Table 1

The performance of all three algorithms IQP-Cplex, Greedy and TSP-based on the $ 100 $ simulated instances for the $ n $-station datasets, where $ n \in \{16, 17, \cdots, 20\} $. In this experiment, a light truck is dispatched with its capacity $ Q = 15 $ and its own weight ignored. Rows 3–5 (6–8, respectively) contain the average carbon emissions (average travel distances, respectively) and their standard deviations over the $ 100 $ instances, in the solutions by the three algorithms.The last row records the average running times of IQP-Cplex and the standard deviations"

Fig.1

The performances of the three algorithms IQP-Cplex, Greedy and TSP-based on the $ 100 $ simulated instances of the $ 20 $-station dataset, when a light service vehicle of capacity $ Q = 15 $ is deployed: (a) The carbon emissions and (b) the travel distances. Note that in the two plots, the instances are sorted in different orders for better viewing"

Fig.2

The running time of IQP-Cplex on the $ 100 $ simulated instances of the $ 20 $-station dataset, where the instances are sorted in increasing running time order"

Fig.3

The service paths generated by the three algorithms on two simulated instances of the $ 20 $-station dataset, on the left of which Greedy significantly outperforms TSP-based in carbon emission and on the right TSP-based significantly outperforms Greedy. (a) the paths by IQP-Cplex, with emission 121.13 and travel distance 52.52 (left) and emission 117.22 and travel distance 65.68 (right); (b) the paths by Greedy, with emission 146.90 and travel distance 53.67 (left) and emission 277.57 and travel distance 55.87 (right); (c) the paths by TSP-based, with emission 353.48 and travel distance 97.41 (left) and emission 176.41 and travel distance 68.82 (right). In the figures, the dots represent labelled stations with the depot labelled $ 0 $; a directed edge tells from which station to another the service vehicle moves along the streets"

Table 2

The performance of the two algorithms Greedy and TSP-based on the $ 100 $ instances for each of the $ 25 $-station and $ 110 $-station datasets. In the rows 3–6 (7–10, 11–14, respectively), a light (medium, large, respectively) truck is dispatched with its capacity $ Q = 15 $ ($ 25, 50 $, respectively) and its weight equivalent to $ a_0 = 0 $ ($ 10, 20 $, respectively) bicycles"

Table 3

The performance of the two algorithms Greedy and TSP-based on the $ 100 $ instances for each of the $ 25 $-station and $ 110 $-station datasets, using a combination of a light (medium, large, respectively) truck and extra $ 5 $ ($ 10 $, respectively) bicycles"

Table 4

The performance of the two algorithms Greedy and TSP-based on a collection of $ 100 $ simulated instances for the $ 110 $-station dataset, where the simulated surplus or shortage is limited to $ 1 $ and the vehicle capacity $ Q \in \{1, 2, 4, 8\} $ (the weight of the vehicle is $ 0 $)"