# Integrated Optimization of Order Allocation and Last-Mile Multi-Temperature Joint Distribution for Fresh Agriproduct Community Retail

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Problem Description and Model Formulation

#### 3.1. Problem Description

#### 3.2. Objective Function

#### 3.2.1. Maturity Penalty Cost

#### 3.2.2. Distribution Cost

#### 3.2.3. Refrigeration Cost

#### 3.3. Constraints

#### 3.4. Model Formulation

## 4. Mixed Genetic Algorithm

#### 4.1. Reduction of Solution Space

#### 4.2. Efficient Chromosome Coding Method

#### 4.3. Implementation of MGA

Algorithm 1. MGA | ||

Input: (Initialize Solution $S$, set crossover probability ${p}_{c}$, mutation probability ${p}_{m}$, population size $N$, the number of evolutionary iterations $G$.) | ||

1: | generate a solution $S$ using the k-means clustering method | Section 4.1 |

2: | set ${S}_{best}:=S$ | |

3: | While$(G\le {G}_{max}$) | Section 4.2 |

4: | for $i$ to ${N}^{\prime}$ | |

5: | evaluation of individual populations ${f}_{i}$ | |

6: | end for | |

7: | select parents ${P}_{1}$ from $S$ using roulette selection | |

8: | select parents ${P}_{2}$ from $S$ using crossover and mutation | |

9: | generate solution ${S}^{\prime}$ | |

10: | if ${S}^{\prime}$ is better than ${S}_{best},$ then | |

11: | ${S}_{best}={S}^{\prime}$ | |

12: | $S:={S}^{\prime}$ | |

13: | end if | |

14: | end while | |

15: | return ${S}_{best}$ |

## 5. Numerical Experiments

#### 5.1. A Case Study of Fresh E-Commerce in the Gulou District of Nanjing City

^{2}·°C), ${p}_{1}$ = 3.64 CNY/kCal, S = 29.903 m

^{2}, $\Delta {T}_{1}$ = 0 °C, $\Delta {T}_{2}$ = 20 °C, $\Delta {T}_{3}$ = 40 °C, ${c}_{1}$ = 1.245 CNY/kCal, $\omega $ = 1.95 CNY/kCal/h, f = 150 CNY. The maturity penalty parameters are set as follows: ${\gamma}_{1}$ = 0.833 CNY/unit, ${\gamma}_{2}$ = 1.667 CNY/unit (citing the data from Hou [15]). The MGA parameters are set as follows: $N$ = 100, $M$ = 1000, ${p}_{c}$ = 0.95, and ${p}_{m}$ = 0.1. The objective function’s parameters are assumed to be ${\lambda}_{1}={\lambda}_{2}={\lambda}_{3}=$ 1/3.

#### 5.2. Medium- to Large-Scale Numerical Experiments

## 6. Discussion and Conclusions

#### 6.1. Academic Implications

#### 6.2. Managerial Implications

#### 6.3. Limitations and Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Notations | |

$i$ | If $i=0$, front warehouse, else $i=1,\dots ,{N}^{\prime}$, community nodes |

$j$ | If $j=0$, front warehouse, else $j=1,\dots ,{N}^{\prime}$, community nodes |

$k$ | Vehicle, $k=1,\dots ,K$ |

$s$ | Temperature zone type $s=1,\dots ,S$ |

$p$ | Commodity type, $p=1,\dots ,P$ |

${p}^{\prime}$ | Commodity type, ${p}^{\prime}=1,\dots ,P$ |

Index Sets | |

N | Set of nodes including one front warehouse and multiple consumers |

N′ | Set of consumer nodes, N′ = N/{0} |

K | Set of vehicles |

S | Set of temperature zone types |

P | Set of commodity types purchased by customers |

Parameters | |

${d}_{ip}$ | The demand quantity of category $p$ of customers $i$ (kg) |

${\gamma}_{1}$ | Unit increase rate of earliness penalty cost (CNY/min) |

${\gamma}_{2}$ | Unit increase rate of tardiness penalty cost (CNY/min) |

$f$ | Fixed usage cost of vehicle (CNY) |

$\omega $ | Unit distribution cost of vehicle (CNY/kCal/h) |

$n$ | Number of vehicles |

${q}_{s}$ | Loading capacity of vehicle $s$ temperature layer (ton) |

$a$ | Order unit weight picking time (min/kg) |

${\tau}_{ij}$ | Distribution time between consumer $i$ and $j$ (min) |

${p}_{1}$ | Unit refrigerant price (CNY/kCal) |

${c}_{1}$ | Heat load coefficient during loading and unloading process (CNY/kCal) |

$R$ | Heat transfer coefficient ($\mathrm{kCal}/(\mathrm{h}\xb7{\mathrm{m}}^{2}\xb7\xb0\mathrm{C}$) |

$A$ | Average surface area of refrigerator (${\mathrm{m}}^{2}$) |

$\Delta {T}_{1}$ | The temperature difference between inside and outside of the room temperature compartment (°C) |

$\Delta {T}_{2}$ | The temperature difference between inside and outside of the refrigerated compartment (°C) |

$\Delta {T}_{3}$ | The temperature difference between inside and outside of the frozen compartment (°C) |

$\left[{E}_{i},{L}_{i}\right]$ | Customer $i$ Satisfaction Time Window (h) |

$M$ | A large positive constant |

Decision Variables | |

${x}_{ij}^{k}$ | Binary decision variable. If ${x}_{ij}^{k}=1$, vehicle k serves from consumer $i$ to consumer $j$ |

${y}_{i}^{k}$ | Binary decision variable. If ${y}_{i}^{k}=1$, consumer $i$ is served by vehicle k |

${y}_{s}^{k}$ | Binary decision variable. If ${y}_{s}^{k}=1$, the vehicle $k$ is used to deliver $s$ temperature zone product |

${z}_{ip}^{k}$ | Binary decision variable. If ${z}_{ip}^{k}=1$, the category $p$ of consumer $i$ is loaded in vehicle $k$ |

${\lambda}_{p{p}^{\prime}}$ | Binary decision variable. If ${\lambda}_{p{p}^{\prime}}=1$, categories $p$ and ${p}^{\prime}$ of fresh food are incompatible in temperature layer and they should be loaded in different temperature zones of fresh food are incompatible in temperature layer and they should be loaded in different temperature zones |

${t}_{i}^{k}$ | Arrival time of vehicle $k$ at consumer $i$ |

$t{s}_{i}^{k}$ | Start picking time of vehicle $k$ for consumer $i$ order |

$t{f}_{i}^{k}$ | Finish picking time of vehicle $k$ for consumer $i$ order |

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**Figure 1.**Diagram for integrated multi-item packing and MTJD for fresh agriproduct supply. The layout of MCV in (

**a**) is shown in (

**b**).

**Figure 2.**Fresh produce e-commerce online order processing and front warehouse-to-door allocation scheduling diagram.

**Figure 6.**Schematic diagram of spatial coordinates. (

**a**) Geographic location on the Gao De map. (

**b**) Position of the coordinates.

**Figure 9.**Comparison of the computational performance of MGA, GA, and VNS. (

**a**) Comparison of CPU time between MGA, GA, and VNS. (

**b**) Comparison of the iteration number between MGA, GA, and VNS.

Stream | Literature | Research Problem |
---|---|---|

VRP with MTJD | [8] | Developing an advanced MTDJ system for the cold food delivery chain. |

[9] | Suitable operational networks of MTJD technique. | |

[10] | The optimal routing distance, as generated by MTDJ. | |

[13] | Design a multi-temperature packaging model for perishable foods to optimize routing. | |

VRPTW under MTJD | [11] | The heterogeneous multi-type fleet vehicle routing problem, with time windows and an incompatible loading constraint. |

[12] | Analyzing the constraints of loading volume. | |

[14] | Addressing the time window allocation problem for product complexity. | |

[15] | Based on real-time traffic information to solve the dynamic multi-compartment VRP. | |

[16] | Jointly optimized hub location and MTJD for the perishable product supply chain. |

Stream | Literature | Research Problem |
---|---|---|

Order splitting | [18] | Reducing distribution costs by clustering SKUs. |

[19] | Deciding from which facility the items in the order should be fulfilled. | |

[20] | Multi-echelon inventory control and order splitting problems. | |

[21] | Splitting a single multi-item order in the distribution center. | |

[22] | Integrating multi-suborder models via transshipment between warehouses. | |

Order merging | [23] | Order delivery consolidation-based business-to-consumer (B2C) distribution. |

[24] | Package consolidation approach to the split-order fulfillment problem. | |

[25] | Optimizing e-commerce warehouse order processing. | |

[26] | Coordinating distribution between suppliers and customers via integration centers. | |

[27] | Merging distribution from central warehouses to retailers. |

Stream | Literature | E-Commerce Mode |
---|---|---|

Order picking + distribution | [29] | Online retailing |

[30] | Front warehouse mode | |

Order integration + distribution | [31] | Takeaway system |

[32] | E-commerce | |

Order splitting + distribution | [33] | O2O |

[34] | Online retailing | |

Order allocation + distribution | [35] | E-tailing |

[36] | Last-mile delivery | |

Warehouse distribution integration | [37] | On-line purchasing |

[38] | Emergency rescue |

Community Number | Coordinates (km) | Time Window | Community Number | Coordinates (km) | Time Window |
---|---|---|---|---|---|

1 | (2.685, −25.687) | (8:00–8:30) | 9 | (9.763, 2.793) | (12:00–12:30) |

2 | (2.6, 17.556) | (10:00–10:30) | 10 | (−24.949, −2.746) | (17:30–18:00) |

3 | (−4.799, −0.186) | (17:00–17:30) | 11 | (15.499, 4.483) | (12:30–13:00) |

4 | (−10.866, 0.266) | (17:00–17:30) | 12 | (−4.133, −25.03) | (8:00–8:30) |

5 | (3.088, −16.762) | (8:00–8:30) | 13 | (24.157, 4.51) | (13:00–13:30) |

6 | (8.178, 20.509) | (9:30–10:00) | 14 | (−9.741, 18.33) | (9:30–10:00) |

7 | (−13.247, −8.611) | (15:00–15:30) | 15 | (−18.668, −1.16) | (16:30–17:00) |

8 | (−0.907, −18.268) | (8:00–8:30) | 16 | (−17.818, 2.789) | (17:30–18:00) |

Community Number | Room Temperature 18~25 °C (s = 1) | Refrigeration 0~5 °C (s = 2) | Refrigeration −18~−25 °C (s = 3) | |
---|---|---|---|---|

Delicatessen (kg) | Vegetables (kg) | Fruit (kg) | Meat (kg) | |

1 | 106.2 | 96.4 | 66.1 | 43.3 |

2 | 83.4 | 75.8 | 51.9 | 34.0 |

3 | 194.1 | 176.3 | 120.8 | 79.2 |

4 | 38.8 | 35.2 | 24.2 | 15.8 |

5 | 775.8 | 704.6 | 482.9 | 316.7 |

6 | 129.9 | 117.9 | 80.8 | 53.0 |

7 | 207.8 | 188.7 | 129.4 | 84.8 |

8 | 176.4 | 160.2 | 109.8 | 72.0 |

9 | 423.4 | 384.5 | 263.5 | 172.8 |

10 | 103.8 | 94.3 | 64.6 | 42.4 |

11 | 168.2 | 152.7 | 104.7 | 68.6 |

12 | 147.8 | 134.2 | 92.0 | 60.3 |

13 | 211.6 | 192.1 | 131.7 | 86.4 |

14 | 91.8 | 83.4 | 57.2 | 37.5 |

15 | 97.1 | 88.2 | 60.5 | 39.6 |

16 | 188.7 | 171.4 | 117.5 | 77.0 |

Number | Optimal Vehicle Routing | |
---|---|---|

Vehicle 1 | 0 → 9 → 0 | |

Vehicle 2 | 0 → 3 → 4 → 16 → 15 → 10 → 0 | |

Vehicle 3 | 0 → 7 → 0 | |

Vehicle 4 | 0 → 8 → 12 → 1 → 0 | |

Vehicle 5 | 0 → 11 → 13 → 0 | |

Vehicle 6 | 0 → 5 → 0 | |

Vehicle 7 | 0 → 14 → 12 → 6 → 0 | |

Experimental results | Number of vehicles | Iteration time [s] |

7 | 59.9 |

Case | No. Comm. | GA | VNS | MGA | |||
---|---|---|---|---|---|---|---|

CPU Time (s) | Iteration | CPU Time (s) | Iteration | CPU Time (s) | Iteration | ||

1 | 20 | 64.98 | 149 | 59.46 | 273 | 55.33 | 116 |

2 | 40 | 120.10 | 243 | 157.46 | 144 | 100.45 | 57 |

3 | 60 | 131.25 | 517 | 231.92 | 311 | 124.73 | 72 |

4 | 80 | 185.36 | 420 | 315.07 | 255 | 135.48 | 130 |

5 | 100 | 198.60 | 309 | 421.19 | 155 | 160.86 | 44 |

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## Share and Cite

**MDPI and ACS Style**

Zhan, Y.; Jiang, Y.
Integrated Optimization of Order Allocation and Last-Mile Multi-Temperature Joint Distribution for Fresh Agriproduct Community Retail. *Sustainability* **2022**, *14*, 9790.
https://doi.org/10.3390/su14159790

**AMA Style**

Zhan Y, Jiang Y.
Integrated Optimization of Order Allocation and Last-Mile Multi-Temperature Joint Distribution for Fresh Agriproduct Community Retail. *Sustainability*. 2022; 14(15):9790.
https://doi.org/10.3390/su14159790

**Chicago/Turabian Style**

Zhan, Yajun, and Yiping Jiang.
2022. "Integrated Optimization of Order Allocation and Last-Mile Multi-Temperature Joint Distribution for Fresh Agriproduct Community Retail" *Sustainability* 14, no. 15: 9790.
https://doi.org/10.3390/su14159790