Dynamic vehicle routing for a dual-channel distribution center with stochastic demands and shared resources

doi:10.23919/JSEE.2025.000139

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (6): 1501-1531.doi: 10.23919/JSEE.2025.000139

• SYSTEMS ENGINEERING • Previous Articles

Dynamic vehicle routing for a dual-channel distribution center with stochastic demands and shared resources

Mei XU¹(), Feng YANG¹^,*(), Ting CHEN²()

¹ School of Management, University of Science and Technology of China, Hefei 230026, China
² School of Foreign Language, Hefei Normal University, Hefei 230601, China

Received:2025-03-05 Online:2025-12-18 Published:2026-01-07
Contact: Feng YANG E-mail:xmadyy@mail.ustc.edu.cn;fengyang@ustc.edu.cn;tinachen@mail.ustc.edu.cn
About author:
XU Mei was born in 1994. She received her B.S. and M.S. degrees in information management and information systems and in management science and engineering from Nanjing University of Posts and Telecommunications in 2016 and 2019, respectively. Currently, she is pursuing her Ph.D. degree in management science and engineering at the University of Science and Technology of China. Her research interests include supply chain management, logistics management, and path optimization. E-mail: xmadyy@mail.ustc.edu.cn

YANG Feng was born in 1977. He received his B.S. and Ph.D. degrees in finance by the University of Science and Technology of China in 2000 and 2006, respectively. He is a professor in the School of Management, University of Science and Technology of China. His research interests include multi-objective optimization and multi-criteria decision modeling. E-mail: fengyang@ustc.edu.cn

CHEN Ting was born in 1983. She received her B.S. and M.S. degrees in tourism management from Anhui Universit in 2005 and 2008, respectively. She received her Ph.D. degree in business administration from the University of Science and Technology of China in 2019. She is a professor at Hefei Normal University. Her research interests include platform supply chain and operations management. E-mail: tinachen@mail.ustc.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (71991464/71991460;72301261;72001066) and 2024 Anhui Province High-end Talent Introduction and Cultivation Project.

Abstract

Abstract:

This paper addresses a dynamic vehicle routing problem with stochastic requests in a dual-channel distribution center that utilizes shared vehicle resources to serve two types of customers: offline corporate clients (CCs) with fixed and stochastic batch demands, and online individual customers (ICs) with single-unit demands. To manage stochastic batch demands from CCs, this paper proposes three recourse policies under a differentiated resource-sharing scheme: the waiting-tour-based (WTB) policy, the advance-tour-based (ATB) policy, and the advance-customer-based (ACB) policy. These policies differ in their response priorities to random requests and the scope of route reoptimization. The problem is formulated as a two-stage stochastic recourse programming model, where the first stage establishes routes for fixed demands. In the second stage, we construct three stochastic recourse programming models corresponding to the proposed recourse policies. To solve these models, this paper develop rolling horizon algorithms integrated with mathematical programming models or metaheuristic algorithms. Extensive numerical experiments validate the effectiveness of the proposed algorithms and policies. The results indicate that both the ATB and ACB policies lead to cost savings compared to the WTB policy, especially when stochastic demands are urgent and delivery resources are quite limited. Specifically, when the number of ICs is small, the expected total cost savings can exceed 12%, and in some scenarios, savings of over 20% can be achieved. When the number of ICs is large, some scenarios can achieve cost savings exceeding 7%. Furthermore, the ACB policy yields lower costs, fewer worsened ICs, fewer trips, and less vehicle time than the ATB policy.

Key words: dynamic vehicle routing, stochastic request, dual-channel distribution, stochastic recourse programming, rolling horizon algorithm

Mei XU, Feng YANG, Ting CHEN. Dynamic vehicle routing for a dual-channel distribution center with stochastic demands and shared resources[J]. Journal of Systems Engineering and Electronics, 2025, 36(6): 1501-1531.

Figures/Tables 17

Table 1

Table 2

Notation in the second stage model"

Parameter	Definition
$ {T} $	Set of periods during a day’s working hours. $ {T}=\{\mathrm{1,2},\cdots ,Z\} $
$ \varOmega $	Set of random scenarios for demand realization. $ \varOmega =\{1, 2, \cdots , \|\varOmega \left\|\right\} $
$ {N}_{\tau \omega }^{+} $	Set of nodes of CCs that generate new requests in period $ \tau -1 $ in scenario $ \omega $. $ \left\|{N}_{\tau \omega }^{+}\right\|={n}_{\tau \omega }^{+} $
$ {N}_{\tau \omega }^{\#} $/$ {N}_{\tau \omega }^{-} $	Set of nodes of CCs/ICs whose trip departure times are no earlier than the start of period $ \tau $ in the latest schedule in scenario $ \omega $
$ {N}_{\tau \omega }^{\mathrm{*}} $	$ {N}_{\tau \omega }^{\mathrm{*}}={N}_{\tau \omega }^{\#}\cup {N}_{\tau \omega }^{-} $
$ {\overrightarrow{N}}_{\tau \omega }^{+} $	$ {{\overrightarrow{N}}_{\tau \omega }^{+}}=N^{+}_{\tau \omega }\cup {N}_{\tau \omega }^{\#} $
$ {N}_{\tau \omega }' $	$ {N}_{\tau \omega }'={N}_{\tau \omega }^{+}\cup {N}_{\tau \omega }^{\#}\cup {N}_{\tau \omega }^{-} $
$ {N}_{\tau \omega } $	$ {N}_{\tau \omega }=\left\{0\right\}\cup {N}_{\tau \omega }^{+}\cup {N}_{\tau \omega }^{\#}\cup {N}_{\tau \omega }^{-} $
$ {N}_{\omega }^{+} $	Set of CCs that generate new requests in scenario $ \omega $. $ {N}_{\omega }^{+}={N}_{1\omega }^{+}\cup {N}_{2\omega }^{+}\cup \cdots \cup {N}_{Z\omega }^{+} $
$ {G}_{\tau \omega }' $	Set of trips in the latest schedule in scenario $ \omega $, satisfying (i) active trips: the departure time is no earlier than the start of period $ \tau $, or (ii) inactive trips. $ {G}_{\tau \omega }'=\{{G}_{1\tau \omega }',{G}_{2\tau \omega }',\cdots ,{G}_{H\tau \omega }'\} $
$ {y}_{ij\tau \omega } $	Binary parameter. If node $ j $ is served after node $ i $ after the start of period $ \mathrm{\tau } $ in the latest schedule in scenario $ \omega $, $ {y}_{ij\tau \omega }=1 $; otherwise, $ {y}_{ij\tau \omega }=0 $. Note that $ {y}_{0i\tau \omega }={y}_{i0\tau \omega }=1(i\in {N}_{\tau \omega }^{+}) $. $ i,j\in {N}_{\tau \omega } $
$ {t}_{\tau } $	Start time of period $ \mathrm{\tau } $
$ [\underline{{t}_{i\omega }'},\overline {{t}_{i\omega }'}] $	Lower and upper bounds for the delivery time window of node $ i $’s new request in scenario $ \omega $. $ i\in {N}_{\tau \omega }^{+} $
$ {x}_{ik{g}'\tau \omega }' $	Binary variable. If node $ i $ is served on tour $ {g}' $ of vehicle $ k $ in period $ \mathrm{\tau } $ and scenario $ \omega $, $ {x}_{ik{g}'\omega }'=1 $; otherwise, $ {x}_{ik{g}'\omega }'=0 $. $ i\in {N}_{\tau \omega }',k\in K,{g}'\in {G}_{k\tau \omega }' $

Table 2

Table 3

Fig 1

Fig 2

Table 4

Table 5

Table 6

Table 7

Table 8

Fig 3

Table 9

Table 10

Fig 4

Table 11

Table 12

Table 13

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Parameter	Definition
$ N $	Set of transportation nodes, indexed by $ i $ and $ j $. Note that $ i=0 $ denotes the depot. $ N=\left\{0\right\}\cup {N}^{+}\cup {N}^{-}=\{\mathrm{0,1},2,\cdots ,{n}^{+},{n}^{+}+1,{n}^{+}+2,\mathrm{ }\cdots ,{n}^{+}+{n}^{-}\} $
$ {N}^{+} $	Set of CCs. $ {N}^{+}=\{\mathrm{1,2},\cdots ,{n}^{+}\} $
$ {N}^{-} $	Set of ICs. $ {N}^{-}=\{{n}^{+}+1,{n}^{+}+2,\mathrm{ }\cdots ,{n}^{+}+{n}^{-}\} $
$ {\overrightarrow{N}}^{-} $	Set of nodes of ICs and the depot. $ {\overrightarrow{N}}^{-}=\left\{0\right\}\cup {N}^{-} $
$ {N}' $	Set of nodes of customers. $ {N}'={N}^{+}\cup {N}^{-} $
$ K $	Set of vehicles. $ K=\{\mathrm{1,2},\cdots ,H\} $
$ G $	Set of trips. $ G=\{\mathrm{1,2},\cdots ,F\} $
$ Q $	Maximum capacity of vehicles
$ {\mathrm{sp}} $	Travel speed of vehicles
$ {t}_{ij} $	Travel time between transportation node $ i $ and transportation node $ j $. $ i,j\in N $
$ {s}_{i} $	Service time at transportation node $ i $. $ i\in N $
$ \underline{{t}_{i}},\overline {{t}_{i}} $	Lower and upper bounds of the delivery time window for node $ i $. $ i\in N $
$ M $	A fixed, sufficiently large number
$ {x}_{ikg} $	Binary variable. If node $ i $ is served on tour $ g $ of vehicle $ k $, $ {x}_{ikg}=1 $; otherwise, $ {x}_{ikg}=0 $. $ i\in {N}',k\in K,g\in G $
$ {y}_{ij} $	Binary variable. If node $ j $ is served immediately after node $ i $, $ {y}_{ij}=1 $; otherwise, $ {y}_{ij}=0 $. $ i,j\in N $
$ {r}_{kg} $	Ready time for tour $ g $ of vehicle $ k $. $ k\in K,g\in G $
$ {d}_{kg} $	Departure time for tour $ g $ of vehicle $ k $. $ k\in K,g\in G $
$ {c}_{i} $	Arrival time for node $ i $. $ i\in {N}' $
$ {b}_{i} $	Service start time for node $ i $. $ i\in {N}' $
$ {l}_{i} $	Late delivery time for node $ i $. $ i\in {N}' $
$ {p}_{k} $	Return time for vehicle $ k $ to the depot after completing all trips. $ k\in K $
$ {o}_{k} $	Overwork time for vehicle $ k $. $ k\in K $

Parameter	Definition
$ {N}_{\tau \omega }^{\#} $/$ {N}_{\tau \omega }^{-} $	Set of nodes of CCs/ICs that belong to trips with a return time later than $ {t}_{\tau } $ in the latest schedule in scenario $ \omega $
$ {\tilde {G}}_{\tau \omega }' $	Set of ongoing trips at $ {t}_{\tau } $ in the latest schedule in scenario $ \omega $. $ {\tilde {G}}_{\tau \omega }'=\{{\tilde {G}}_{1\tau \omega }',{\tilde {G}}_{2\tau \omega }',\cdots ,{\tilde {G}}_{H\tau \omega }'\} $
$ {\overrightarrow{G}}_{\tau \omega }' $	$ {\overrightarrow{G}}_{\tau \omega }'={G}_{\tau \omega }'\cup {\tilde {G}}_{\tau \omega }' $, $ {\overrightarrow{G}}_{\tau \omega }'=\{{\overrightarrow{G}}_{1\tau \omega }',{\overrightarrow{G}}_{2\tau \omega }',\cdots ,{\overrightarrow{G}}_{H\tau \omega }'\} $
$ {v}_{ik{g}'\tau \omega } $	Binary parameter. If node $ i $ is the current destination of the ongoing tour at $ {t}_{\tau } $ in the latest schedule in scenario $ \omega $, $ {v}_{ik{g}'\tau \omega }=1 $; otherwise, $ {v}_{ik{g}'\tau \omega }=0 $. $ i\in {N}_{\tau \omega }^{\mathrm{*}},k\in K,{g}'\in {\tilde {G}}_{k\tau \omega }' $
$ {z}_{i\tau \omega }' $	Binary variable. If the vehicle returns to the depot early after servicing node $ i $ in period $ \mathrm{\tau } $ and scenario $ \omega $, $ {z}_{i\tau \omega }'=0 $; otherwise, $ {z}_{i\tau \omega }'=1 $. $ i\in {N}_{\tau \omega } $
$ {y}_{ij\tau \omega }' $	Binary variable. If node $ j $ is served after node $ i $ in period $ \mathrm{\tau } $ and scenario $ \omega $, $ {y}_{ij\tau \omega }'=1 $; otherwise, $ {y}_{ij\tau \omega }'=0 $. $ i,j\in {N}_{\tau \omega } $

$ {n}^{+} $	Group C0				Group C1				Group C2
$ {n}^{+} $	Cost/CNY	Time/s	$\text{cs}_\text{to} $/%	$\text{cs}_\text{bs} $/%	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%
2	158.19	0.60	−	−	156.95	220.33	0.78	4.98	157.05	219.60	0.72	4.35
3	255.34	2.70	−	−	214.13	1039.38	16.14	30.00	223.87	996.77	12.32	24.65
4	219.97	12.41	−	−	208.31	4189.46	5.30	20.66	209.05	4011.15	4.96	20.36
5	324.13	19.56	−	−	323.40	6192.03	0.23	10.04	323.40	6011.72	0.23	10.23
6	228.81	14.54	−	−	227.14	7043.57	0.73	11.80	227.12	6845.27	0.74	11.92
Average	237.29	9.96	−	−	225.99	3736.95	4.64	15.49	228.10	3616.90	3.79	14.30

$ {n}^{+} $	Group C3				Group C4				Group C5
$ {n}^{+} $	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%
2	156.85	247.27	0.85	5.61	157.06	186.73	0.71	4.30	157.07	182.99	0.71	4.23
3	213.72	1080.25	16.30	31.34	214.19	824.24	16.12	31.34	215.28	811.41	15.69	30.34
4	209.87	4265.01	4.59	20.66	209.97	4300.86	4.55	20.66	208.19	3325.82	5.36	20.66
5	323.38	6475.14	0.23	10.04	323.45	6535.39	0.21	10.04	323.48	5009.37	0.20	9.92
6	227.16	7727.40	0.72	12.26	229.95	6726.92	−0.50	31.09	227.13	6212.30	0.73	11.88
Average	226.20	3959.01	4.54	15.98	226.92	3714.83	4.22	19.48	226.23	3108.38	4.54	15.41

$ {n}^{+} $	$ {n}^{-} $	$ H-Q-{\mathrm{sp}} $	WTB policy		ATB policy		ACB policy
			CPLEX		CPLEX		CPLEX		SA-RR		ALNS-RR
			Cost/CNY	Time/s	Cost/CNY	Time/s	Cost/CNY	Time/s	Cost/CNY	Time/s	Cost/CNY	Time/s
2	13	3-3-60	131.34	0.47	131.34	0.85	131.21	4.11	131.21	44.93	131.21	42.36
	14	3-3-60	173.08	0.44	147.64	1.03	141.99	2.34	141.99	47.20	141.99	49.81
	15	3-3-60	145.53	1.81	145.53	0.75	144.58	1490.56	144.58	47.58	144.58	46.48
	16	3-3-60	160.14	0.50	160.14	1.19	160.08	14969.26	160.08	53.14	160.08	55.81
	17	3-3-60	154.26	0.63	152.90	1.15	−	−	152.87	54.88	152.87	52.26
3	13	4-3-60	154.71	1.01	149.06	1.91	149.06	4.32	149.06	128.08	149.06	127.41
	14	4-3-60	156.76	1.89	156.76	2.13	156.74	15.95	156.74	136.70	156.74	158.78
	15	4-3-60	179.79	1.93	179.39	3.24	179.36	1469.62	179.36	141.70	179.36	165.68
	16	4-3-60	216.57	2.39	185.61	3.63	185.54	63093.18	185.54	163.98	185.54	164.70
	17	4-3-60	175.96	1.92	174.78	3.24	−	−	173.68	160.65	173.68	177.90

$ {n}^{+}/H $	WTB policy		ATB policy				ACB policy with SA-RR				ACB policy with ALNS-RR
$ {n}^{+}/H $	Cost/CNY	Time/s	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%
2-3	159.60	0.64	155.34	1.65	2.67	12.32	154.54	136.95	3.17	11.08	154.81	135.11	3.00	10.61
2-4	161.91	0.96	160.88	1.67	0.63	15.56	160.21	161.80	1.05	9.54	160.24	170.70	1.03	9.54
3-4	206.11	2.70	194.10	6.96	5.83	15.55	190.43	647.94	7.61	21.06	188.75	667.39	8.42	20.62
3-5	189.98	3.73	183.81	7.14	3.25	9.34	182.57	690.19	3.90	13.42	181.55	775.73	4.44	15.94
4-5	194.96	13.55	191.03	24.06	2.01	20.38	190.09	2309.22	2.50	21.94	190.41	2383.42	2.33	18.31
4-6	205.99	9.23	194.77	28.36	5.44	20.65	194.40	2454.87	5.62	22.36	194.37	2837.40	5.64	24.83
5-6	326.67	34.24	324.23	110.01	0.75	10.34	323.97	3634.61	0.83	8.41	323.94	4063.31	0.83	10.17
5-7	336.29	23.19	329.83	69.66	1.92	14.91	326.06	3680.46	3.04	12.51	326.22	4451.27	2.99	13.40
6-7	314.85	16.14	278.07	58.07	11.68	19.04	275.22	3912.97	12.59	23.85	274.48	4860.39	12.82	24.30
6-8	313.40	15.05	273.97	45.96	12.58	18.87	271.37	4068.90	13.41	20.51	271.69	4366.01	13.31	20.31
Average	240.97	11.94	228.60	35.35	5.13	15.98	226.88	2169.79	5.85	16.94	226.65	2471.07	5.95	17.31

Dynamic vehicle routing for a dual-channel distribution center with stochastic demands and shared resources

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Figure	Trip	Moment-Vehicle 1	Moment-Vehicle 2	Moment-Vehicle 3
Fig. 3(a)	1	8.30-8.90-9.70	8.30-9.60-11.10	8.30-9.10-9.61-9.87-11.05
	2	10.00-11.56-11.84-12.85-14.40	11.40-12.98-13.23-13.78-18.02	11.35-11.70-12.40-12.78-14.77
	3	14.70-15.38-15.93-17.21	−	−
Fig. 3(b)	1	8.30-8.90-9.70	8.30-9.60-11.10	8.30-9.10-9.61-9.87-11.05
	2	10.00-11.56-11.84-12.85-14.40	11.40-12.98-13.23-13.78-18.02	11.35-11.70-12.40-12.78-14.77
	3	14.70-15.31-16.11	−	15.07-15.75-16.30-17.51
Fig. 3(c)	1	8.30-8.90-9.70	8.30-9.60-11.10	8.30-9.10-9.61-9.87-11.05
	2	10.00-11.56-11.84-12.85-14.40	11.40-12.98-13.23-13.78-18.02	11.35-11.70-12.40-12.78-14.77
	3	14.70-15.31-16.11	−	15.07-16.37-17.88
	4	16.41-17.08-17.64-18.85	−	−
Fig. 3(d)	1	8.30-8.90-9.70	8.30-9.60-11.10	8.30-9.10-9.61-9.87-11.05
	2	10.00-11.56-11.84-12.85-14.40	11.40-12.98-13.23-13.78-18.02	11.35-11.70-12.40-13.20
	3	14.70-15.38-16.15	−	13.50-14.10-14.90
	4	−	−	15.20-15.88-16.43-17.64
Fig. 3(e)	1	8.30-8.90-9.70	8.30-9.60-11.10	8.30-9.10-9.61-9.87-11.05
	2	10.00-11.56-11.84-12.85-14.40	11.40-12.98-13.23-13.78-18.02	11.35-11.70-12.40-13.20
	3	14.70-16.01-17.51	−	13.50-14.10-14.90
	4	17.81-18.48-19.25	−	15.20-15.88-16.43-17.64
Fig. 3(f)	1	8.30-8.90-9.70	8.30-9.60-11.10	8.30-9.10-9.61-9.87-11.05
	2	10.00-11.56-11.84-12.85-14.40	11.40-12.98-13.23-13.78-18.02	11.35-11.70-12.40-13.20
	3	14.70-15.38-16.25-16.80-17.57	−	13.50-14.10-14.90
Fig. 3(g)	1	8.30-8.90-9.70	8.30-9.60-11.10	8.30-9.10-9.61-9.87-11.05
	2	10.00-11.56-11.84-12.85-14.40	11.40-12.98-13.23-13.78-18.02	11.35-11.70-12.40-13.20
	3	14.70-16.01-17.51	−	13.50-14.10-14.90
	4	−	−	15.20-15.88-16.74-17.30-18.07

Policy	Vehicle	Cost related to trips/CNY			Overtime cost/ CNY	Total cost/ CNY
Policy	Vehicle	Period 0	Period 3	Period 4	Overtime cost/ CNY	Total cost/ CNY
WTB	1	1: 8.81 7-3-10: 24.66	−	1: 61.04 13-15: 14.05	5.08	205.76
	2	2: 14.41 12-11-16: 20.40	−	−	0.14
	3	4-8-6: 13.81 9-5-14: 14.00	−	2: 29.36	−
ATB	1	1: 8.81	−	7-3-10: 24.66 2: 14.68 14: 11.86	7.51	155.18
	2	2: 14.41	−	12-11-16: 20.40	0.14
	3	4-8-6: 13.81	9-5: 13.00	1: 12.94 13-15: 12.96	−
ACB	1	1: 8.81	−	7-3-10: 24.66 2: 14.68	−	138.86
	2	2: 14.41	−	12-11-16: 20.40	0.14
	3	4-8-6: 13.81	9-5: 13.00	1: 12.94 14-15-13: 15.57	0.44

$ {\alpha }_\text{3} $	ATB policy/%						ACB policy/%
$ {\alpha }_\text{3} $	$ \text{cs}_\text{travel} $	$ \text{cs}_\text{fixed} $	$ \text{cs}_\text{CC} $	$ \text{cs}_\text{IC} $	$ \text{cs}_\text{overtime} $	$ \text{cs}_\text{to} $	$ \text{cs}_\text{travel} $	$ \text{cs}_\text{fixed} $	$ \text{cs}_\text{CC} $	$ \text{cs}_\text{IC} $	$ \text{cs}_\text{overtime} $	$ \text{cs}_\text{to} $
10	−0.35	−0.47	13.85	0.72	2.96	0.25	−0.34	−0.52	16.89	3.75	7.83	0.72
20	−0.66	−0.82	23.51	1.29	7.98	0.85	−0.57	−0.76	27.01	3.27	9.04	1.47
30	−0.95	−1.10	29.71	1.55	7.94	1.55	−0.76	−0.99	32.00	3.41	11.84	2.22
40	−1.17	−1.33	37.64	−4.86	2.37	2.34	−0.91	−1.23	39.81	−2.76	9.90	3.20
50	−1.55	−1.70	43.07	−7.77	−4.12	3.19	−1.05	−1.37	43.13	−2.43	8.59	4.14
60	−1.78	−1.90	44.73	−10.39	−9.99	4.04	−1.05	−1.37	43.73	−3.08	8.08	5.08
70	−1.88	−1.90	45.48	−12.43	−12.59	4.95	−0.95	−1.31	43.75	−2.62	9.05	5.94
80	−2.20	−2.35	49.04	−17.84	−17.00	5.78	−1.20	−1.76	46.58	−8.25	5.08	6.61
90	−2.35	−2.55	49.68	−17.52	−15.99	6.78	−1.42	−1.99	48.35	−7.51	5.93	7.73
100	−2.55	−2.94	51.35	−20.59	−17.59	7.57	−1.39	−2.33	48.77	−10.55	6.35	8.38
Average	−1.54	−1.71	38.81	−8.79	−5.60	3.73	−0.96	−1.36	39.00	−2.68	8.17	4.55

Group	$ {n}^{+} $	FR	WTB policy	ATB policy			ACB policy
Group	$ {n}^{+} $	Cost/CNY	Cost/CNY	Cost/CNY	$ \text{cs}_\text{to} $	$ \text{cs}_\text{bs} $	Cost/CNY	$ \text{cs}_\text{to} $	$ \text{cs}_\text{bs} $
W1	2	114.51	158.19	157.76	0.27	2.67	156.77	0.90	6.08
	3	147.22	255.34	232.59	8.91	16.96	224.22	12.19	30.63
	4	150.52	219.97	209.27	4.86	20.66	207.38	5.72	20.66
	5	211.62	324.13	323.68	0.14	8.23	323.36	0.24	10.38
	6	183.71	228.81	227.18	0.71	12.26	227.11	0.74	12.26
	Average	161.52	237.29	230.10	2.98	12.15	227.77	3.96	16.00
W2	2	132.35	189.97	189.22	0.39	4.06	188.73	0.65	4.89
	3	161.40	224.57	223.71	0.38	8.48	223.15	0.63	10.56
	4	184.39	384.74	337.26	12.34	18.15	334.68	13.01	19.09
	5	280.61	742.00	632.14	14.81	22.80	630.15	15.07	23.55
	6	204.90	399.64	399.64	0.00	0.00	399.62	0.01	0.01
	Average	192.73	388.18	356.39	5.58	10.70	355.27	5.88	11.62
W3	2	114.51	133.40	133.40	0.00	0.00	132.98	0.31	0.45
	3	146.19	166.85	166.85	0.00	0.09	166.84	0.01	0.09
	4	149.41	186.25	186.14	0.06	1.57	185.20	0.56	11.37
	5	210.53	269.94	269.94	0.00	0.00	269.85	0.03	0.17
	6	183.68	221.47	221.47	0.00	0.05	221.44	0.01	4.72
	Average	160.86	195.58	195.56	0.01	0.34	195.26	0.19	3.36

$ {n}^{+}-H $	$ Q $	FR	WTB policy	ATB policy			ACB policy
$ {n}^{+}-H $	$ Q $	Cost/CNY	Cost/CNY	Cost/CNY	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%	Cost/CNY	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%
2-3	3	138.18	180.26	180.26	0.00	0.00	168.25	6.66	15.22
	4	84.26	158.19	157.76	0.27	2.67	156.77	0.90	6.08
	5	97.03	128.18	126.63	1.21	11.92	126.41	1.38	12.70
	6	87.06	162.01	136.40	15.81	41.55	137.66	15.03	41.09
	7	84.26	120.21	113.12	5.90	30.79	112.78	6.18	31.14
	Average	98.16	149.77	142.83	4.64	17.39	140.37	6.03	21.24
2-4	3	131.28	161.25	157.26	2.47	26.36	156.98	2.65	27.56
	4	111.31	155.19	143.99	7.22	31.73	139.97	9.81	33.60
	5	95.01	137.68	129.47	5.96	29.96	130.66	5.10	29.98
	6	86.00	138.21	130.50	5.58	33.55	131.85	4.60	33.82
	7	82.14	102.71	101.84	0.85	9.26	101.59	1.09	11.76
	Average	101.15	139.01	132.61	4.42	26.17	132.21	4.65	27.34
3-4	3	147.22	255.34	232.59	8.91	16.96	213.51	16.38	30.47
	4	122.71	158.33	154.56	2.38	12.26	154.23	2.59	13.23
	5	107.50	208.15	160.80	22.75	37.74	163.56	21.42	40.89
	6	98.32	162.52	142.37	12.40	22.83	143.75	11.55	22.83
	7	93.35	297.41	157.46	47.06	69.64	160.16	46.15	70.85
	Average	113.82	216.35	169.56	18.70	31.89	167.04	19.62	35.66
3-5	3	144.49	182.02	181.57	0.25	1.31	181.30	0.40	3.38
	4	120.65	152.87	151.58	0.84	24.58	151.44	0.94	28.02
	5	105.32	168.10	153.40	8.74	27.86	153.40	8.74	27.93
	6	96.10	143.18	128.04	10.57	33.68	131.25	8.33	33.68
	7	93.19	229.53	150.75	34.32	56.69	150.82	34.29	57.86
	Average	111.95	175.14	153.07	10.95	28.82	153.64	10.54	30.17

$ {n}^{+}/H $	WTB policy		ATB policy				ACB policy with SA-RR				ACB policy with ALNS-RR
$ {n}^{+}/H $	Cost/CNY	Time/s	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%
2-4	175.84	1.12	175.18	5.51	0.38	5.21	174.78	176.40	0.60	3.93	174.74	204.85	0.63	4.41
2-5	196.50	1.24	194.92	5.68	0.81	4.76	193.98	193.82	1.28	4.67	194.01	203.81	1.27	4.55
3-4	214.05	7.28	211.20	119.32	1.33	12.08	208.18	750.47	2.74	13.95	208.61	846.62	2.54	13.11
3-5	221.64	6.65	220.49	34.78	0.52	15.94	219.55	848.27	0.94	16.26	219.07	889.56	1.16	15.96
4-5	241.44	32.60	240.31	265.27	0.47	7.03	238.98	2917.89	1.02	5.88	239.18	3249.24	0.94	8.19
4-6	272.09	59.69	271.99	104.47	0.04	1.88	267.44	3188.40	1.71	10.67	267.48	3455.40	1.70	7.78
5-6	279.63	74.91	278.72	153.87	0.33	5.45	272.43	4440.27	2.58	9.87	272.66	4422.25	2.50	9.68
5-7	270.60	45.53	270.30	96.13	0.11	1.68	265.81	4539.94	1.77	7.89	265.97	4717.46	1.71	6.56
6-7	326.51	191.88	326.41	319.70	0.03	1.60	323.88	4787.90	0.81	6.05	324.19	4835.49	0.71	5.79
6-8	320.86	88.53	319.90	201.73	0.30	6.26	317.13	5005.59	1.16	7.93	317.43	5488.78	1.07	7.23
Average	251.92	50.94	250.94	130.64	0.39	6.20	248.22	2684.89	1.47	8.92	248.33	2831.35	1.42	8.47

$ {n}^{+}/H $	WTB policy		ATB policy				ACB policy with SA-RR				ACB policy with ALNS-RR
$ {n}^{+}/H $	Cost/CNY	Time/s	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%	Cost/CNY	Time/s	$ \text{cs}_\text{to} $/%	$ \text{cs}_\text{bs} $/%
2-5	178.51	2.39	177.96	22.52	0.31	1.99	177.74	252.05	0.44	1.75	177.74	248.48	0.43	1.50
2-6	208.13	3.41	208.11	27.61	0.01	1.64	207.83	282.88	0.15	0.68	208.04	322.11	0.04	0.58
3-5	199.44	12.77	199.01	197.35	0.22	7.15	198.68	1001.12	0.38	9.00	198.48	1047.97	0.49	9.29
3-6	222.93	18.70	222.85	118.14	0.03	6.48	222.51	1048.76	0.19	6.25	222.58	1333.76	0.16	5.13
4-6	249.17	103.55	248.86	953.67	0.12	4.86	248.37	3853.16	0.32	4.31	248.47	4055.40	0.28	5.87
4-7	267.57	191.24	267.43	562.37	0.05	1.56	265.91	4456.39	0.62	4.23	265.49	4471.23	0.78	5.48
5-7	235.85	75.56	234.84	817.27	0.43	6.54	233.91	5248.05	0.82	7.98	234.04	6108.27	0.77	7.73
5-8	258.06	69.58	258.04	493.20	0.01	2.40	256.96	5915.16	0.43	4.55	256.88	6481.91	0.46	3.79
6-8	240.06	60.81	239.85	479.92	0.09	3.04	239.26	5838.46	0.33	5.45	239.35	6770.34	0.30	5.11
6-9	264.34	111.80	263.95	641.41	0.15	1.95	263.21	6330.27	0.43	4.34	263.44	6985.03	0.34	4.63
Average	232.41	64.98	232.09	431.34	0.14	3.82	231.44	3422.63	0.42	5.00	231.45	3782.45	0.41	5.04