Reverse logistics sourcing models with multiproduct reliability constraints

We consider a multiproduct sourcing problem where each finished product must meet explicit reliability requirements. The critical reliability of each product is determined by its components, and the objective is to source the components at a minimum cost from a combination of new and used sources while ensuring each product meets its critical reliability requirement. We develop two models to determine optimal sourcing policies: an exact model that uses mixed integer non-linear programming, and an approximate model that uses integer linear programming. We perform computational tests on a large number of diverse benchmark problems and compare the solution quality and computational time of each model. We find that while the exact model requires significant amounts of time for modest-sized problems, the approximation model provides near-optimal solutions across all problem characteristics in very small amounts of time. We also characterise circumstances whereby cost savings can be realised through used sources.