1 Set Solutions = , TotalCosts = , TravelCosts = , PenaltyCosts = , Reliabilities = ; |
2 Calculate the expected travel time for each edge (, ) (, , ) in CVRPSTT |
according to its distribution function; |
3 For to step , do: |
4 Transform CVRPSTT to the well-known CVRP in which the maximum vehicle working |
time is set to that cannot be exceeded by any vehicle and the travel time |
between any pair of nodes is replaced with its expected value; |
5 Solve the CVRP () by using any existing heuristic and insert the obtained solution OS into |
Solutions; |
6 Set TotalCost = 0, where TotalCost denotes the expected total cost for solution OS, |
TravelCost = 0, where TravelCost denotes the expected travel cost for solution OS, |
PenaltyCost = 0, where PenaltyCost denotes the expected penalty cost for solution OS, and |
Reliability = 0, where Reliability denotes the reliability for solution OS; |
7 For to step 1, do: |
8 Construct the simulant travel time matrix, each element of which is generated |
according to its travel time distribution function and indicates the simulant travel time |
for an edge, for example (, ) for the travel time of edge (, ); |
9 Calculate the total cost, denoted as C1, the travel cost, denoted as C2, the penalty |
cost, denoted as C3, and the reliability, denoted as C4 for solution OS according to |
their definitions in Section 2 by using to substitute the travel time of each edge |
(, ) and using W to represent the maximum vehicle working time that cannot be |
exceeded by any vehicle; |
10 Set TotalCost TotalCost + C1/, TravelCost TravelCost + C2/, |
PenaltyCost PenaltyCost + C3/, and Reliability Reliability + C4/; |
11 Next ; |
12 Insert TotalCost into TotalCosts, TravelCost into TravelCosts, PenaltyCost into |
PenaltyCosts, and Reliability into Reliabilities; |
13 Next ; |
14 Get the minimum expected total cost from TotalCosts and its corresponding solution CS from |
Solutions. |
15 Improve the solution CS by a method that is further described in Algorithm 2; |
16 Return the improved solution CS and its corresponding total cost, travel cost, penalty |
cost and reliability, which have been updated in step 15. |