Abstract
This paper deals with the vehicle routing problem involved with fuzzy/imprecise vehicle travel times and customer service times, these fuzzy/imprecise times are represented as fuzzy numbers and interpreted as possibility distributions. According to the same consideration as the stochastic programming with recourse, we treate the inŽuence of the fuzziness of travel times and service times as recourse cost. and solve the fuzzy vehicle routing problem through twostage decisions. As the result, a two-stage possibilistic programming model is formulated. By choosing an appropriate definition of fuzzy mean, we can show that the proposed model is equivalent to an ordinary crisp programming problem. Furthermore, We propose a solution method based on Ant Colony System (ACS) to obttain the best solution of the problem. Finally, some examples are given to illustrate the two-stage model and the solution algorithm.
