order to enhance the capability in solving both discrete and continuous nonconvex decision problems. The utility of the RLT scheme in generating facets and tight valid inequalities for important discrete classes of problems will also be explored. This will benefit other algorithms for mixed-integer zero-one problems. The methodology developed will be specialized to solve indefinite and concave quadratic programs, linear complementarily problems, location-allocation problems, and fixed-charge problems that arise in the different aforementioned applications.
