A Simulation-Based Algorithm for the Capacitated Vehicle Routing Problem with Stochastic Travel Times

Algorithm 2

The method of improving a solution generated by a CVRP heuristic.

1 Set the incumbent solution IS = CS, where CS is obtained from step 14 of Algorithm 1;

2 Fabricate a solution IS′ whose expected total cost is set to an infinite value that cannot be

    exceeded by the total cost of any solution;

3 While the expected total cost of IS is less than that of IS′, do:

4   Set IS′ = IS, Solutions = Ø;

5   Fetch the vehicle that returns to depot at the earliest expected time from all vehicles in IS

      and denote the vehicle’s route by er;

6   Fetch the vehicle that returns to depot at the latest expected time from all vehicles in IS

      and denote the vehicle’s route by lr;

7   For each customer node cn of lr, do:

8     For each position ep of er, into which a customer node can be inserted, do:

9      Delete cn from lr and insert cn into er at its position ep;

10       Insert the solution obtained from the above step into Solutions;

11    Next ep;

12   Next cn;

13   Fetch a solution with the least expected travel cost from Solutions into IS;

14   Use Monte Carlo simulation method like steps 6–11 in Algorithm 1 to calculate the expected

      total cost of solution IS;

15 Endwhile;

16 Return the solution IS′.