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.