A Constraint Programming Approach for the Traveling Purchaser Problem

We present a novel approach to the Traveling Purchaser Problem (TPP), based on constraint programming and Lagrangean relaxation. The TPP is a generalization of the Traveling Salesman Problem involved in many real-world applications. Given a set of markets providing products at different prices and a list of products to be purchased, the problem is to determine the route minimizing the sum of the traveling and purchasing costs. We propose in this paper an efficient approach when the number of markets visited in an optimal solution is low. We believe that the real-world applications of this problem often assume a bounded number of visits when they involve a physical routing. It is an actual requirement from our industrial partner which is developing a web application to help their customers' shopping planning. The approach is tested on academic benchmarks. It proves to be competitive with a state of the art branch-and-cut algorithm and can provide in some cases new optimal solutions for instances with up to 250 markets and 200 products.

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