考虑企业配送能力约束的协作配送模型及成本分摊影响研究

doi:10.16381/j.cnki.issn1003-207x.2021.1660

Abstract

Abstract:

Delivery vehicles are limited resources in firms with capital-intensive assets， such as distribution enterprises， which must guarantee high availability and revenue returns. Collaboration via resource sharing among distribution enterprises provides an opportunity to effectively increase the efficiency and sustainability of logistics operations. However， the limitation of the available vehicle capacity will possibly lead to the shortage of distribution capacity and even the failure of collaboration in the distribution process.This problem is modelled as an integer programming which minimizes vehicle routing costs， fixed costs， and possible vehicle rental costs for sub-alliances， named the multi-owner collaborative vehicle routing problem model with limited distribution capability. A vehicle make-up strategy is developed for supplementary vehicles. It allows enterprises with insufficient vehicles to first seek available capacity from members with idle vehicles within the alliance. If their capacity is still not met， vehicle-leasing decisions from other distribution companies outside the alliance must be taken， while paying higher rents as result. Through the vehicle make-up strategy， the cost can be accurately quantified with the model and then a fair and reasonable allocation result is obtained. Then， the Shapley value equation is applied to determine the cost to be shared by each member.Our numerical study on a testbed of instances demonstrates the value of vehicle make-up strategy and the benefits of collaboration. The collaborative distribution leads to significant savings for all members， with a cost reduction of 13.34% to 20.84% compared with individual delivery， even when each alliance members lease a higher-cost vehicle， the total cost savings can reach 12.62% to 19.41%. The benefits of first seeking inside the alliance to find idle vehicles， which are rarely discussed in previous articles， are obvious with a reduction of the additional expenses triggered by vehicle shortages. The numerical results demonstrate that it is still profitable for firms to join collaborative distribution even the delivery capacity is insufficient and need to pay higher rents to lease vehicles. Furthermore， collaboration shows to be particularly attractive for enterprises with high facility reserves， obtaining extra awards through additional cost reduction.The research results have important reference value and practical significance for distribution enterprises who adopt collaborative distribution mechanism and corresponding cost allocation with considering the insufficient vehicle capacity.

Key words: collaborative distribution, distribution capacity constraints, cost savings, Shapley value method

CLC Number:

Weizhen Rao,Xiaohe Miao,lu Liu. Research on Collaborative Distribution Model Considering Distribution Capability Constraints of Enterprises and Its Influence on Cost Allocation[J]. Chinese Journal of Management Science, 2024, 32(7): 106-116.

Figures/Tables 10

企业	$k i$ (辆)	$q d$ (千克)	$e i$ (辆)
1	2	144	1
2	3	182	1
3	1	141	1
4	1	192	1

$j$	$S j$	$D i s n c$	$D i s c$	$S d %$	$C n S$	$C S$	$T C S$	$S c %$
1	{4}	477.9	477.9	0.00	223.4	223.4	243.4	0.00
2	{3}	417.9	417.9	0.00	205.4	205.4	225.4	0.00
3	{3, 4}	895.8	727.5	18.79	428.7	378.2	418.2	10.77
4	{2}	663.5	663.5	0.00	359.1	359.1	378.3	0.00
5	{2, 4}	1141.5	896.7	21.45	582.4	509.0	552.5	11.14
6	{2, 3}	1081.4	906.4	16.18	564.4	511.9	547.6	9.29
7	{2, 3, 4}	1559.4	1173.7	24.73	787.8	672.1	728.7	13.98
8	{1}	467.6	467.6	0.00	260.3	260.3	280.3	0.00
9	{1, 4}	945.5	775.7	17.96	483.7	432.7	473.1	9.66
10	{1, 3}	885.5	668.2	24.54	465.6	400.5	440.5	12.89
11	{1, 3, 4}	1363.4	981.8	27.99	689.0	574.5	634.5	15.28
12	{1, 2}	1131.1	931.8	17.62	619.3	559.5	599.5	8.97
13	{1, 2, 4}	1609.1	1205.7	25.07	842.7	721.7	781.8	13.32
14	{1, 2, 3}	1549.0	1143.6	26.17	824.7	703.1	763.1	13.68
15	{1, 2, 3, 4}	2027.0	1425.9	29.65	1048.1	867.8	947.7	15.93

分摊方法	配送能力	指标	企业1	企业2	企业3	企业4
Shapley	充足	$C i$	260.3	359.1	205.4	223.4
		$φ i$	214.4	311.1	162.6	179.7
		$S c$	17.62	13.34	20.84	19.57
	各租赁 1辆车	$C i$	280.3	378.3	225.4	243.4
		$φ i$	235.4	330.6	181.6	200.1
		$S c$	16.00	12.62	19.41	17.78

序号	组合	企业1		企业2			企业3		企业4
序号	组合	$φ 1$	$S c %$		$φ 2$	$S c %$	$φ 3$	$S c %$	$φ 4$	$S c %$
1	1-1, 2+1	224.4	19.94	301.1		16.13	162.6	20.84	179.7	19.57
2	1-1, 3+1			311.1		13.34	152.6	25.71	179.7	19.57
3	1-1, 4+1			311.1		13.34	162.6	20.84	169.7	24.05
4	2-1, 1+1	204.4	21.47	321.1		15.28	162.6	20.84	179.7	19.57
5	2-1, 3+1	214.4	17.62			152.6	25.71	179.7	19.57
6	2-1, 4+1	214.4	17.62			162.6	20.84	169.7	24.05
7	3-1, 1+1	204.4	21.47	311.1		13.34	172.6	23.43	179.7	19.57
8	3-1, 2+1	214.4	17.62	301.1		16.13	179.7	19.57
9	3-1, 4+1	214.4	17.62	311.1		13.34	169.7	24.05
10	4-1, 1+1	204.4	21.47	311.1		13.34	162.6	20.84	189.7	22.07
11	4-1, 2+1	214.4	17.62	301.1		16.13	162.6	20.84
12	4-1, 3+1	214.4	17.62	311.1		13.34	152.6	25.71

序号	组合	企业1		企业2		企业3		企业4
序号	组合	$φ 1$	$S c %$	$φ 2$	$S c %$	$φ 3$	$S c %$	$φ 4$	$S c %$
1	1-2, 2+1, *+1	244.4	6.11	301.1	16.13	162.6	20.84	179.7	19.57
2	1-2, 3+1, *+1			311.1	13.34	152.6	25.71	179.7	19.57
3	1-2, 4+1, *+1			311.1	13.34	162.6	20.84	169.7	24.05
4	2-2, 1+1, *+1	204.4	21.47	341.1	5.01	162.6	20.84	179.7	19.57
5	2-2, 3+1, *+1	214.4	17.62			152.6	25.71	179.7	19.57
6	2-2, 4+1, *+1	214.4	17.62			162.6	20.84	169.7	24.05
7	3-2, 1+1, *+1	204.4	21.47	311.1	13.34	192.6	6.23	179.7	19.57
8	3-2, 2+1, *+1	214.4	17.62	301.1	16.13			179.7	19.57
9	3-2, 4+1, *+1	214.4	17.62	311.1	13.34			169.7	24.05
10	4-2, 1+1, *+1	204.4	21.47	311.1	13.34	162.6	20.84	209.7	6.13
11	4-2, 2+1, *+1	214.4	17.62	301.1	16.13	162.6	20.84
12	4-2, 3+1, *+1	214.4	17.62	311.1	13.34	152.6	25.71

序号	组合	$T C$	企业1		企业2		企业3		企业4
序号	组合	$T C$	$φ 1$	$S c %$	$φ 2$	$S c %$	$φ 3$	$S c %$	$φ 4$	$S c %$
1	1-1	887	234.1	16.48	311.4	13.28	161.3	21.48	180.6	19.16
2	1-2	908	254.2	15.36	311.5	13.26	161.7	21.27	180.5	19.21
3	1-3	927	273.9	14.50	311.1	13.37	161.3	21.47	181.1	18.92
4	2-1	887	214.3	17.66	330.5	12.64	161.7	21.27	180.8	19.06
5	2-2	907	215.6	17.18	350.4	11.76	161.2	21.51	180.1	19.36
6	2-3	927	214.2	17.70	370.5	11.42	161.7	21.26	180.8	19.05
7	2-4	947	213.7	17.91	391.2	10.91	161.3	21.48	181.2	18.88
8	3-1	888	215.1	17.35	311.1	13.36	180.8	19.78	180.7	19.12
9	3-2	907	214.0	17.79	311.4	13.29	201.1	18.06	180.9	19.01
10	4-1	887	214.7	17.51	311.6	13.21	159.8	22.20	201.2	17.34
11	4-2	907	214.1	17.76	311.4	13.28	161.0	21.62	220.9	16.12

References 26

1	Song R D， Lau H C， Luo Xue， et al. Coordinated delivery to shopping malls with limited docking capacity［J］. Transportation Science， 2022， 56（2）： 501-527.
2	van Zon M， Spliet R， van den Heuvel W. The joint network vehicle routing game［J］. Transportation Science， 2021， 55（1）： 179-195.
3	Gansterer M， Hartl R F. Shared resources in collaborative vehicle routing［J］. Top， 2020， 28（1）： 1-20.
4	Hacardiaux T， Tancrez J S. Assessing the en-vironmental benefits of horizontal cooperationusing a location-inventory model［J］. Central European Journal of Operations Research， 2020， 28（4）： 1363-1387.
5	刘家利，马祖军. 存在车辆租赁及共享且有时间窗的多配送中心开环VRP［J］. 系统工程理论与实践， 2013， 33（3）： 666-675.
	Liu J L， Ma Z J. Multi-depot open vehicle routing problem with time windows based on vehicle leasing and sharing［J］. Systems Engineering—Theory & Practice， 2013， 33（3）： 666-675.
6	徐东洋，李昆鹏，崔利刚，田倩南. 供需未匹配的多车场多车型多货品可拆分取送货车辆路径问题［J］. 中国管理科学， 2021， 29（1）： 127-137.
	Xu D Y， Li K P， Cui L G， et al. Multi-commodity unpaired supply-demand and split pickup and delivery vehicle routing problem with multi-depot and multi-type trucks［J］. Chinese Journal of Management Science， 2021， 29（1）： 127-137.
7	徐小峰，姜明月，邓忆瑞. 整合逆向物流协同配送动态路径优化问题研究［J］. 管理科学学报， 2021， 24（10）： 106-126.
	Xu X F， Jiang M Y， Deng Y R. Dynamic vehicle routing problem with simultaneous pickup and delivery incollaborative distribution under demand concurrent［J］. Journal of Management Sciences in China， 2021， 24（10）： 106-126.
8	饶卫振，朱庆华，刘从虎. 在线组建协作配送联盟中企业成本节约相对量估算方法研究［J］. 系统工程理论与实践， 2019， 39（3）： 659-672.
	Rao W Z， Zhu Q H， Liu C H. An estimation method for computing cost saving percentage of distribution enterprises in collaborative environment： Used for forming collaborative distribution coalition online［J］. Systems Engineering—Theory&Practice， 2019， 39（3）： 659-672.
9	Li Y， Chen H X， Prins C. Adaptive large neighborhood search for the pickup and delivery problem with time windows， profits， and reserved requests［J］. European Journal of Operational Research， 2016， 252（1）： 27-38.
10	Adenso-Díaz B， Lozano S， Garcia-Carbajal S，et al. Assessing partnership savings in horizontal cooperation by planning linked deliveries［J］. Transportation Research Part A： Policy and Practice， 2014， 66： 268-279.
11	Mancini S， Gansterer M， Hartl R F. The col-laborative consistent vehicle routing problem with workload balance［J］. European Journal of Operational Research， 2021， 293（3）： 955-965.
12	Guajardo M， Rönnqvist M. A review on cost allocation methods in collaborative transportation［J］. International Transactions in Operational Research， 2016， 23（3）： 371-392.
13	Shapley L S. A value for n-person games［J］. Contributions to the Theory of Games， 1953，2（28）： 307-317.
14	Schmeidler D. The nucleolus of a characteristic function game［J］. SIAM Journal on Applied Mathematics， 1969， 17（6）： 1163-1170.
15	Cuervo D P， Vanovermeire C， Sörensen K.Determining collaborative profits in coalitions formed by two partners with varying characteristics［J］. Transportation Research Part C： Emerging Technologies， 2016， 70： 171-184.
16	饶卫振，朱庆华，金淳，等. 协作车辆路径成本分摊问题的B-T Shapley方法［J］. 管理科学学报， 2019， 22（1）： 107-126.
	Rao W Z， Zhu Q H， Jin C， et al. A binary tree Shapley method for cost sharing of the collaborative vehicle routing problem［J］. Systems Engineering—Theory & Practice，2019， 22（1）： 107-126.
17	饶卫振，张云东，刘从虎，于灏，侯艳辉.一种求解协作配送成本分摊问题核仁解的近似迭代算法［J］. 系统工程理论与实践， 2019， 39（6）： 1517-1534.
	Rao W Z， Zhang Y D， Liu C H， et al. An approximate iterative algorithm for generating cost sharing nucleolus of collaborative vehicle routing problem［J］.Systems Engineering—Theory & Practice， 2019，39（6）： 1517-1534.
18	Wang Y， Li Q， Guan X Y， et al. Collaborative multi-depot pickup and delivery vehicle routing problem with split loads and time windows［J］. Knowledge-Based Systems， 2021， 231： 107412.
19	叶银芳，李登峰，余高锋. 联合订货区间值EOQ模型及变权Shapley值成本分摊方法［J］. 中国管理科学， 2019， 27（10）： 90-99.
	Ye Y F， Li D F， Yu G F. Joint replenishment interval-valued EOQ model andcost allocation approach based on variable-weighted Shapley value［J］. Chinese Journal of Management Science， 2019， 27（10）： 90-99.
20	胡石清. 社会合作中利益如何分配？——超越夏普利值的合作博弈“宗系解”［J］. 管理世界，2018， 34（6）： 83-93.
	Hu S Q. How to distribute the benefits in social cooperation？ “The Clique Solution” of cooperative game surpassing Shapley value［J］. Management World， 2018， 34（6）： 83-93.
21	Ferrell W， Ellis K， Kaminsky P， et al. Horizontal collaboration： Opportunities for improved logistics planning［J］. International Journal of Production Research， 2020， 58（14）： 4267-4284.
22	Krajewska M A， Kopfer H， Laporte G， et al. Horizontal cooperation among freight carriers： Request allocation and profit sharing［J］. Journal of the Operational Research Society， 2008， 59（11）： 1483-1491.
23	Luo Z X， Qin H， Zhang D Z， et al. Adaptive large neighborhood search heuristics for the vehicle routing problem with stochastic demands and weight-related cost［J］. Transportation Research Part E： Logistics and Transportation Review， 2016， 85： 69-89.
24	Augerat P， Naddef D， Belenguer J M， et al. Computational results with a branch and cut code for the capacitated vehicle routing problem［R］. Working Paper，Institut National Polytechnique， 1995.
25	Marinakis Y， Iordanidou G R， Marinaki M. Particle swarm optimization for the vehicle routing problem with stochastic demands［J］.Applied Soft Computing， 2013， 13（04）： 1693-1704.
26	Marinakis Y， Marinaki M， Spanou P.A memetic differential evolution algorithm for the vehicle routing problem with stochastic demands［M］//Fister I， Fister Jr I. Adaptation and Hybridization in Computational Intelligence. vol 18.Cham： Springer， 2015， 185-204.

Instance	PSO^[25]		HGA^[26]		MDE^[26]		ALNS
Instance	best	Gap(%)	best	Gap(%)	best	Gap(%)	best	Gap(%)
A-n32-k5	822	0.14	836	1.90	821	0.00	837	2.05
A-n33-k5	687	1.78	693	2.73	684	1.36	675	0.00
A-n33-k6	770	3.44	762	2.47	763	2.50	744	0.00
A-n37-k5	708	1.82	702	1.01	695	0.01	698	0.39
A-n38-k5	757	0.89	756	0.75	752	0.31	750	0.00
A-n39-k6	848	0.26	867	2.53	846	0.00	853	0.87
A-n45-k6	997	0.24	1008	1.30	997	0.19	995	0.00
A-n45-k7	1175	2.04	1239	7.59	1213	5.30	1152	0.00
A-n55-k9	1124	0.00	1168	3.90	1151	2.37	1126	0.17
A-n60-k9	1454	6.38	1517	10.99	1483	8.50	1367	0.00
E-n22-k4	391	3.16	385	1.61	379	0.04	384	1.33
E-n33-k4	847	0.00	849	0.23	848	0.10	847	0.00
E-n51-k5	545	3.86	550	4.87	549	4.68	525	0.00
P-n19-k2	214	0.40	217	1.88	215	1.12	213	0.00
P-n22-k2	229	5.32	223	2.39	229	5.32	218	0.00
P-n40-k5	471	2.00	471	1.97	472	2.20	462	0.00
P-n50-k8	659	0.18	658	0.00	664	0.91	700	6.42
P-n50-k10	740	4.55	755	6.76	725	2.44	707	0.00
P-n51-k10	795	1.28	806	2.60	789	0.46	785	0.00
P-n60-k10	773	1.39	803	5.37	791	3.71	762	0.00
AVGRGAP		1.96		3.14		2.08		0.56

[1]	Jun Xie,He Huang. Optimal Marketing Strategy of E-commerce Platform with Product Returns [J]. Chinese Journal of Management Science, 2024, 32(10): 313-324.
[2]	Quan Xiao,Shanshan Wan,Xing Zhang,Shuqin Cai. User's Quality Perception and Satisfaction Towards Mobile Live Streaming Commerce Platform from the Perspective of IT Affordance [J]. Chinese Journal of Management Science, 2024, 32(10): 181-193.
[3]	Weiwei Li,Pingtao Yi,Lu Wang. Situation Oriented Evaluation Approaches Based on Behavior Characteristics Analysis and the Application [J]. Chinese Journal of Management Science, 2024, 32(10): 171-180.
[4]	Xuelong Chen,Zhong Zhang,Yue Li. Generation of Emergency Response Plan for Unconventional Emergencies from the Perspective of Improvisational Decision-Making [J]. Chinese Journal of Management Science, 2024, 32(10): 109-122.
[5]	Wanting Hu,Jingjing Ding,Liang Liang. Joint Reserve Model of Government and Enterprise for Relief Materials Based on a Delegated Reserve Contract with Option [J]. Chinese Journal of Management Science, 2024, 32(9): 101-112.
[6]	Weizhen Rao,Shuqi Li,Zhixing Luo. Research on Collaborative Recycling Logistics Mode of E-waste Considering Recovery Rate Improvement [J]. Chinese Journal of Management Science, 2024, 32(9): 225-236.
[7]	Qingming Zou,Chun Liu,Yu Cao. Carbon Emission Reduction and Financing Policy of Low-carbon Supply Chain with Yield Uncertainty and Fairness Concerns under Carbon Cap-and-Trade Mechanism [J]. Chinese Journal of Management Science, 2024, 32(9): 248-259.
[8]	Yidan He,Zhengwen He,Nengmin Wang,Zhiqiang Ma. Resource-constrained Max-NPV Multi-project Scheduling Optimization under Sharing Economy Environment [J]. Chinese Journal of Management Science, 2024, 32(9): 260-270.
[9]	Qiang Chen,Junmei Rong,Xuhua Chang,Lei Gong. Scientific Research Assessment and Patent Examination Strategies of University Considering Differencesin Reward and Punishment [J]. Chinese Journal of Management Science, 2024, 32(9): 313-322.
[10]	Ruxin Nie,Zhangpeng Tian,Heming Liang. A Consensus Method for Large-Scale Group Decision-Making Based on Behavior Management under Social Network Environments [J]. Chinese Journal of Management Science, 2024, 32(9): 35-47.
[11]	Lu Chen,Haiyan Xu,Jinmuzi Zhang,Liang He. Study on Fuzzy Power Asymmetric Conflict Analysis Based on the Graph Model [J]. Chinese Journal of Management Science, 2024, 32(9): 59-69.
[12]	Yang Liu,Qianqian Deng,Zhiping Fan,Qi Zhang. Research on Ride-hailing Platform’s Open Platform Strategy and Its Efficiency Analysis [J]. Chinese Journal of Management Science, 2024, 32(9): 82-92.
[13]	Yuelong Zheng,Chunguang Bai,Dengfeng Li. Research on the Supply Decision of Industrial General Purpose Technologies Considering Market-oriented Development [J]. Chinese Journal of Management Science, 2024, 32(8): 127-138.
[14]	Zhong Shen,Xingmei Li. An Expanded Model for Project Portfolio Selection with Considering of Three Synergies [J]. Chinese Journal of Management Science, 2024, 32(8): 139-148.
[15]	Xiaona Li,Weimin Ma. Water Saving Service Outsourcing for High Water Consumption Enterprises under Demand Uncertainty [J]. Chinese Journal of Management Science, 2024, 32(8): 230-240.

Research on Collaborative Distribution Model Considering Distribution Capability Constraints of Enterprises and Its Influence on Cost Allocation

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 10

References 26

Related Articles 15

Metrics

Comments

Recommended 0