<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Swap trailer transport organisation problem originates from the traditional vehicle routing problem (VRP). Most of the studies on the problems assume that the travelling times of vehicles are fixed values. In this paper, the uncertainties of driving times are considered and a chance constrained programming problem is proposed. An improved simulated annealing algorithm is used to solve the problem proposed. The model and algorithm described in this paper are studied through a case study, and the influence of uncertainty on the results is analysed. The conclusion of this study provides theoretical support for the practice of trailer pickup transport.</p></abstract>

Swap trailer transport organisation problem originates from the traditional vehicle routing problem (VRP). Most of the studies on the problems assume that the travelling times of vehicles are fixed values. In this paper, the uncertainties of driving times are considered and a chance constrained programming problem is proposed. An improved simulated annealing algorithm is used to solve the problem proposed. The model and algorithm described in this paper are studied through a case study, and the influence of uncertainty on the results is analysed. The conclusion of this study provides theoretical support for the practice of trailer pickup transport.

Solution to Chance Constrained Programming Problem in Swap Trailer Transport Organisation based on Improved Simulated Annealing Algorithm

Research Institute of Highway Ministry of Transport

Transport Planning and Research Institute, Ministry of Transport

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Swap trailer transport organisation problem originates from the traditional vehicle routing problem (VRP). Most of the studies on the problems assume that the...

Node number	1	2	3	4	5	6	7	8	9	10	11
1	0	1	2	1	2	1	3	1	0	0	0
2	1	0	6	0	4	7	18	0	1	3	3
3	1	4	0	1	2	2	3	1	1	1	1
4	1	0	1	0	0	0	0	0	1	0	0
5	2	3	2	0	0	1	1	0	1	0	0
6	1	6	2	0	2	0	5	0	0	1	1
7	3	15	3	0	1	4	0	1	2	1	1
8	1	0	1	0	0	0	1	0	0	0	0
9	0	1	1	1	1	0	2	0	0	0	0
10	0	2	1	0	1	1	1	0	0	0	0
11	0	3	1	0	0	1	1	0	0	0	0

Node number	Time window	Node number	Time window	Node number	Time window
1	7:00–19:00	5	7:30–13:00	9	9:30–16:00
2	9:00–15:00	6	9:30–14:00	10	10:00–18:00
3	8:30–17:00	7	8:00–17:00	11	8:30–15:30
4	8:00–17:30	8	9:00–16:30

Node number	1	2	3	4	5	6	7	8	9	10	11
1	0	60	40	100	80	55	90	75	25	105	110
2	60	0	80	155	100	70	130	115	75	160	130
3	40	80	0	120	45	30	50	105	55	100	150
4	100	155	120	0	160	145	135	50	80	50	85
5	80	100	45	160	0	30	45	145	100	130	185
6	55	70	30	145	30	0	65	130	80	130	165
7	90	130	50	135	45	65	0	135	100	100	185
8	75	115	105	50	145	130	135	0	50	85	50
9	25	75	55	80	100	80	100	50	0	85	90
10	105	160	100	50	130	128	100	85	85	0	130
11	110	130	150	85	185	165	185	50	90	130	0

The value of $σ_{ij}^{2}$ \sigma _{ij}^2	0	1	4	9	16
Number of tractors	47	49	58	75	103
C(unit: L)	14,123	14,264	15,405	17,716	22,500
TK(unit: t·km)	567238	567238	567238	567238	567238
RT	4.23	4.11	3.48	2.69	1.96
E(unit: g)	67.97	68.65	74.14	85.26	108.29

Solution to Chance Constrained Programming Problem in Swap Trailer Transport Organisation based on Improved Simulated Annealing Algorithm

Published Online: Feb 28, 2020

Page range: 47 - 54

Received: Nov 12, 2019

Accepted: Jan 14, 2020

DOI: https://doi.org/10.2478/amns.2020.1.00005

Keywords
road transport, swap trailer transport, tractor despatching, random driving time, simulated annealing algorithm

© 2020 Tao Li et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Freight volume between urban nodes (unit: veh)

Time windows of semi-trailer distribution points in each urban node

Distance between urban nodes (unit: km)

Solution results of tractor despatching schemes with different variances

Node number	1	2	3	4	5	6	7	8	9	10	11
1	0	1	2	1	2	1	3	1	0	0	0
2	1	0	6	0	4	7	18	0	1	3	3
3	1	4	0	1	2	2	3	1	1	1	1
4	1	0	1	0	0	0	0	0	1	0	0
5	2	3	2	0	0	1	1	0	1	0	0
6	1	6	2	0	2	0	5	0	0	1	1
7	3	15	3	0	1	4	0	1	2	1	1
8	1	0	1	0	0	0	1	0	0	0	0
9	0	1	1	1	1	0	2	0	0	0	0
10	0	2	1	0	1	1	1	0	0	0	0
11	0	3	1	0	0	1	1	0	0	0	0

Node number	1	2	3	4	5	6	7	8	9	10	11
1	0	60	40	100	80	55	90	75	25	105	110
2	60	0	80	155	100	70	130	115	75	160	130
3	40	80	0	120	45	30	50	105	55	100	150
4	100	155	120	0	160	145	135	50	80	50	85
5	80	100	45	160	0	30	45	145	100	130	185
6	55	70	30	145	30	0	65	130	80	130	165
7	90	130	50	135	45	65	0	135	100	100	185
8	75	115	105	50	145	130	135	0	50	85	50
9	25	75	55	80	100	80	100	50	0	85	90
10	105	160	100	50	130	128	100	85	85	0	130
11	110	130	150	85	185	165	185	50	90	130	0

Node number	1	2	3	4	5	6	7	8	9	10	11
1	0	1	2	1	2	1	3	1	0	0	0
2	1	0	6	0	4	7	18	0	1	3	3
3	1	4	0	1	2	2	3	1	1	1	1
4	1	0	1	0	0	0	0	0	1	0	0
5	2	3	2	0	0	1	1	0	1	0	0
6	1	6	2	0	2	0	5	0	0	1	1
7	3	15	3	0	1	4	0	1	2	1	1
8	1	0	1	0	0	0	1	0	0	0	0
9	0	1	1	1	1	0	2	0	0	0	0
10	0	2	1	0	1	1	1	0	0	0	0
11	0	3	1	0	0	1	1	0	0	0	0

Node number	1	2	3	4	5	6	7	8	9	10	11
1	0	60	40	100	80	55	90	75	25	105	110
2	60	0	80	155	100	70	130	115	75	160	130
3	40	80	0	120	45	30	50	105	55	100	150
4	100	155	120	0	160	145	135	50	80	50	85
5	80	100	45	160	0	30	45	145	100	130	185
6	55	70	30	145	30	0	65	130	80	130	165
7	90	130	50	135	45	65	0	135	100	100	185
8	75	115	105	50	145	130	135	0	50	85	50
9	25	75	55	80	100	80	100	50	0	85	90
10	105	160	100	50	130	128	100	85	85	0	130
11	110	130	150	85	185	165	185	50	90	130	0

Solution to Chance Constrained Programming Problem in Swap Trailer Transport Organisation based on Improved Simulated Annealing Algorithm

Published Online: Feb 28, 2020

Page range: 47 - 54

Received: Nov 12, 2019

Accepted: Jan 14, 2020

DOI: https://doi.org/10.2478/amns.2020.1.00005

Keywordsroad transport, swap trailer transport, tractor despatching, random driving time, simulated annealing algorithm

© 2020 Tao Li et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Freight volume between urban nodes (unit: veh)

Time windows of semi-trailer distribution points in each urban node

Distance between urban nodes (unit: km)

Solution results of tractor despatching schemes with different variances

Keywords
road transport, swap trailer transport, tractor despatching, random driving time, simulated annealing algorithm

Node number	1	2	3	4	5	6	7	8	9	10	11
1	0	1	2	1	2	1	3	1	0	0	0
2	1	0	6	0	4	7	18	0	1	3	3
3	1	4	0	1	2	2	3	1	1	1	1
4	1	0	1	0	0	0	0	0	1	0	0
5	2	3	2	0	0	1	1	0	1	0	0
6	1	6	2	0	2	0	5	0	0	1	1
7	3	15	3	0	1	4	0	1	2	1	1
8	1	0	1	0	0	0	1	0	0	0	0
9	0	1	1	1	1	0	2	0	0	0	0
10	0	2	1	0	1	1	1	0	0	0	0
11	0	3	1	0	0	1	1	0	0	0	0

Node number	1	2	3	4	5	6	7	8	9	10	11
1	0	60	40	100	80	55	90	75	25	105	110
2	60	0	80	155	100	70	130	115	75	160	130
3	40	80	0	120	45	30	50	105	55	100	150
4	100	155	120	0	160	145	135	50	80	50	85
5	80	100	45	160	0	30	45	145	100	130	185
6	55	70	30	145	30	0	65	130	80	130	165
7	90	130	50	135	45	65	0	135	100	100	185
8	75	115	105	50	145	130	135	0	50	85	50
9	25	75	55	80	100	80	100	50	0	85	90
10	105	160	100	50	130	128	100	85	85	0	130
11	110	130	150	85	185	165	185	50	90	130	0