In this paper a reformulation technique is presented that takes a given linear zero-one programming problem, converts it into a zero-one polynomial programming problem, and then relinearizes it into an extended linear program. It is shown that the strength of the resulting reformulation depends on the degree of the terms used to produce the polynomial program at the intermediate step of this method. In fact, as this degree varies from one up to the number of variables in the problem, a hierarchy of sharper representations is obtained with the final relaxation representing the convex hull of feasible solutions. The reformulation technique readily extends to produce a similar hierarchy of linear relaxations for zero-one polynomial programming problems. A characterization of the convex hull in the original variable space is also available through a projection process. The structure of this convex hull characterization (or its other relaxations) can be exploited to generate strong or facetial valid inequalities through appropriate surrogates in a computational framework. The surrogation process can also be used to study various classes of facets for different combinatorial optimization problems. Some examples are given to illustrate this point.Petersen 1971 ), Glover and Woolsey (1974), and Glover 1975 ). Computational strategies for exploiting the structure of this reformulation were presented for zero-one quadratic programming problems in Adams and Sherali (1986). The analysis in the present

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This paper is concerned with the solution of linearly constrained zero-one quadratic programming problems. Problems of this kind arise in numerous economic, location decision, and strategic planning situations, including capital budgeting, facility location, quadratic assignment, media selection, and dynamic set covering. A new linearization technique is presented for this problem which is demonstrated to yield a tighter continuous or linear programming relaxation than is available through other methods. An implicit enumeration algorithm which uses Lagrangian relaxation, Benders' cutting planes, and local explorations is designed to exploit the strength of this linearization. Computational experience is provided to demonstrate the usefulness of the proposed linearization and algorithm.zero-one quadratic programming, linearization techniques, implicit enumeration, Lagrangian relaxation, Benders' decomposition

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