Joint Distribution-Inventory Optimization and Simulation for Cold Chain Logistics Considering Order Substitution

doi:10.16182/j.issn1004731x.joss.22-1232

Abstract

Abstract:

The most important purpose of cold chain logistics is to ensure product freshness, and how to reduce the cost of order distribution on this basis is an urgent problem for cold chain companies. For consumers, product quality and food safety are their main needs. Therefore, by taking the distribution center as the research object, the products were divided into different grades according to the initial freshness of the products before distribution, and the overall freshness of the products was improved by adopting the grade upward substitution mode for orders that do not meet the delivery requirements so that customers can obtain products with better quality as much as possible and get their needs met. At the same time, a two-layer planning model was established based on minimum freshness, inventory, and other constraints to jointly optimize the distribution and inventory allocation problems. The upper layer model determines the order distribution and inventory allocation scheme with the goal of minimizing the sum of transportation costs, cargo loss costs, and other cost. The lower model determines the order that needs to be replaced and the product grade that needs to be replaced with the goal of minimizing order substitution costs. An improved adaptive genetic algorithm and a cplex solver were used to solve the upper and lower model respectively. The solved distribution scheme wasverified by a simulation model that simulated road congestion and re-added to the double-layer model for planning. The solution shows that order substitution can effectively reduce the operating costs of enterprises and obtain more realistic order distribution and inventory allocation schemes.

Key words: inventory route optimization, freshness, order substitution, road congestion, cold chain logistics simulation, genetic algorithm

CLC Number:

TP301

Wan Yuanpeng, Liang Chengji, Wang Sihong, Wang Yu. Joint Distribution-Inventory Optimization and Simulation for Cold Chain Logistics Considering Order Substitution[J]. Journal of System Simulation, 2024, 36(3): 578-594.

Figures/Tables 24

Fig. 1

Table 1

Set

符号	含义
C	各需求节点集合， $C ⊂ 0,1, 2, ⋯, c$ ，c为需求节点个数，0表示配送中心节点
$D i j$	需求点i到需求点j的距离， $i, j ∈ C, i ≠ j$
K	配送中心所有车辆集合， $K ⊂ 1,2, ⋯, k$ ，k为配送中心冷藏车数量
Q	货物质量等级集合， $Q ⊂ 1,2, ⋯, q$ ，越新鲜的产品质量等级越小
e	用质量等级为e的产品替代质量等级为q的产品， $e ⊂ Q$ ，其中 $e = q - 1$
W	冷藏车制冷温度， $W ⊂ 1,2, ⋯, w$ ，单位为°C
p	货物的单价集合， $p ⊂ p 1, p 2, ⋯, p q$

Table 1

Table 2

Parameters

符号	含义
$t k$	车辆 $k$ 装载完所有生鲜产品后的出库时间
$T c$	生鲜产品在仓库内存储时的库存制冷温度
$A k i$	车辆 $k$ 到达需求点 $i$ 时的时间
$d i q$	分配给需求点 $i$ 产品等级为 $q$ 的数量
$p q$	等级为 $q$ 的产品的单价
$P r$	冷藏车发动机的功率(开制冷压缩机、空调等)，在不同的冷藏温度下取值不同
$η$	冷藏车传动效率
$G$	冷藏车当前载重(当前运输时刻下车辆重量)
$a$	当前运输时刻下冷藏车的加速度
$v$	冷藏车运输过程中的实时速度
$ρ$	当前空气密度
$C d$	空气动力阻力系数
$C r$	冷藏车滚动阻力系数
$S A$	车辆正表面面积
$ψ$	燃料空气质量比
$f e$	冷藏车发动机摩擦系数
$N$	冷藏车发动机转速
$d e$	冷藏车发动机排量
$h d$	柴油燃料热值
$φ$	柴油g/s到L/s的转换因子
$ξ$	冷藏车车厢的热传导系数
$S c$	冷藏车车厢的平均表面积
$S b$	冷藏车车厢开口面积
$h A$	空气表面对流传热系数
$T o$	订单配送过程中室外温度
$d o$	与开门频率有关的参数
$t i j$	从需求点i到j的时间
$t k i$	冷藏车 $k$ 在需求点 $i$ 的服务时间
$p d$	单位柴油价格
$p s$	驾驶员的单位工资(小时)
$p f$	单位热量需要制冷剂的成本
$A$	Arrhenius方程因子
$E$	活化能
$R$	摩尔气体常数

Table 2

Table 3

Decision variables

符号	含义
X_ijk	当车辆k从需求点i行驶到j进行货物运输时， X_ijk =1，否则为0
H_iq	当分配给需求点i的q等级产品需要进行换货处理时， H_iq =1，否则为0
T_K	车辆k在运输配送过程中的制冷温度为开尔文K。与摄氏度T_C的换算关系为 $T C = T K - 273.15$

Table 3

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Table 4

Table 5

Table 6

Values for parameters related to refrigerated trucks

参数	取值	参数	取值
v/(km/h)	90	N/(Rev/s)	36.67
$P r$	5~7	d_e/L	45
$η$	0.45	S_c/m²	10.5
$ρ$ /(kg/m³)	1.204 1	S_b/m²	4.1
C_d	0.6	d_o	0.25~1.5
C_r	0.01	h_d/(KJ/g)	44
S_A/m²	4.032	p_d/(元/L)	7.5
$ψ$	1	p_s/(元/h)	30
f_e/(KJ/Rev/L)	0.2

Table 6

Table 7

Table 8

Table 9

Table 10

Table 11

Table 12

Table 13

Table 14

Fig. 9

Fig. 10

References 24

1	吴旭. 城市生鲜农产品冷链物流库存与配送协同优化研究[D]. 北京: 北京交通大学, 2019.
	Wu Xu. Research on Collaborative Optimization of Cold Chain Logistics Inventory and Distribution of Urban Fresh Agricultural Products[D]. Beijing: Beijing Jiaotong University, 2019.
2	陈军. 考虑消费者选择行为的农产品质量分级博弈分析[J]. 运筹与管理, 2020, 29(10): 68-75.
	Chen Jun. Game Analysis of Agri-food Quality Classification Under Consumer Selection Behavior[J]. Operations Research and Management Science, 2020, 29(10): 68-75.
3	Ji Ying, Du Jianhui, Han Xiaoya, et al. A Mixed Integer Robust Programming Model for Two-echelon Inventory Routing Problem of Perishable Products[J]. Physica A: Statistical Mechanics and Its Applications, 2020, 548: 124481.
4	Azadeh A, Elahi S, Farahani M H. A Genetic Algorithm-taguchi Based Approach to Inventory Routing Problem of a Single Perishable Product with Transshipment[J]. Computers & Industrial Engineering, 2017, 104: 124-133.
5	Hsiao Y H, Chen Muchen, Chin C L. Distribution Planning for Perishable Foods in Cold Chains with Quality Concerns: Formulation and Solution Procedure[J]. Trends in Food Science & Technology, 2017, 61: 80-93.
6	CHAN F T S, Wang Z X, Goswami A, et al. Multi-objective Particle Swarm Optimisation Based Integrated Production Inventory Routing Planning for Efficient Perishable Food Logistics Operations[J]. International Journal of Production Research, 2020, 58(17): 5155-5174.
7	Li Yantong, Chu Feng, Yang Zhen, et al. A Production Inventory Routing Planning for Perishable Food with Quality Consideration[J]. IFAC-PapersOnLine, 2016, 49(3): 407-412.
8	巫威眺, 王殿雷, 马昌喜. 液化天然气库存路径问题建模与算法[J]. 中国公路学报, 2022, 35(11): 252-270.
	Wu Weitiao, Wang Dianlei, Ma Changxi. Model and Algorithm for Inventory Routing Problem of Liquified Natural Gas[J]. China Journal of Highway and Transport, 2022, 35(11): 252-270.
9	赵志学, 李夏苗, 周鲜成, 等. 考虑交通拥堵的冷链物流城市配送的GVRP研究[J]. 计算机工程与应用, 2020, 56(1): 224-231.
	Zhao Zhixue, Li Xiamiao, Zhou Xiancheng, et al. Research on Green Vehicle Routing Problem of Cold Chain Distribution: Considering Traffic Congestion[J]. Computer Engineering and Applications, 2020, 56(1): 224-231.
10	赵邦磊, 桂海霞, 李慧宗, 等. 考虑交通状况的冷链物流路径优化[J]. 制造业自动化, 2021, 43(4): 90-95.
	Zhao Banglei, Gui Haixia, Li Huizong, et al. Cold Chain Logistics Route Optimization Considering Traffic Condition[J]. Manufacturing Automation, 2021, 43(4): 90-95.
11	王恒, 徐亚星, 王振锋, 等. 基于道路状况的生鲜农产品配送路径优化[J]. 系统仿真学报, 2019, 31(1): 126-135.
	Wang Heng, Xu Yaxing, Wang Zhenfeng, et al. Distribution Routing Optimization of Fresh Agricultural Products Based on Road Conditions[J]. Journal of System Simulation, 2019, 31(1): 126-135.
12	吴瑶, 马祖军. 时变路网下带时间窗的易腐食品生产-配送问题[J]. 系统工程理论与实践, 2017, 37(1): 172-181.
	Wu Yao, Ma Zujun. Time-dependent Production-Delivery Problem with Time Windows for Perishable Foods[J]. Systems Engineering-Theory & Practice, 2017, 37(1): 172-181.
13	王淑云, 姜樱梅, 王宪杰. 变质率呈Weibull分布的一体化三级冷链库存策略研究[J]. 管理工程学报, 2015, 29(2): 229-239.
	Wang Shuyun, Jiang Yingmei, Wang Xianjie. An Integrated Three-echelon Inventory Model for Cold Chain Items with Weibull Distribution[J]. Journal of Industrial Engineering and Engineering Management, 2015, 29(2): 229-239.
14	黎莎, 修睿, 计明军. 基于新鲜度动态变化的冷链物流库存分配与运输路径联合优化[J]. 系统工程, 2021, 39(5): 69-80.
	Li Sha, Xiu Rui, Ji Mingjun. Integrated Optimization of Cold Chain Logistics Inventory Allocation and Transportation Route Based on Dynamic Freshness[J]. Systems Engineering, 2021, 39(5): 69-80.
15	Wu Wentao, Beretta Claudio, Cronje Paul, et al. Environmental Trade-offs in Fresh-fruit Cold Chains by Combining Virtual Cold Chains with Life Cycle Assessment[J]. Applied Energy, 2019, 254: 113586.
16	张福生, 何成芳, 朱鸿杰. 基于腐烂指数的草莓采后货架期预测模型[J]. 江苏农业科学, 2016, 44(2): 320-323.
17	Xiao Yiyong, Zhao Qiuhong, Kaku Ikou, et al. Development of a Fuel Consumption Optimization Model for the Capacitated Vehicle Routing Problem[J]. Computers & Operations Research, 2012, 39(7): 1419-1431.
18	Wu Weitiao, Zhou Wei, Lin Yue, et al. A Hybrid Metaheuristic Algorithm for Location Inventory Routing Problem with Time Windows and Fuel Consumption[J]. Expert Systems with Applications, 2021, 166: 114034.
19	Leng Longlong, Zhang Chunmiao, Zhao Yanwei, et al. Biobjective Low-Carbon Location-Routing Problem for Cold Chain Logistics: Formulation and Heuristic Approaches[J]. Journal of Cleaner Production, 2020, 273: 122801.
20	朱桂阳, 贾涛, 林峰, 等. 考虑缺货的两阶段腐败一体化库存—路径模型[J]. 工业工程与管理, 2016, 21(5): 62-68.
	Zhu Guiyang, Jia Tao, Lin Feng, et al. Integrated Inventory Routing Problem with In-transit and Retail Deterioration Allowing for Lost Sale[J]. Industrial Engineering and Management, 2016, 21(5): 62-68.
21	肖智豪, 胡志华, 朱琳. 求解冷链物流时间依赖型车辆路径问题的混合自适应大邻域搜索算法[J]. 计算机应用, 2022, 42(9): 2926-2935.
	Xiao Zhihao, Hu Zhihua, Zhu Lin. Hybrid Adaptive Large Neighborhood Search Algorithm for Solving Time-dependent Vehicle Routing Problem in Cold Chain Logistics[J]. Journal of Computer Applications, 2022, 42(9): 2926-2935.
22	孙波, 姜平, 周根荣, 等. 基于改进遗传算法的AGV路径规划[J]. 计算机工程与设计, 2020, 41(2): 550-556.
	Sun Bo, Jiang Ping, Zhou Genrong, et al. AGV Optimal Path Planning Based on Improved Genetic Algorithm[J]. Computer Engineering and Design, 2020, 41(2): 550-556.
23	Qin Gaoyuan, Tao Fengming, Li Lixia. A Vehicle Routing Optimization Problem for Cold Chain Logistics Considering Customer Satisfaction and Carbon Emissions[J]. International Journal of Environmental Research and Public Health, 2019, 16(4): 576.
24	Wang Songyi, Tao Fengming, Shi Yuhe. Optimization of Location-Routing Problem for Cold Chain Logistics Considering Carbon Footprint[J]. International Journal of Environmental Research and Public Health, 2018, 15(1): 86.

需求点编号	客户点坐标/km	客户需求量/t	产品需求等级	卸货时间/min
0	(105,105)
1	(123,147)	[1.2,1,1.3]	[3,3,2]	[12,10,13]
2	(105,51)	[2,1.5,1.2]	[3,2,3]	[20,15,12]
3	(145,135)	[1.3,1.4,1.6]	[1-3]	[13-14,16]
4	(165,61)	[1.7,1.3,1.7]	[2,3,1]	[17,13,17]
5	(46,90)	[1.5,1.9,1.4]	[2,1,2]	[15,19,14]
6	(74,90)	[1.3,1.8,1.7]	[3,3,2]	[13,18,17]
7	(61,150)	[1.6,1.4,1.8]	[1,1,2]	[16,14,18]
8	(30,129)	[1.8,1.3,1.3]	[2,3,3]	[18,13,13]
9	(166,180)	[1.7,2,1.5]	[1,2,1]	[17,20,15]
10	(90,179)	[1.9,1.5,1.8]	[1,3,1]	[19,15,18]
11	(60,195)	[1.5,1.4,1.6]	[3,3,2]	[15,12,16]
12	(15,105)	[1.2,1.4,2]	[3,3,2]	[12,14,20]
13	(90,75)	[1.6,1.9,1.6]	[2,3,3]	[16,19-20]
14	(45,30)	[1.9,1.3,1.7]	[1,2,1]	[19,13,17]
15	(90,15)	[1.6,1.7,1.4]	[2,1,2]	[16,17,14]
16	(30,60)	[1.4,1.4,1.8]	[3,1,3]	[14,14,18]
17	(15,90)	[1.4,1.2,1.6]	[1,2,1]	[14,12,16]
18	(60,120)	[1.5,1.6,1.5]	[3,1,3]	[15,16,15]
19	(45,180)	[1.2,1.5,1.3]	[2,2,1]	[12,15,13]
20	(135,195)	[1.8,1.4,1.6]	[3,2,3]	[18,14,16]

项目	第一次迭代	第二次迭代	第三次迭代
上层模型成本/元	142 386	135 068	124 626
下层模型成本/元	8 637	3 975	0
上层模型订单替换率/%	33.3	10	0
总计成本/元	151 023	139 043	124 626

项目	第一次模拟	第二次模拟
双层模型成本/元	124 626	129 825
仿真模型成本/元	6 012	0
双层模型订单替换率/%	13.3	0
总计成本/元	130 638	129 825

车辆编号	制冷温度/℃	第一次配送方案	第二次配送方案
1	3	0-5-17-16-14-0	0-19-11-0
2	3	0-6-13-2-15-0	0-12-4-0
3	3	0-18-8-7-19-0
4	3	0-1-20-10-11-0
5	3	0-3-9-12-4-0

车辆编号	制冷温度/℃	第一次配送方案	第二次配送方案
1	3	0-2-15-13-6-0	0-11-0
2	3	0-5-17-16-14-0
3	3	0-18-8-19-11-0
4	3	0-7-10-20-9-0
5	3	0-3-12-1-4-0