考虑贸易信贷周期的中欧班列联合补货决策

doi:10.16381/j.cnki.issn1003-207x.2021.0344

Abstract

Abstract:

With the uncertainties increase in market demands，fragmentary orders are becoming common practices in foreign trade between China and Europe， which brings great pressure on choosing the best transportation means for traders replenishing multi-items. Based on the fast development of China-Europe railway express （CERE）， it provides a new option for transportation mode selection after CERE by passing its survival stage. Facing orders with many varieties and small batches， China-Europe businesses traders can make synthetically and flexible decisions between maritime and train transportations based on the time sensitivities of commodities in market and time consuming in transportation. In academic， joint replenishment problem （JRP） is the research area that dealing with multi-item joint replenishment and transportation. Therefore， under China-Europe trade circumstance， the stochastic demand JRP is expanded by considering trade credit during the transportation period in CERE. In specific， with the objective of minimum total cost， by considering the time cost of lead-time and assuming the trade credit is introduced to the business trader， a novel stochastic JRP model with trade credit during the period of CERE transportation is constructed， in which 0-1 decision variables are utilized to control whether a transportation mode is selected. In light of the NP-hard nature of JRP， a new hybrid differential lightning search algorithm （DLSA） is developed to solve the proposed JRP. In numerical experiments， the best combination of searching parameters， the searching stableness and effectiveness of DLSA have been analyzed. Through experimenting on different scale of JRP cases， DLSA shows the best stableness and searching effectiveness comparing to DE， BBDE and LSA in solving SJRP and JRP-T but with the worse searching efficiency. Managerial insights are obtained：（1） Trade credit not only helps traders positively response to the trends of small orders and replenishment increasing， but also shortens retailers’ replenishment lead-time. （2） Under a specific transportation mode， traders are inclined to choose carriers with lower prices than those with shorter transportation time. （3） From the perspective of traders， it is confirmed that the best strategy for improving the competitiveness of CERE in the short term is adopting a lower freight transportation rate. （4） Government plays a vital role in promoting CERE development， especially for CERE at different maturity stages.

Key words: joint replenishment, China-Europe railway express, trade credit, lead time, intelligence algorithm

CLC Number:

F252.3

Ligang Cui,Xiaolin Liu,Jie Deng,Dongyang Xu. Stochastic Multi-item Joint Replenishment Problem Considering Trade Creditunder China-Europe Trade[J]. Chinese Journal of Management Science, 2024, 32(4): 76-88.

Figures/Tables 17

参数	参数定义	参数	参数定义
$n$	货品种类	$R i$	货品 $i$ 的最高库存水平
$i$	货品编号， $i = 1 ? n$ 。	$μ i$	货品 $i$ 的需求率均值
$M$	供应商提供的贸易信贷周期长度	$σ i$	货品 $i$ 的需求率标准差
$A$	主要订购成本	$Φ$	$M ≤ L i$ 的货品集合
$a i$	货品 $i$ 的次要订购成本	$Ω$	$L i ≤ M ≤ k i T + L i$ 的货品集合
$p i$	单位货品 $i$ 的缺货惩罚成本	$Θ$	$k i T + L i ≤ M$ 的货品集合
$P i$	单位货品 $i$ 的采购价格	$C t$	运输成本
$c i$	单位货品 $i$ 的销售价格	$C o$	订购成本
$I e$	资金收益利率	$C l$	缺货成本
$I p$	单位资金占用成本	$C h$	仓储成本
$h i$	单位货品 $i$ 的仓储成本	$C P$	资金占用成本
$S$	单位固定运输成本	$C e$	资金收益
$s r i$	单位货品 $i$ 的铁路运输成本	$T C$	总成本
$s o i$	单位货品 $i$ 的海路运输成本	$k i$	货品 $i$ 的采购周期乘子（决策变量）
$s i$	单位货品 $i$ 的可变运输成本	$K$	由 $n$ 个 $k i$ 组成的向量（决策变量）
$L r$	货品 $i$ 通过铁路运输的提前期	$T$	基础采购周期（决策变量）
$L o$	货品 $i$ 通过海运运输的提前期	$y i$	$y i = 0$ 表示货品 $i$ 通过铁路运输， $y i = 1$ 表示通过海运运输（决策变量）
$L i$	货品 $i$ 的提前期	$z i$	货品 $i$ 的安全库存因子（决策变量）

参数	item1	item2	item3	item4	item5	item6
$M$ (year)	50/365	50/365	50/365	50/365	50/365	50/365
$A$ ($/order)	200	200	200	200	200	200
$a i$ ($/order)	45	46	47	44	45	47
$μ i$ (units/year)	10000	5000	3000	1000	600	200
$σ i$ (units/year)	2500	1000	700	500	300	150
$S$ ($/order)	200	200	200	200	200	200
$s r i$ ($/units)	1.5	1.5	1.5	1.5	1.5	1.5
$s o i$ ($/units)	1	1	1	1	1	1
$h i$ ($/year/units)	1	1	1	1	1	1
$p i$ ($/year)	25	20	15	30	35	28
$P i$ ($/units)	10	20	30	35	40	40
$c i$ ($/units)	35	50	45	65	75	70
$L r$ (year)	20/365	20/365	20/365	20/365	20/365	20/365
$L o$ (year)	60/365	60/365	60/365	60/365	60/365	60/365

算法	Best results				Ave.TC	Std.Err.	Ave CPU T(s)	Best. Freq.
算法	$T C$	$k i$ s	$z i$ s	$T$	Ave.TC	Std.Err.	Ave CPU T(s)	Best. Freq.
DLSA	10447.81	1,1,1,1,2,3	2.5632,2.4848,2.3806,2.6259,2.4369,2.2004	0.1296	10447.81	3.90E-12	0.37	30
BBDE	10447.81	1,1,1,1,2,3	2.5632,2.4848,2.3806,2.6259,2.4369,2.2004	0.1296	10463.32	34.71	0.06	22
DE	10447.81	1,1,1,1,2,3	2.5632,2.4848,2.3806,2.6259,2.4369,2.2004	0.1296	10447.81	1.09E-05	0.12	17
LSA	10447.81	1,1,1,1,2,3	2.5632,2.4848,2.3806,2.6259,2.4369,2.2004	0.1296	10465.06	21.68	0.69	11

算法	Best results					Ave.TC	Std.Err.	Ave CPU T(s)	Best. Freq.
算法	$T C$	$k i$ s	$y i$ s	$z i$ s	$T$	Ave.TC	Std.Err.	Ave CPU T(s)	Best. Freq.
DLSA	46185.08	1,1,1,1,2,3	1,1,0,0,0,0	2.2711,2.0561,1.9794,2.2234,1.8884,1.5648	0.1808	46185.08	5.26E-11	0.45	30
BBDE	46185.08	1,1,1,1,2,3	1,1,0,0,0,0	2.2711,2.0561,1.9794,2.2234,1.8884,1.5648	0.1808	46538.84	490.33	0.07	4
DE	46185.08	1,1,1,1,2,3	1,1,0,0,0,0	2.2711,2.0561,1.9794,2.2234,1.8884,1.5648	0.1808	46185.43	0.84	0.16	7
LSA	46517.29	1,1,2,2,2,4	1,1,1,0,0,0	2.3302,2.1198,1.5740,1.9397,1.9701,1.4903	0.1547	47363.46	591.28	1.92	0

参数	$- Δ ? 80 %$	$- Δ ? 60 %$	$- Δ ? 40 %$	$- Δ ? 20 %$	$Δ 0 ? %$	$+ Δ ? 20 %$	$+ Δ ? 40 %$	$+ Δ ? 60 %$	$+ Δ ? 80 %$
$μ i$	24842.02	31034.36	36211.36	41286.70	46185.08	50907.42	55560.00	60172.28	64751.75
$σ i$	33347.38	36779.59	40027.80	43133.12	46185.08	48996.05	51764.40	54251.57	56430.63
$A$	45264.38	45502.25	45734.25	45961.78	46185.08	46404.37	46619.82	46821.67	47018.05
$a i$	45168.69	45431.16	45687.83	45939.03	46185.08	46426.26	46661.06	46882.01	47099.26
$h i$	39013.18	40927.33	42747.69	44504.14	46185.08	47800.32	49375.72	50915.60	52423.48
$p i$	41526.33	43846.20	44951.24	45673.69	46185.08	46558.66	46865.56	47125.23	47349.78
$S$	40584.77	42349.13	43820.27	45064.51	46185.08	47183.16	48091.78	48944.67	49750.39
$P i$	38921.23	41098.17	43033.78	44662.00	46185.08	47385.12	48521.22	49309.79	49998.39
$I p$	37747.53	40217.90	42446.93	44368.57	46185.08	47678.55	49108.07	50190.01	51172.08
$s r i$	25333.19	31273.19	37213.19	43153.19	46185.08	46747.33	46966.27	46966.27	46966.27
$s o i$	31126.27	35086.27	38978.92	42607.33	46185.08	48872.00	49093.19	49093.19	49093.19
$L r$	44576.15	45106.01	45462.40	45822.27	46185.08	46403.89	46601.55	46800.17	46966.27
$L o$	37330.52	40110.95	42795.26	44932.43	46185.08	47010.26	47815.14	48302.03	48755.73
$c i$	46246.47	46236.70	46226.92	46210.52	46185.08	46159.59	46134.04	46108.44	46082.79
$I e$	47420.17	47116.97	46813.77	46503.95	46185.08	45866.16	45547.19	45228.17	44909.09
$M$	50442.62	49555.67	48446.00	47330.18	46185.08	44871.57	42950.28	40963.84	39264.76

信贷周期	$T C$	$k i$ s	$y i$ s	$z i$ s	$T$
$M = 0$	51316.10	1,1,1,1,2,3	1,1,1,0,0,0	2.2327,2.0146,1.7830,2.0406,1.7646,1.4554	0.1998
$M = 50 / 365$	46185.08	1,1,1,1,2,3	1,1,0,0,0,0	2.2711,2.0561,1.9794,2.2234,1.8884,1.5648	0.1808

参数（单位）	范围
$μ i$ (units/year)	$10, 1000 × 10$
$σ i$ (units/year)	$r a n d · μ i$
$A$ ($)	$100, 300$
$a i$ ($)	$35, 55$
$h i$ ($/year/units)	$0.5, 2.5$
$p i$ ($/year/units)	$20, 70$
$s r i$ ($/units)	$1.3, 1.8$
$s o i$ ($/units)	$0.8, 1.2$
$P i$ ($/units)	$20, 60$
$c i$ ($/units)	$1 + r a n d · P i$

数量

k i

y i

z i

T

5,5,3,2,4,4,2,3,3,2,

2,4,5,2,2,2,5,3,3,5

1,1,1,0,1,1,0,1,1,0,

0,1,1,0,0,0,1,1,1,0

1.86,1.85,2.00,2.93,1.96,1.98,2.91,1.99,2.14,2.60,

2.70,2.08,1.93,2.71,2.61,2.74,1.80,2.11,2.08,2.11

0.0410

5,4,3,2,4,5,2,3,3,2,

2,5,5,2,2,2,5,3,2,4,

4,2,5,2,2,2,2,2,3,3

1,1,1,0,1,1,0,1,1,0,

0,1,1,0,0,0,1,1,1,0,

1,0,1,0,0,0,0,0,1,1

1.99,1.94,1.96,2.97,2.00,2.01,2.93,1.93,2.14,2.52,

2.69,1.97,2.06,2.59,2.43,2.82,1.92,2.06,2.23,2.01,

1.85,2.56,2.21,2.71,2.43,2.33,2.71,2.76,2.48,1.86

0.0408

5,5,3,2,3,4,2,3,2,2,

2,4,5,2,2,2,3,4,2,3,

5,2,4,2,3,2,2,2,3,4,

4,3,4,5,2,2,2,2,4,3

1,0,1,0,1,1,0,1,1,0,

0,1,1,0,0,0,1,1,1,0,

1,0,0,0,0,0,0,0,1,1,

1,0,1,0,0,1,0,0,1,1

1.38,1.97,1.88,2.36,2.79,2.09,2.23,1.94,2.35,2.85,

2.50,2.13,1.68,2.36,2.80,2.22,1.96,2.09,2.54,2.07,

1.70,2.33,2.30,2.65,2.19,2.59,2.76,2.94,2.60,1.81,

1.56,2.48,2.21,2.29,2.80,2.10,2.99,2.47,2.20,2.03,

0.0398

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F	CR	0.10	0.20	0.30	0.40	0.50	0.60	0.70	0.80	0.90
0.60	Ave.TC	46185.08	46194.28	46198.64	46189.44	46185.08	46204.48	46199.38	46219.66	46236.69
	Std.Err.	1.59E-11	50.39	55.02	23.89	1.13E-11	84.94	54.98	91.81	76.67
	Ave.Times	0.44	0.43	0.43	0.43	0.43	0.43	0.43	0.43	0.43
0.70	Ave.TC	46185.08	46185.08	46190.18	46185.08	46192.56	46189.98	46195.80	46215.01	46277.87
	Std.Err.	1.07E-09	4.77E-11	24.09	1.70E-11	36.97	23.97	33.58	94.39	154.01
	Ave.Times	0.43	0.43	0.43	0.43	0.43	0.43	0.45	0.43	0.44
0.80	Ave.TC	46185.08	46194.27	46186.57	46185.08	46185.08	46185.08	46191.12	46215.87	46252.14
	Std.Err.	3.66E-04	50.33	5.65	1.35E-08	1.72E-10	5.56E-10	25.30	81.75	117.90
	Ave.Times	0.43	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44
0.90	Ave.TC	46185.08	46185.82	46185.08	46185.08	46195.02	46185.08	46195.29	46204.25	46266.02
	Std.Err.	0.01	4.06	2.34E-06	3.90E-06	50.41	2.25E-09	33.27	69.89	154.33
	Ave.Times	0.44	0.44	0.44	0.44	0.45	0.44	0.44	0.44	0.46
1.00	Ave.TC	46185.96	46185.09	46185.08	46185.08	46185.08	46185.08	46190.18	46233.02	46236.38
	Std.Err.	4.12	0.01	2.25E-04	1.98E-05	6.99E-06	2.54E-05	24.09	118.78	65.98
	Ave.Times	0.44	0.45	0.45	0.45	0.45	0.45	0.45	0.45	0.45

序号	算法	N	SJRP			SJRP-T
序号	算法	N	t	df	Sig.	t	df	Sig.
Pair1	DLSA-DE	30	-5.00	29	0.000	-3.01	29	0.005
Pair2	DLSA-BBDE	30	-2.66	29	0.013	-4.45	29	0.000
Pair3	DLSA-LSA	30	-4.34	29	0.000	-12.52	29	0.000
Pair4	DE-BBDE	30	-2.66	29	0.013	-4.45	29	0.000
Pair5	DE-LSA	30	-4.34	29	0.000	-12.52	29	0.000
Pair6	BBDE-LSA	30	0.34	29	0.739	-5.45	29	0.000

数量	DLSA				DE				BBDE
数量	Best.TC	Ave.TC	Std,Err	Ave.time	Best.TC	Ave.TC	Std,Err	Ave.time	Best.TC	Ave.TC	Std,Err	Ave.time
10	126266.31	128931.43	781.95	0.51	126274.48	127014.01	879.07	0.25	126266.31	130470.44	2489.06	0.08
12	153077.95	153527.60	429.11	0.58	150375.00	153616.59	1357.43	0.28	151289.19	155445.28	2207.16	0.07
15	179102.65	181492.64	1123.88	0.70	175185.36	180266.46	1949.58	0.34	175690.28	183067.58	4259.67	0.08
20	241991.96	246946.77	2107.90	0.92	240302.91	243242.63	1653.57	0.45	234687.85	243940.73	5774.89	0.10
24	297247.45	300028.38	1931.31	1.07	291664.33	295088.33	1790.33	0.53	281611.79	294623.54	8803.71	0.10
29	385669.39	393713.28	4098.25	1.26	379185.34	384358.11	3142.15	0.63	370485.37	385375.63	8709.82	0.12

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Stochastic Multi-item Joint Replenishment Problem Considering Trade Creditunder China-Europe Trade

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