Solving the asymmetric traveling purchaser problem

The Asymmetric Traveling Purchaser Problem (ATPP) is a generalization of the Asymmetric Traveling Salesman Problem with several applications in the routing and the scheduling contexts. This problem is defined as follows. Let us consider a set of products and a set of markets. Each market is provided with a limited amount of each product at a known price. The ATPP consists in selecting a subset of markets such that a given demand of each product can be purchased, minimizing the routing cost and the purchasing cost. The aim of this article is to evaluate the effectiveness of a branch-and-cut algorithm based on new valid inequalities. It also proposes a transformation of the ATPP into its symmetric version, so a second exact method is also presented. An extensive computational analysis on several classes of instances from literature evaluates the proposed approaches. A previous work by Singh and Oudheusden published in 1999 solves instances with up to 25 markets and 100 products, while the here-presented approaches prove optimality on instances with up to 200 markets and 200 products.