An ant colony system approach for fuzzy traveling salesman problem with time windows

Traveling salesman problem with time windows (TSPTW) is a well-known problem in logistics management. It seeks to find a minimum cost tour among customers while all customers are visited at their time windows. To better reflect the real situations of logistics management, this paper concentrates on customers’ satisfaction aspect of TSPTW, extends the basic mathematical modeling of the problem to fuzzy traveling salesman problem with time windows (FTSPTW), and presents an ant colony system algorithm to solve the problem. One advantage of this new modeling is its flexibility which enables us to optimize the delivery process in the network of customers with different satisfaction patterns and different priorities. The other advantage is that by the use of fuzzy time windows, not only customers’ preference for tolerable interval of time for service but also desirable time for service can be considered. Numerical results for a well-known benchmark problem and a real case study both confirm that optimization of the customers’ satisfaction is completely different from traditionally minimizing the total traveling time as well as the proposed algorithm which considers that customers’ favorites is completely superior to the algorithm that only pays attention to minimizing total travel time. These results provide an opportunity for future comparisons of different solution methods for the FTSPTW.