# Optimization of Truck–Cargo Online Matching for the Less-Than-Truck-Load Logistics Hub under Real-Time Demand

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## Abstract

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## 1. Introduction

- In order to respond to the real-time LTL logistics demand, we designed an online matching algorithm. Since information is input and output in real time, and decisions are made based on partial information, theoretically there is no optimal online algorithm. However, small numerical case study demonstrates that the optimization of our algorithm results in a small gap compared to the Gurobi solver but significantly reduces the computing time.
- The online matching algorithm studied in this paper creatively introduces the double-layer nested time window mechanism. In the empirical case, we verified the effectiveness of the double-layer nested time window and conducted sensitivity analysis of other algorithm parameters. In addition, the scenario of zone partitioning is considered, which shows that for this problem, the judgment of the algorithm performs better without zone partitioning.

## 2. Literature Review

#### 2.1. Research on Logistics Vehicle Scheduling Problem

#### 2.2. Research on Vehicle–Cargo Matching Problem

#### 2.3. Contribution Statements

## 3. Problem Definition and Model Formulation

#### 3.1. Problem Description and Assumptions

#### 3.2. Model Notations

#### 3.3. Model Formulation

## 4. Solution Algorithm

#### 4.1. Coding and Decoding

#### 4.1.1. Coding Strategy

#### 4.1.2. Decoding Strategy

#### 4.2. The Solution Process of the Online Matching Algorithm

Algorithm 1: Online Matching Algorithm |

INPUT: Create list of orders $O$, struct of trucks to be dispatched $R$, list of waybills $P$, set of truck types $L=\left\{1,2,\cdots m\right\}$. Define the ${r}^{th}$ generated order as ${o}_{r}$, the number of unitized units for order ${o}_{r}$ as ${a}_{r}$, and the pickup node number for order ${o}_{r}$ as ${s}_{r}$. Define the loading efficiency condition for each truck as $m$.STEP 1: Orders generated by different cooperative pickup nodes enter list $O$ in chronological sequence. STEP 2: Order Processing Time Window Judgment. Check all orders in list $O$ at regular online checking interval ${T}_{0}$. Checks whether there is an order ${o}_{r}$ in the current order list $O$ that has reached the order processing time window ${T}_{1}$ and, if so, sets the status of the order ${o}_{r}$ to Pending.STEP 3: Order consolidation schemes generation. Generates all consolidation schemes that satisfy the loading efficiency condition for each truck type.The specific judgment process: Determine whether there are a certain number of orders in the current list $O$ with the quantity of unitized units can exactly satisfy the loading efficiency condition of each truck type, i.e., $m\times {Q}^{l}\le {a}_{r}+{\displaystyle \sum _{k\in {r}_{j}}{a}_{k}}\le {Q}^{l}$. STEP 4: Selection Operator. Using total costs as an objective to select the optimal consolidation scheme.The specific selection process: Obtain the lowest total cost of truck service sequence for all feasible schemes, including the truck transportation cost to service all orders in the scheme and the fixed dispatch cost for using such a type of truck. Temporarily store the optimal consolidation scheme (including related orders, the lowest total costs, truck service sequence, etc.) for pending order ${o}_{r}$ to the struct $R$. STEP 5: Dispatch Time Window Judgment. Allow the order with successful consolidation to wait in the order list for ${T}_{2}$ mins for a better solution. If, at the moment of the regular online check, there is an order ${o}_{r}$ in list $O$ that has reached the dispatch time window ${T}_{2}$, the order ${o}_{r}$ must be processed at that moment. Sets the status of the order ${o}_{r}$ to Processing.Repeat STEP 3 and STEP 4 to temporarily store the optimal consolidation scheme for the order ${o}_{r}$ under processing to the struct $R$. Compare all consolidation schemes related to order ${o}_{r}$ in struct $R$, select the one with the lowest total cost and output it to the waybill list $P$. Removes all the related orders from the list $O$. STEP 6: Repeat the above steps until all the orders are processed, then end the algorithm. All the orders are in the list $P$, and order list $O$ is empty. |

## 5. Experiments and Data Analysis

#### 5.1. Small Numerical Case

#### 5.1.1. Input Data

#### 5.1.2. Results Analysis

#### 5.2. Empirical Case

#### 5.2.1. Input Data

#### 5.2.2. Results Analysis

#### 5.3. Managerial Insights

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

#### Appendix A.1. The Distances between the Nodes

Node 0 | Node 1 | Node 2 | Node 3 | Node 4 | |
---|---|---|---|---|---|

Node 0 | 0 | 4 | 6 | 3 | 3 |

Node 1 | 4 | 0 | 3 | 6 | 7 |

Node 2 | 6 | 3 | 0 | 2 | 3 |

Node 3 | 3 | 6 | 2 | 0 | 2 |

Node 4 | 3 | 7 | 3 | 2 | 0 |

Node 0 | Node 1 | Node 2 | Node 3 | Node 4 | Node 5 | Node 6 | Node 7 | |
---|---|---|---|---|---|---|---|---|

Node 0 | 0 | 50 | 8 | 5 | 30 | 35 | 86 | 74 |

Node 1 | 50 | 0 | 40 | 45 | 20 | 90 | 150 | 55 |

Node 2 | 8 | 40 | 0 | 3 | 22 | 38 | 84 | 70 |

Node 3 | 5 | 45 | 3 | 0 | 25 | 40 | 80 | 75 |

Node 4 | 30 | 20 | 22 | 25 | 0 | 60 | 110 | 50 |

Node 5 | 35 | 90 | 38 | 40 | 60 | 0 | 60 | 104 |

Node 6 | 86 | 150 | 84 | 80 | 110 | 60 | 0 | 152 |

Node 7 | 74 | 55 | 70 | 75 | 50 | 104 | 152 | 0 |

#### Appendix A.2. Truck and Unitized Implement Parameters

Truck Type | Loading Length (m) | Loading Width (m) | Weight Capacity (t) | Number of Unitized Units Can Be Loaded (pcs) | Unit Dispatch Cost (RMB/trip) | Unit Transportation Cost (RMB/pcs·km) |
---|---|---|---|---|---|---|

Type I | 4.2 | 2.15 | 27 | 12 | 280 | 0.35 |

Type II | 6.8 | 2.45 | 56 | 20 | 300 | 0.30 |

Type III | 12 | 2.45 | 81 | 44 | 340 | 0.20 |

Unitized Implement Type | Length (m) | Width (m) | Height (m) |
---|---|---|---|

Assembly cage | 1.2 | 1 | 0.89 |

Pallet | 1.2 | 1 | 0.15 |

#### Appendix A.3. The Matching Relationship between the Different Types of Trucks and the Unitized Units

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Mode | Express | LTL Logistics | FTL Logistics |
---|---|---|---|

Target market | C2C, B2C | B2B | B2B |

Shipment weight | <30 kg | 30 kg~3 t | >3 t |

Market concentration | high | comparatively low | low |

Timeliness requirement | high | comparatively low | low |

**Table 2.**The main features of the previous relevant survey studies and our study (logistics vehicle scheduling problem).

Authors (Year) | Application Scenario | Model | Objective | Algorithm |
---|---|---|---|---|

Giovanni et al. [6] (2018) | Express logistics | - | - | Neighborhood search heuristic algorithm |

Shi et al. [7] (2019) | B2C e-commerce | Integer programming model | Minimize the number of feasible routes selected | Online intelligent scheduling approach |

Wang et al. [9] (2023) | Bulky cargo logistics | Mixed-integer programming model | Maximize the average loading rate of vehicles and minimize the total operating costs | Extended nondominated sorting genetic algorithm-II |

Diefenbach et al. [12] (2023) | In-plant logistics | Integer programming model | Minimize the number of required vehicles | Decomposition scheme based on branch-and-check approach |

Low et al. [13] (2014) | Production scheduling with delivery | Nonlinear programming model | Minimize the total cost | Adaptive genetic algorithm |

Wang et al. [14] (2019) | Machine scheduling | Nonlinear programming model | Minimize the total carbon emissions | Tabu search hybrid algorithm |

Fathollahi-Fard et al. [15] (2021) | Production scheduling | Mixed-integer linear programming model | Maximize the social benefits | Learning-based heuristic algorithm |

Ganji et al. [16] (2020) | Integrated scheduling of production and distribution | Mixed-integer nonlinear programming model | Minimize total distribution costs, carbon emission, and customer dissatisfaction | NSGAII algorithm |

Yagmur et al. [17] (2021) | Integrated scheduling of production and distribution | Mixed-integer programming model | Minimize the sum of total tour time and total tardiness | Memetic Algorithm |

Kang et al. [18] (2019) | Crowdsourced parcel delivery | - | - | Learning-based logistics planning and scheduling algorithm |

Wehbi et al. [19] (2022) | Urban delivery system | Mixed-integer linear programming model | Minimize the total time of delivery | Heuristic algorithm |

Gu et al. [20] (2023) | Drone delivery | Markov decision process | Maximize the total profits | Heuristic solution approach framework |

This study | LTL logistics | Mixed-integer nonlinear programming model | Minimize the total cost | Online matching algorithm |

**Table 3.**The main features of the previous relevant survey studies and our study (vehicle–cargo matching problem).

Authors (Year) | Freight Transportation | Passenger Transportation | Static Matching Problem | Dynamic Matching Problem | Multi-Type Vehicle | Integrated Loading Problem | Integrated Scheduling Problem | Algorithm |
---|---|---|---|---|---|---|---|---|

Tian et al. [21] (2022) | √ | √ | √ | Improved dynamic Bayesian network | ||||

Yu et al. [22] (2023) | √ | √ | Weed optimization algorithm | |||||

Wang et al. [23] (2022) | √ | √ | √ | √ | Hybrid quantum particle swarm algorithm | |||

Yücel et al. [24] (2022) | √ | √ | √ | √ | √ | ALNS algorithm | ||

Li et al. [25] (2020) | √ | √ | √ | Heuristic-based algorithm | ||||

Ni et al. [26] (2023) | √ | √ | √ | NSGA II | ||||

Deng et al. [27] (2023) | √ | √ | √ | √ | Particle swarm and genetic algorithm | |||

Iris et al. [28] (2018) | √ | √ | √ | Randomized construction heuristic approach | ||||

Agatz et al. [29] (2012) | √ | √ | _ | |||||

Guo et al. [30] (2021) | √ | √ | Robust optimization | |||||

Zhan et al. [31] (2023) | √ | √ | √ | Artificial bee colony algorithm | ||||

Meshkani et al. [32] (2023) | √ | √ | Two-step ride-matching algorithm | |||||

Zhou et al. [33] (2022) | √ | √ | √ | Insertion heuristic method | ||||

Qin et al. [34] (2021) | √ | √ | √ | Two-stage KM-based approach | ||||

This study | √ | √ | √ | Future research | √ | Online Algorithm |

Set: | |

$N=\left\{0,1,2,\dots n+1\right\}$ | Set of nodes, the total number of nodes is $n+2$ |

$\left\{0,n+1\right\}\subseteq N$ | Core hub node set |

${N}^{\prime}=\left\{1,2,3\cdots n\right\}\subseteq N$ | Cooperative pickup node set |

$J={J}_{1}\cup {J}_{2}\cdots {J}_{n}$ | Set of orders for $n$ cooperative pickup nodes |

$L=\left\{1,2,\cdots ,m\right\}$ | Set of pickup truck types, the total number of truck types is $m$ |

$K={K}_{1}\cup {K}_{2}\cdots {K}_{m}$ | Set of trucks |

${J}^{lk}$ | Order set for truck $k$ services |

Parameters: | |

${c}_{l}^{dispatch}$ | Fixed dispatch cost for truck type $l$ |

${c}_{l}^{trans}$ | Unit transportation cost of truck type $l$ |

${d}_{ij}$ | Transportation distance from node $i$ to node $j$ |

${Q}^{l}$ | Capacity of truck type $l$ |

${Q}_{{i}_{a}}^{lk}$ | The total load of truck $k$ of type $l$ after serving order $a$ generated by node $i$ |

${q}_{{i}_{a}}$ | The quantity of unitized units for order $a$ generated by node $i$ |

${q}_{i}$ | The number of orders generated by node $i$ |

${T}_{{i}_{a}}$ | The generation time of order $a$ generated by node $i$ |

${T}_{{i}_{a}}^{lk}$ | Time for truck $k$ of type $l$ to arrive at node $i$ and ready to start serving order $a$ |

${T}_{1}$ | Order processing time window |

Decision variables: | |

${x}_{{i}_{a}}^{l}$ | Binary variable, equal to 1 if the order $a$ generated by node $i$ is transported by a truck of type $l$, otherwise, equal to 0 |

${w}_{{i}_{a}}^{lk}$ | Binary variable, equal to 1 if the order $a$ generated by node $i$ is transported by truck $k$ of type $l$, otherwise, equal to 0 |

${z}_{i}^{lk}$ | Binary variable, equal to 1 if truck $k$ of type $l$ service node $i$, otherwise, equal to 0 |

${y}_{{i}_{a}{j}_{b}}^{lk}$ | Binary variable, equal to 1 if the truck $k$ of type $l$ services order $a$ generated by node $i$ and followed by services order $b$ generated by node $j$, otherwise, equal to 0 |

Order Sequence Number | Node Number | Cargo Volume | Order Generation Time |
---|---|---|---|

1 | 2 | 1 | 8:20:03 |

2 | 3 | 9 | 8:27:33 |

3 | 1 | 3 | 8:31:54 |

4 | 1 | 1 | 8:33:27 |

5 | 2 | 17 | 8:36:08 |

6 | 2 | 13 | 8:37:33 |

7 | 2 | 10 | 8:38:57 |

8 | 1 | 13 | 8:39:11 |

9 | 4 | 11 | 8:40:30 |

10 | 3 | 5 | 8:42:33 |

11 | 3 | 6 | 8:42:55 |

12 | 4 | 17 | 8:47:39 |

13 | 1 | 11 | 8:47:43 |

14 | 4 | 12 | 8:49:12 |

Parameters | Description | Value |
---|---|---|

$m$ | Truck loading efficiency requirement | 90% |

${T}_{0}$ | Regular online checking interval | 3 min |

Algorithm | Waybill No. | Waybill Generation Time | Number of Online Checking | Truck Type | Cargo Volume (pcs) | Cost (RMB) | Loading Efficiency | Truck Service Sequence i.e., →Node Number(Order Sequence Number)→ |
---|---|---|---|---|---|---|---|---|

Online Matching Algorithm | 1 | 8:43:05 | 8 | 3 | 44 | 428 | 100.00% | 0 → 3(2) → 3(10) → 2(6) → 2(7) → 2(1) → 3(11) → 0 |

2 | 8:54:37 | 12 | 3 | 44 | 454.4 | 100.00% | 0 → 1(3) → 1(4) → 2(5) → 4(9) → 4(14) → 0 | |

3 | 9:03:15 | 15 | 3 | 41 | 454.8 | 93.18% | 0 → 4(12) → 1(8) → 1(13) → 0 | |

Gurobi | 1 | 8:47:46 | - | 3 | 41 | 454.8 | 93.18% | 0 → 1(1) → 2(7) → 1(2) → 1(4) → 1(3) → 0 |

2 | 8:49:12 | - | 3 | 44 | 410.4 | 100.00% | 0 → 3(9) → 3(11) → 4(14) → 4(13) → 0 | |

3 | 8:42:35 | - | 3 | 44 | 436.8 | 100.00% | 0 → 3(10) → 2(5) → 2(8) → 2(6) → 4(12) → 0 |

Scheme No. | ${\mathit{T}}_{1}$ (min) | Total Number of Trips | Truck Type I | Truck Type II | Truck Type III | Total Cost (Algorithm) (RMB) | Total Cost (Gurobi) (RMB) | Gap | Algorithm Runtime (Algorithm/Gurobi) (s) |
---|---|---|---|---|---|---|---|---|---|

1 | 21 | 3 | 0 | 0 | 3 | 1337.2 | 1293.8 | 3.25% | 73.16/3159.36 |

2 | 20.5 | 3 | 0 | 0 | 3 | 1337.2 | 1294.4 | 3.20% | 72.86/3150.9 |

3 | 20 | 3 | 0 | 0 | 3 | 1337.2 | 1302 | 2.63% | 36.75/3025.75 |

4 | 19.5 | 3 | 0 | 0 | 3 | 1337.2 | 1302 | 2.63% | 37.34/2769.47 |

5 | 19 | 3 | 0 | 0 | 3 | 1337.2 | 1320.8 | 1.23% | 41.06/2896.25 |

6 | 18.5 | 3 | 0 | 0 | 3 | 1353.6 | 1345.4 | 0.61% | 64.22/2078.93 |

7 | 18 | 3 | 0 | 0 | 3 | 1345.4 | 1329 | 1.22% | 22.01/1856.65 |

Scheme No. | Total Number of Trips | Truck Type I | Truck Type II | Truck Type III | Truck Cargo Volume (pcs) | Average Loading Efficiency | AWT (min) | Total Cost (RMB) | Gap with Gurobi | Algorithm Runtime (s) |
---|---|---|---|---|---|---|---|---|---|---|

0 (Gurobi) | 3 | 0 | 0 | 3 | 44/44/41 | 97.73% | - | 1302 | - | 3025 |

1 (Original order data) | 3 | 0 | 0 | 3 | 44/44/41 | 97.73% | 13.28 | 1337.2 | 2.70% | 342.051 |

2 | 3 | 0 | 0 | 3 | 43/43/43 | 97.73% | 14.93 | 1329.6 | 2.12% | 279.595 |

3 | 3 | 0 | 0 | 3 | 43/44/42 | 97.73% | 12.27 | 1303.6 | 0.12% | 304.148 |

4 | 3 | 0 | 0 | 3 | 44/44/41 | 97.73% | 14.73 | 1329 | 2.07% | 156.398 |

5 | 3 | 0 | 0 | 3 | 44/44/41 | 97.73% | 14.93 | 1302.6 | 0.05% | 155.728 |

6 | 3 | 0 | 0 | 3 | 44/44/41 | 97.73% | 14.12 | 1320.8 | 1.44% | 71.076 |

Waybill No. | Waybill Generation Time | Number of Online Checking | Truck Type | Cargo Volume (pcs) | Cost (RMB) | Loading Efficiency | Truck Service Sequence i.e., →Node Number(Order Sequence Number)→ |
---|---|---|---|---|---|---|---|

1 | 8:43:05 | 8 | 3 | 44 | 1440 | 100% | 0 → 5(1) → 4(2) → 4(3) → 4(4) → 4(8) → 4(10) → 4(11) → 0 |

2 | 9:00:22 | 14 | 3 | 43 | 1415 | 97.73% | 0 → 5(5) → 4(9) → 4(12) → 4(20) → 4(21) → 0 |

3 | 9:00:22 | 14 | 3 | 41 | 1160 | 93.18% | 0 → 1(6) → 1(14) → 1(22) → 4(13) → 0 |

4 | 9:03:15 | 15 | 3 | 44 | 1915.2 | 100% | 0 → 7(7) → 7(18) → 1(15) → 1(17) → 1(23) → 0 |

5 | 9:14:46 | 19 | 3 | 44 | 1642.4 | 100% | 0 → 7(16) → 7(26) → 7(30) → 0 |

6 | 9:17:39 | 20 | 3 | 44 | 1695.2 | 100% | 0 → 7(19) → 7(25) → 4(27) → 4(36) → 0 |

7 | 9:26:17 | 23 | 3 | 44 | 868 | 100% | 0 → 4(24) → 4(31) → 4(33) → 4(41) → 4(44) → 0 |

8 | 9:29:10 | 24 | 3 | 44 | 1220 | 100% | 0 → 1(28) → 1(29) → 1(32) → 1(34) → 1(40) → 1(42) → 1(48) → 4(35) → 0 |

9 | 9:40:41 | 28 | 3 | 44 | 868 | 100% | 0 → 4(37) → 4(39) → 4(55) → 4(62) → 0 |

10 | 9:43:34 | 29 | 3 | 40 | 1524 | 90.91% | 0 → 7(38) → 7(49) → 7(65) → 0 |

11 | 9:46:27 | 30 | 3 | 44 | 1220 | 100% | 0 → 1(43) → 1(45) → 1(46) → 1(57) → 4(47) → 4(50) → 0 |

12 | 9:52:13 | 32 | 3 | 44 | 1220 | 100% | 0 → 1(51) → 1(66) → 4(52) → 0 |

13 | 9:55:05 | 33 | 3 | 44 | 1220 | 100% | 0 → 1(53) → 1(54) → 1(56) → 4(67) → 4(73) → 0 |

14 | 9:57:58 | 34 | 3 | 44 | 868 | 100% | 0 → 4(58) → 4(59) → 4(70) → 0 |

15 | 10:00:51 | 35 | 3 | 44 | 1220 | 100% | 0 → 1(60) → 1(74) → 4(61) → 4(88) → 0 |

16 | 10:03:44 | 36 | 3 | 44 | 1220 | 100% | 0 → 1(63) → 1(68) → 1(81) → 4(76) → 0 |

17 | 10:03:44 | 36 | 3 | 44 | 1220 | 100% | 0 → 1(64) → 4(78) → 4(89) → 3(75) → 0 |

18 | 10:06:37 | 37 | 3 | 44 | 1220 | 100% | 0 → 1(69) → 4(72) → 4(86) → 0 |

19 | 10:09:29 | 38 | 3 | 43 | 1028 | 97.73% | 0 → 5(71) → 3(80) → 3(101) → 0 |

20 | 10:12:22 | 39 | 3 | 44 | 1220 | 100% | 0 → 1(77) → 1(83) → 4(82) → 4(84) → 0 |

21 | 10:15:15 | 40 | 3 | 44 | 1695.2 | 100% | 0 → 7(79) → 7(97) → 4(85) → 0 |

22 | 10:21:01 | 42 | 3 | 44 | 1220 | 100% | 0 → 1(87) → 4(90) → 4(92) → 0 |

23 | 10:23:53 | 43 | 3 | 44 | 1220 | 100% | 0 → 1(91) → 1(93) → 4(94) → 3(104) → 0 |

24 | 10:26:46 | 44 | 3 | 44 | 1220 | 100% | 0 → 1(95) → 1(98) → 3(106) → 0 |

25 | 10:26:46 | 44 | 3 | 43 | 856 | 97.73% | 0 → 4(96) → 4(103) → 4(107) → 4(108) → 0 |

26 | 10:29:39 | 45 | 3 | 44 | 1220 | 100% | 0 → 4(99) → 1(100) → 1(105) → 0 |

27 | 10:32:32 | 46 | 2 | 18 | 624 | 90.00% | 0 → 4(102) → 4(111) → 0 |

28 | 10:46:56 | 51 | 3 | 44 | 1202.4 | 100% | 0 → 1(109) → 1(110) → 1(115) → 1(119) → 2(114) → 0 |

29 | 10:55:34 | 54 | 1 | 12 | 322 | 100% | 0 → 3(112) → 0 |

30 | 10:58:27 | 55 | 3 | 40 | 1140 | 90.91% | 0 → 1(113) → 1(117) → 0 |

31 | 11:07:05 | 58 | 3 | 41 | 1160 | 93.18% | 0 → 1(116) → 1(122) → 1(123) → 4(124) → 3(121) → 0 |

32 | 11:07:05 | 58 | 2 | 17 | 810 | 85.00% | 0 → 1(118) → 0 |

33 | 11:15:44 | 61 | 2 | 18 | 678 | 90.00% | 0 → 5(120) → 0 |

34 | 11:30:08 | 66 | 3 | 41 | 1693 | 93.18% | 0 → 5(125) → 4(134) → 1(127) → 1(131) → 0 |

35 | 11:35:53 | 68 | 3 | 40 | 420 | 90.91% | 0 → 3(126) → 3(136) → 0 |

36 | 11:38:46 | 69 | 3 | 44 | 1220 | 100% | 0 → 1(128) → 1(130) → 4(137) → 0 |

37 | 11:41:39 | 70 | 3 | 44 | 1220 | 100% | 0 → 4(129) → 4(139) → 4(141) → 1(132) → 1(135) → 1(138) → 0 |

38 | 11:47:25 | 72 | 3 | 42 | 844 | 95.45% | 0 → 3(133) → 2(143) → 4(142) → 0 |

39 | 12:01:49 | 77 | 1 | 7 | 427 | 58.33% | 0 → 4(140) → 0 |

40 | 12:10:27 | 80 | 2 | 14 | 594 | 70.00% | 0 → 5(144) → 0 |

41 | 12:24:51 | 85 | 3 | 44 | 1220 | 100% | 0 → 4(145) → 1(148) → 1(150) → 0 |

42 | 12:24:51 | 85 | 3 | 44 | 1052.8 | 100% | 0 → 5(146) → 2(151) → 3(152) → 0 |

43 | 12:27:44 | 86 | 3 | 44 | 1220 | 100% | 0 → 1(147) → 1(153) → 3(149) → 0 |

44 | 12:50:46 | 94 | 3 | 40 | 420 | 90.91% | 0 → 3(154) → 3(156) → 3(157) → 0 |

45 | 12:53:39 | 95 | 1 | 7 | 525 | 58.33% | 0 → 1(155) → 0 |

46 | 13:08:03 | 100 | 3 | 41 | 2193.2 | 93.18% | 0 → 6(158) → 4(161) → 2(159) → 0 |

47 | 13:19:34 | 104 | 3 | 40 | 820 | 90.91% | 0 → 3(160) → 3(163) → 0 |

48 | 13:28:13 | 107 | 2 | 15 | 570 | 75.00% | 0 → 4(162) → 0 |

49 | 13:39:44 | 111 | 3 | 44 | 2328.8 | 100% | 0 → 6(164) → 4(165) → 4(169) → 2(167) → 2(170) → 0 |

50 | 13:54:08 | 116 | 3 | 42 | 844 | 95.45% | 0 → 4(166) → 4(171) → 4(172) → 4(173) → 0 |

51 | 13:59:53 | 118 | 3 | 41 | 1160 | 93.18% | 0 → 1(174) → 1(178) → 4(179) → 2(168) → 3(177) → 0 |

52 | 14:14:17 | 123 | 3 | 44 | 1695.2 | 100% | 0 → 7(175) → 3(181) → 3(183) → 0 |

53 | 14:14:17 | 123 | 3 | 41 | 996 | 93.18% | 0 → 5(176) → 5(182) → 3(180) → 3(184) → 0 |

54 | 14:34:27 | 130 | 3 | 44 | 868 | 100% | 0 → 4(185) → 4(198) → 3(186) → 3(189) → 3(200) → 0 |

55 | 14:37:20 | 131 | 3 | 44 | 2029.6 | 100% | 0 → 6(187) → 5(196) → 2(195) → 3(188) → 0 |

56 | 14:37:20 | 131 | 3 | 44 | 868 | 100% | 0 → 4(190) → 4(191) → 4(193) → 0 |

57 | 14:40:13 | 132 | 2 | 19 | 870 | 95.00% | 0 → 1(192) → 4(194) → 4(199) → 0 |

58 | 14:48:51 | 135 | 1 | 8 | 324.8 | 66.67% | 0 → 2(197) → 0 |

Scheme No. | ${\mathit{T}}_{1}$ (min) | ${\mathit{T}}_{2}$ (min) | Total Number of Trips | Truck Type I | Truck Type II | Truck Type III | Average Loading Efficiency | AWT (min) | Total Cost (RMB) |
---|---|---|---|---|---|---|---|---|---|

1 | 9 | 1.0 | 75 | 12 | 23 | 40 | 90.78% | 7.28 | 71,646 |

2 | 9 | 1.25 | 72 | 12 | 18 | 42 | 89.16% | 7.25 | 71,023 |

3 | 9 | 1.5 | 71 | 11 | 18 | 42 | 89.65% | 7.43 | 70,544 |

4 | 10.5 | 1.0 | 69 | 7 | 20 | 42 | 91.67% | 8.52 | 70,568 |

5 | 10.5 | 1.25 | 67 | 6 | 18 | 43 | 92.15% | 8.6 | 70,070 |

6 | 10.5 | 1.5 | 68 | 6 | 20 | 42 | 92.24% | 8.85 | 70,247 |

7 | 12 | 1.0 | 67 | 12 | 11 | 44 | 97.37% | 8.97 | 69,047 |

8 | 12 | 1.25 | 67 | 12 | 11 | 44 | 93.95% | 8.97 | 68,149 |

9 | 12 | 1.5 | 64 | 10 | 8 | 46 | 92.41% | 9.03 | 67,683 |

10 | 14.5 | 1.0 | 64 | 6 | 13 | 45 | 92.16% | 9.8 | 67,610 |

11 | 14.5 | 1.25 | 61 | 4 | 11 | 46 | 93.79% | 11 | 67,445 |

12 | 14.5 | 1.5 | 61 | 4 | 11 | 46 | 93.79% | 11.02 | 67,385 |

13 | 16.0 | 1.0 | 60 | 5 | 8 | 47 | 94.47% | 11.6 | 67,130 |

14 | 16.0 | 1.25 | 59 | 4 | 8 | 47 | 94.80% | 11.75 | 66,251 |

15 | 16.0 | 1.5 | 60 | 5 | 8 | 47 | 94.00% | 12.25 | 66,035 |

16 | 17.5 | 1.0 | 60 | 5 | 8 | 47 | 94.05% | 13.05 | 66,984 |

17 | 17.5 | 1.25 | 59 | 3 | 9 | 47 | 94.03% | 13.12 | 67,551 |

18 | 17.5 | 1.5 | 58 | 3 | 7 | 48 | 94.24% | 12.97 | 67,630 |

19 | 19.0 | 1.0 | 61 | 6 | 8 | 47 | 92.45% | 13.58 | 66,856 |

20 | 19.0 | 1.25 | 62 | 6 | 10 | 46 | 92.73% | 13.93 | 67,008 |

21 | 19.0 | 1.5 | 58 | 4 | 6 | 48 | 93.58% | 14.3 | 68,127 |

22 | 20.5 | 1.0 | 59 | 5 | 6 | 48 | 92.43% | 15 | 66,201 |

23 | 20.5 | 1.25 | 58 | 4 | 6 | 48 | 94.59% | 14.6 | 65,195 |

24 | 20.5 | 1.5 | 57 | 3 | 6 | 48 | 95.79% | 14.8 | 66,017 |

25 | 22.0 | 1.25 | 57 | 3 | 6 | 48 | 95.06% | 15.82 | 67,101 |

Serial No. | ${\mathit{T}}_{0}$ (min) | Total Number of Trips | Truck Type I | Truck Type II | Truck Type III | Average Loading Efficiency | AWT (min) | Total Cost (RMB) |
---|---|---|---|---|---|---|---|---|

1 | 2 | 57 | 3 | 6 | 48 | 96.08% | 13.8 | 66,470 |

2 | 2.5 | 58 | 4 | 6 | 48 | 94.21% | 14.18 | 67,310 |

3 | 3 | 58 | 4 | 6 | 48 | 94.59% | 14.6 | 65,195 |

4 | 3.5 | 58 | 4 | 6 | 48 | 94.63% | 14.77 | 66,193 |

5 | 4 | 57 | 3 | 6 | 48 | 95.15% | 15.47 | 67,837 |

6 | 4.5 | 57 | 2 | 7 | 48 | 95.02% | 15.13 | 66,324 |

Scenario | Total Number of Trips | Truck Type I | Truck Type II | Truck Type III | Average Loading Efficiency | AWT (min) | Total Cost (RMB) |
---|---|---|---|---|---|---|---|

No consolidation | 200 | 109 | 91 | 0 | 66.7% | 0 | 106,443.4 |

No time windows | 160 | 73 | 78 | 9 | 72.25% | 1.48 | 98,770 |

Single time window | 60 | 5 | 8 | 47 | 93.35% | 13.86 | 67,764 |

Optimal solution | 58 | 4 | 6 | 48 | 94.59% | 14.60 | 65,195 |

Waybill No. | Truck Type | Cargo Volume (pcs) | Cost (RMB) | Loading Efficiency | Waybill No. | Truck Type | Cargo Volume (pcs) | Cost (RMB) | Loading Efficiency |
---|---|---|---|---|---|---|---|---|---|

1 | 2 | 20 | 720 | 100.00% | 14 | 3 | 41 | 422 | 93.18% |

2 | 3 | 43 | 1028 | 97.73% | 15 | 2 | 17 | 351 | 85.00% |

3 | 1 | 9 | 311.5 | 75.00% | 16 | 2 | 15 | 1074 | 75.00% |

4 | 1 | 1 | 283.5 | 8.33% | 17 | 2 | 16 | 348 | 80.00% |

5 | 2 | 14 | 342 | 70.00% | 18 | 2 | 19 | 1314.6 | 95.00% |

6 | 3 | 43 | 1036.6 | 97.73% | 19 | 2 | 20 | 396 | 100.00% |

7 | 1 | 2 | 287 | 16.67% | 20 | 3 | 44 | 1044 | 100.00% |

8 | 2 | 15 | 615 | 75.00% | 21 | 3 | 42 | 424 | 95.45% |

9 | 3 | 40 | 420 | 90.91% | 22 | 2 | 19 | 357 | 95.00% |

10 | 2 | 15 | 345 | 75.00% | 23 | 1 | 9 | 821.8 | 75.00% |

11 | 2 | 14 | 367.2 | 70.00% | 24 | 2 | 19 | 761.7 | 95.00% |

12 | 2 | 14 | 594 | 70.00% | 25 | 1 | 8 | 324.8 | 66.67% |

13 | 3 | 44 | 1052.8 | 100.00% |

Waybill No. | Truck Type | Cargo Volume (pcs) | Cost (RMB) | Loading Efficiency | Waybill No. | Truck Type | Cargo Volume (pcs) | Cost (RMB) | Loading Efficiency |
---|---|---|---|---|---|---|---|---|---|

1 | 3 | 44 | 868 | 100.00% | 26 | 3 | 41 | 1160 | 93.18% |

2 | 3 | 44 | 1220 | 100.00% | 27 | 3 | 44 | 1220 | 100.00% |

3 | 3 | 44 | 1915.2 | 100.00% | 28 | 1 | 9 | 469 | 75.00% |

4 | 3 | 42 | 1583.2 | 95.45% | 29 | 3 | 44 | 1220 | 100.00% |

5 | 3 | 44 | 1220 | 100.00% | 30 | 3 | 44 | 1220 | 100.00% |

6 | 3 | 44 | 868 | 100.00% | 31 | 3 | 44 | 1220 | 100.00% |

7 | 3 | 40 | 1524 | 90.91% | 32 | 3 | 44 | 1220 | 100.00% |

8 | 3 | 43 | 856 | 97.73% | 33 | 2 | 19 | 870 | 95.00% |

9 | 3 | 44 | 1220 | 100.00% | 34 | 1 | 7 | 427 | 58.33% |

10 | 3 | 44 | 1220 | 100.00% | 35 | 3 | 44 | 1220 | 100.00% |

11 | 3 | 44 | 1220 | 100.00% | 36 | 2 | 16 | 780 | 80.00% |

12 | 3 | 44 | 1220 | 100.00% | 37 | 1 | 10 | 630 | 83.33% |

13 | 3 | 44 | 868 | 100.00% | 38 | 1 | 7 | 525 | 58.33% |

14 | 3 | 44 | 1220 | 100.00% | 39 | 3 | 40 | 820 | 90.91% |

15 | 3 | 44 | 1220 | 100.00% | 40 | 1 | 10 | 490 | 83.33% |

16 | 3 | 44 | 1695.2 | 100.00% | 41 | 2 | 15 | 570 | 75.00% |

17 | 3 | 44 | 1220 | 100.00% | 42 | 3 | 41 | 832 | 93.18% |

18 | 3 | 44 | 868 | 100.00% | 43 | 3 | 42 | 1633.6 | 95.45% |

19 | 3 | 44 | 1220 | 100.00% | 44 | 1 | 12 | 532 | 100.00% |

20 | 3 | 44 | 1695.2 | 100.00% | 45 | 1 | 2 | 350 | 16.67% |

21 | 3 | 44 | 1220 | 100.00% | 46 | 3 | 44 | 1220 | 100.00% |

22 | 3 | 44 | 1220 | 100.00% | 47 | 2 | 20 | 660 | 100.00% |

23 | 3 | 41 | 1160 | 93.18% | 48 | 2 | 15 | 570 | 75.00% |

24 | 2 | 19 | 870 | 95.00% | 49 | 1 | 2 | 322 | 16.67% |

25 | 1 | 9 | 469 | 75.00% | 50 | 2 | 13 | 534 | 65.00% |

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## Share and Cite

**MDPI and ACS Style**

Tang, W.; Chen, X.; Lang, M.; Li, S.; Liu, Y.; Li, W.
Optimization of Truck–Cargo Online Matching for the Less-Than-Truck-Load Logistics Hub under Real-Time Demand. *Mathematics* **2024**, *12*, 755.
https://doi.org/10.3390/math12050755

**AMA Style**

Tang W, Chen X, Lang M, Li S, Liu Y, Li W.
Optimization of Truck–Cargo Online Matching for the Less-Than-Truck-Load Logistics Hub under Real-Time Demand. *Mathematics*. 2024; 12(5):755.
https://doi.org/10.3390/math12050755

**Chicago/Turabian Style**

Tang, Weilin, Xinghan Chen, Maoxiang Lang, Shiqi Li, Yuying Liu, and Wenyu Li.
2024. "Optimization of Truck–Cargo Online Matching for the Less-Than-Truck-Load Logistics Hub under Real-Time Demand" *Mathematics* 12, no. 5: 755.
https://doi.org/10.3390/math12050755