考虑订单替换的冷链配送-库存联合优化与仿真

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

摘要/Abstract

摘要：

冷链物流最重要的目的是保证产品新鲜度，而在此基础上如何降低订单配送的成本是冷链公司急需解决的问题。对消费者来说，产品的质量与食品安全是其主要的需求。因此以配送中心为研究对象，在配送之前根据产品初始新鲜度将产品分成不同的等级，通过对不符合配送要求的订单采用等级向上的替换模式来提升产品整体新鲜度，使客户尽可能获得更好质量的产品，确保顾客的需求得到满足，同时针对配送与库存分配问题进行联合优化，根据最低新鲜度、库存量等为约束建立了双层规划模型，其中上层模型以运输成本、货损成本等之和最小为目标以此确定订单配送以及库存分配方案，下层模型以订单替换成本最小为目标以此确定需要进行订单替换的订单以及替换的产品等级，通过提出改进的自适应遗传算法与cplex分别求解上下层模型，将求解得到的配送方案代入模拟了道路拥堵的仿真模型中进行验证并重新加入双层模型中进行规划；对算例求解的结果表明：订单替换可以有效降低冷链企业运营成本，获得更符合实际的订单配送与库存的分配方案。

关键词: 库存路径优化, 新鲜度, 订单替换, 道路拥堵, 冷链物流仿真, 遗传算法

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

中图分类号:

TP301

万远鹏,梁承姬,王思洪等 . 考虑订单替换的冷链配送-库存联合优化与仿真[J]. 系统仿真学报, 2024, 36(3): 578-594.

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

图/表 24

图1

表1

集合

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， $p ⊂ p 1, p 2, ⋯, p q$

表1

表2

参数

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

表2

表3

决策变量

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 $T C = T K - 273.15$

表3

图2

图3

图4

图5

图6

图7

图8

表4

表5

表6

冷藏车相关参数取值

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

表6

表7

表8

表9

表10

表11

表12

表13

表14

图9

图10

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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