Parametric nonlinear integer programming: The right-hand side case

In this paper, the authors present algorithms for solving families of nonlinear integer programming problems in which the problems are related by having identical objective coefficients and constraint matrix coefficients. They consider two types of right-hand sides which have the forms ^and where is a given set of vectors, is a parametric function and the parameter varies from zero to one. The approach consists primarily of solving the most relaxed problem using branch and search method and then finding the optimal solutions of the proposed parametric programming problems. The application of this methodology to a parametric chance-constrained problem is illustrated with applications in system reliability optimization problems.