Solving quality control problems with an algorithm for minimax programs with coupled constraints

We propose a systematic algorithm to tackle a set of acceptance sampling problems introduced by Seidel [1] and their generalization when no prior knowledge is assumed. The problems are modeled as minimax problems with coupled or decoupled constraints. We use ideas from recent work on bi-level programming, reformulating the problem as a semi-infinite program with disjunctive constraints and employing a two phase discretization method to solve it. We use the KKT conditions of the inner problem of minimax to tighten the relaxation of the semi-infinite problem obtained by discretization. In addition, to avoid convergence trouble, a strategy based on a feasibility test relative to the objective value of the outer program is used.