Many problems, and in particular routing problems, require to find one or many circuits in a weighted graph. The weights often express the distance or the travel time between vertices. We propose in this paper various filtering algorithms for the weighted circuit constraint which maintain a circuit in a weighted graph. The filtering algorithms are typical cost based filtering algorithms relying on relaxations of the Traveling Salesman Problem. We investigate three bounds and show that they are incomparable. In particular we design a filtering algorithm based on a lower bound introduced in 1981 by Christophides et al.. This bound can provide stronger filtering than the classical Held and Karp’s approach when additional information, such as the possible positions of the clients in the tour, is available. This is particularly suited for problems with side constraints such as time windows.

In this paper, we study the problem of configuring a product family which has to satisfy diversified customer requirements. Modular design strategies allow a bill of materials to be generated for various finished products from a limited subset of modules. Simultaneously, a production location must be selected for the manufacture of each module. From a product point-of-view, the strategies adopted are often extreme, proposing either the manufacturing of the total diversity (all possible products) or a limited set of standardized products (only a few products are proposed). The objective of this paper is to investigate intermediate cases on this continuum, in order to better understand the potential for profit. Our comparison is based on the product family configuration (selection of the best modules) that minimizes production and transportation costs under time constraints.