Two-stage Model of Vehicle Routing Problem with Fuzzy Demands and its Ant Colony System Algorithm

In this paper, we deal with the vehicle routing problem where vehicles have finite capacities and demands of customers are uncertain. We represent the uncertain demands by triangular fuzzy numbers and interpret them as possibility distributions. According to the same consideration as the stochastic programming with recourse, we treat the influence of the fuzziness of customers’ demands as recourse cost and formulate the problem as a two-stage possibilistic programming model. Defining the Fuzzy Mean of a fuzzy number as its the generalized mean value, the proposed model is equivalent to an ordinary programming problem and then a solution method based on Ant Colony System (ACS) can be proposed to give the best solution of the problem. Finally, some examples are given to illustrate the two-stage model and the solution algorithm.