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This paper implements a swarm intelligence based algorithm called ant colony optimization to solve the min-max Single Depot Vehicle Routing Problem (SDVRP). A traditional SDVRP tries to minimize the total distance travelled by all the vehicles to all customer locations. The min max SDVRP, on the other hand, tries to minimize the maximum distance travelled by any vehicle. This problem is of specific significance for time-critical applications where one wants to minimize the time taken to attend any customer. The algorithm developed is an extension of SDVRP algorithm developed by Bullnheimer et al. in 1997 based upon ant colony optimization. A computer simulation model using the MATLAB is developed. A comparative study is carried out to evaluate the proposed algorithm's performance with respect to the algorithm developed by Carlsson et al. in terms of the optimality of solution and time taken to reach the solution.