We discuss the problem of combining the conflicting objectives of equity and utilitarianism, for social policy making, in a single mathematical programming model. The definition of equity we use is the Rawlsian one of maximizing the minimum utility over individuals or classes of individuals....

Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms...

We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program with recourse in which the total cost of the capacity expansion and the...

We present two recent integer programming models in molecular biology and study practical reformulations to compute solutions to some of these problems. In extension of previously tested linearization techniques, we formulate corresponding semidefinite relaxations and discuss practical rounding...

This paper introduces an exact algorithm for solving integer programs, neither using cutting planes nor enumeration techniques. It is a primal augmentation algorithm that relies on iteratively substituting one column by columns that correspond to irreducible solutions of certain linear...

We consider the problem of estimating optima of integer programs { max <Emphasis Type="Bold">cx | A <Emphasis Type="Bold">x≤<Emphasis Type="Bold">b,<Emphasis Type="Bold">0≤<Emphasis Type="Bold">x≤<Emphasis Type="Bold">1, <Emphasis Type="Bold">x− integral} where <Emphasis Type="Bold">b<Emphasis Type="Bold">0, <Emphasis Type="Bold">c≥<Emphasis Type="Bold">0 are rational vectors and A is an arbitrary rational m×n matrix. Using randomized rounding we find an efficiently verifiable sufficient condition for optima of such...</emphasis></emphasis></emphasis></emphasis></emphasis></emphasis></emphasis></emphasis></emphasis></emphasis></emphasis>

We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program with recourse in which the total cost of the capacity expansion and the...