# Sustainable Logistics Network Design for Delivery Operations with Time Horizons in B2B E-Commerce Platform

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## Abstract

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## 1. Introduction

- How to find the optimized delivery routes in a sustainable logistics network that help minimize the total delivery time horizon of an order in an e-commerce platform?
- How to mitigate the driver safety concern in the logistics system?
- How to minimize the order packaging and handling times to achieve the lesser delivery time horizon?

## 2. Literature Review

## 3. Problem Description

_{k}, R

_{l}) is shown in Figure 1, where S

_{k}is the set of supplier nodes, where k (k = 1, 2, …, K) is the indexing for suppliers, R

_{l}is the set of retailer nodes, where l (l = 1, 2, …, L) is the indexing of retailers, and O

_{n}is the set of orders placed by the retailers, where n (n = 1, 2, …, N) is the indexing of the orders. Avail

_{nk}is the availability of orders at the supplier node, Dem

_{nl}is the demand at retailer nodes, and x

_{nkl}is the binary decision variable, which helps in the selection of best possible routes with an availability constraint. Table 1 describes the terminologies (sets, parameters, decision variables) used in mathematical model.

#### OBObjective Function

_{k}+ (order packaging time)

_{k}+ (order handling time)

_{k}+ (order traveling time)

_{k}→

_{l}+ (vehicle maintenance time)

_{k}→

_{l}+ (order processing time)

_{l}}

## 4. Solution Methodology

#### Genetic Algorithm

## 5. Numerical Example

#### 5.1. Input Data for 1st Case Scenario

#### 5.2. Output

## 6. Results and Discussion

#### 6.1. Computational Experiments

#### 6.2. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Huang, Y.H.; Blazquez, C.A.; Huang, S.H.; Paredes-Belmar, G.; Latorre-Nuñez, G. Solving the Feeder Vehicle Routing Problem using ant colony optimization. Comput. Ind. Eng.
**2019**, 127, 520–535. [Google Scholar] [CrossRef] - Li, J.; Wang, D.; Zhang, J. Heterogeneous fixed fleet vehicle routing problem based on fuel and carbon emissions. J. Clean. Prod.
**2018**, 201, 896–908. [Google Scholar] [CrossRef] - Rincon-Garcia, N.; Waterson, B.; Cherrett, T.J.; Salazar-Arrieta, F. A metaheuristic for the time-dependent vehicle routing problem considering driving hours regulations—An application in city logistics. Transp. Res. Part A Policy Pract.
**2020**, 137, 429–446. [Google Scholar] [CrossRef] [Green Version] - Ali, A.H.; Melkonyan, A.; Noche, B.; Gruchmann, T. Developing a Sustainable Logistics Service Quality Scale for Logistics Service Providers in Egypt. Logistics
**2021**, 5, 21. [Google Scholar] [CrossRef] - Chen, H.K.; Chou, H.W.; Hsu, C.Y. The linehaul-feeder vehicle routing problem with virtual depots and time windows. Math. Probl. Eng.
**2011**, 2011, 759418. [Google Scholar] [CrossRef] [Green Version] - Chen, T.L.; Cheng, C.Y.; Chen, Y.Y.; Chan, L.K. An efficient hybrid algorithm for integrated order batching, sequencing and routing problem. Int. J. Prod. Econ.
**2015**, 159, 158–167. [Google Scholar] [CrossRef] - Subramanyam, A.; Wang, A.; Gounaris, C.E. A scenario decomposition algorithm for strategic time window assignment vehicle routing problems. Transp. Res. Part B Methodol.
**2018**, 117, 296–317. [Google Scholar] [CrossRef] [Green Version] - Prajapati, D.; Zhou, F.; Cheikhrouhou, N.; Pratap, S. Minimizes the Time Window for Delivery of Orders in B2B E-commerce. In Proceedings of the 5th International Conference on Industrial Engineering (ICIE), Sochi, Russia, 18–19 November 2019; pp. 1–6. [Google Scholar]
- Molina, J.C.; Salmeron, J.L.; Eguia, I.; Racero, J. The heterogeneous vehicle routing problem with time windows and a limited number of resources. Eng. Appl. Artif. Intell.
**2020**, 94, 103745. [Google Scholar] [CrossRef] - Muñoz-Villamizar, A.; Solano-Charris, E.L.; Reyes-Rubiano, L.; Faulin, J. Measuring Disruptions in Last-Mile Delivery Operations. Logistics
**2021**, 5, 17. [Google Scholar] [CrossRef] - Asefi, H.; Shahparvari, S.; Chhetri, P.; Lim, S. Variable fleet size and mix VRP with fleet heterogeneity in Integrated Solid Waste Management. J. Clean. Prod.
**2019**, 230, 1376–1395. [Google Scholar] [CrossRef] - Su, Y.; Jin, S.; Zhang, X.; Shen, W.; Eden, M.R.; Ren, J. Stakeholder-oriented multi-objective process optimization based on an improved genetic algorithm. Comput. Chem. Eng.
**2020**, 132, 106618. [Google Scholar] [CrossRef] - Attari, M.Y.N.; Torkayesh, A.E.; Malmir, B.; Jami, E.N. Robust possibilistic programming for joint order batching and picker routing problem in warehouse management. Int. J. Prod. Res.
**2021**, 59, 4434–4452. [Google Scholar] [CrossRef] - Gu, W.; Cattaruzza, D.; Ogier, M.; Semet, F. Adaptive large neighborhood search for the commodity constrained split delivery VRP. Comput. Oper. Res.
**2019**, 112, 104761. [Google Scholar] [CrossRef] [Green Version] - Sabar, N.R.; Bhaskar, A.; Chung, E.; Turky, A.; Song, A. An Adaptive Memetic Approach for Heterogeneous Vehicle Routing Problems with two-dimensional loading constraints. Swarm Evol. Comput.
**2020**, 58, 100730. [Google Scholar] [CrossRef] - Araee, E.; Manavizadeh, N.; Bosjin, S.A. Designing a multi-objective model for a hazardous waste routing problem considering flexibility of routes and social effects. J. Ind. Prod. Eng.
**2020**, 37, 33–45. [Google Scholar] [CrossRef] - Ancele, Y.; Hà, M.H.; Lersteau, C.; Matellini, D.B.; Nguyen, T.T. Toward a more flexible VRP with pickup and delivery allowing consolidations. Transp. Res. Part C Emerg. Technol.
**2021**, 128, 103077. [Google Scholar] [CrossRef] - Tirkolaee, E.B.; Goli, A.; Pahlevan, M.; Kordestanizadeh, R.M. A robust bi-objective multi-trip periodic capacitated arc routing problem for urban waste collection using a multi-objective invasive weed optimization. Waste Manag. Res.
**2019**, 37, 1089–1101. [Google Scholar] [CrossRef] - Lu, J.; Chen, Y.; Hao, J.K.; He, R. The Time-dependent Electric Vehicle Routing Problem: Model and solution. Expert Syst. Appl.
**2020**, 161, 113593. [Google Scholar] [CrossRef] - Fachini, R.F.; Armentano, V.A. Logic-based Benders decomposition for the heterogeneous fixed fleet vehicle routing problem with time windows. Comput. Ind. Eng.
**2020**, 148, 106641. [Google Scholar] [CrossRef] - Keskin, M.; Çatay, B.; Laporte, G. A simulation-based heuristic for the electric vehicle routing problem with time windows and stochastic waiting times at recharging stations. Comput. Oper. Res.
**2021**, 125, 105060. [Google Scholar] [CrossRef] - Neves-Moreira, F.; Amorim-Lopes, M.; Amorim, P. The multi-period vehicle routing problem with refueling decisions: Traveling further to decrease fuel cost? Transp. Res. Part E Logist. Transp. Rev.
**2020**, 133, 101817. [Google Scholar] [CrossRef] - Nejad Attari, M.Y.; Torkayesh, A.E.; Jami, E.N. Ant Colony Optimization for Multiple Pickup and Multiple Delivery Vehicle Routing Problem with Time Window and Heterogeneous Fleets. Logistics
**2021**, 59, 28. [Google Scholar] [CrossRef] - Prajapati, D.; Zhou, F.; Zhang, M.; Chelladurai, H.; Pratap, S. Sustainable logistics network design for multi-products delivery operations in B2B e-commerce platform. Sādhanā
**2021**, 46, 100. [Google Scholar] [CrossRef] - Cheng, C.Y.; Chen, Y.Y.; Chen, T.L.; Yoo, J.J. Using a hybrid approach based on the particle swarm optimization and ant colony optimization to solve a joint order batching and picker routing problem. Int. J. Prod. Econ.
**2015**, 170, 805–814. [Google Scholar] [CrossRef] - Dwivedi, A.; Jha, A.; Prajapati, D.; Sreenu, N.; Pratap, S. Meta-heuristic algorithms for solving the sustainable agro-food grain supply chain network design problem. Mod. Supply Chain Res. Appl.
**2020**. [Google Scholar] [CrossRef] - Gutierrez, A.; Dieulle, L.; Labadie, N.; Velasco, N. A multi-population algorithm to solve the VRP with stochastic service and travel times. Comput. Ind. Eng.
**2018**, 125, 144–156. [Google Scholar] [CrossRef] - Wu, W.; Zhou, W.; Lin, Y.; Xie, Y.; Jin, W. A hybrid metaheuristic algorithm for location inventory routing problem with time windows and fuel consumption. Expert Syst. Appl.
**2021**, 166, 114034. [Google Scholar] [CrossRef] - Tirkolaee, E.B.; Hosseinabadi, A.A.R.; Soltani, M.; Sangaiah, A.K.; Wang, J. A Hybrid genetic algorithm for multi-trip green capacitated Arc routing problem in the scope of urban services. Sustainability
**2018**, 10, 1366. [Google Scholar] [CrossRef] [Green Version] - Tirkolaee, E.B.; Mahdavi, I.; Esfahani, M.M.S.; Weber, G.W. A hybrid augmented ant colony optimization for the multi-trip capacitated arc routing problem under fuzzy demands for urban solid waste management. Waste Manag. Res.
**2020**, 38, 156–172. [Google Scholar] [CrossRef] - Hamdia, K.M.; Zhuang, X.; Rabczuk, T. An efficient optimization approach for designing machine learning models based on genetic algorithm. Neural Comput. Appl.
**2021**, 33, 1923–1933. [Google Scholar] [CrossRef] - Goodarzian, F.; Kumar, V.; Ghasemi, P. A set of efficient heuristics and meta-heuristics to solve a multi-objective pharmaceutical supply chain network. Comput. Ind. Eng.
**2021**, 158, 107389. [Google Scholar] [CrossRef] - Goodarzian, F.; Kumar, V.; Abraham, A. Hybrid. Meta-Heuristic Algorithms for a Supply Chain Network Considering Different Carbon Emission Regulations Using Big Data Characteristics; Springer: Berlin/Heidelberg, Germany, 2021. [Google Scholar] [CrossRef]
- Daultani, Y.; Cheikhrouhou, N.; Pratap, S.; Prajapati, D. Designing Forward and Reverse Supply Chain Network for Refurbished Products. In Proceedings of the 9th International Conference on Operations and Supply Chain Management, Ho Chi Minh City, Vietnam, 15–18 December 2019; pp. 1–7. [Google Scholar]
- Zhang, M.; Pratap, S.; Zhao, Z.; Prajapati, D.; Huang, G.Q. Forward and reverse logistics vehicle routing problems with time horizons in B2C e-commerce logistics. Int. J. Prod. Res.
**2020**, 1–20. [Google Scholar] [CrossRef] - Prajapati, D.; Harish, A.R.; Daultani, Y.; Singh, H.; Pratap, S. A Clustering Based Routing Heuristic for Last-Mile Logistics in Fresh Food E-Commerce. Glob. Bus. Rev.
**2020**. [Google Scholar] [CrossRef]

Sets and Indices | |
---|---|

${S}_{k}$ | Set of suppliers (k = 1, 2, …, K) |

${R}_{l}$ | Set of local distribution centers (l = 1, 2, …, L) |

${O}_{n}$ | Set of orders (n = 1, 2, …, N) |

Parameters | |

$Avai{l}_{nk}$ | Availability of the order n at supplier k |

$De{m}_{nl}$ | Demand of order n at delivery point l |

$dis{t}_{kl}$ | Time required for maintenance |

Dependent variables | |

${t}^{proc}$ | Total order processing time |

${t}^{travel}$ | Total order packaging time |

${t}^{hand1}$ | Total order handling time at node k |

${t}^{travel}$ | Total traveling time in between node k to node l |

${t}^{ma\mathrm{int}}$ | Total vehicle maintenance time |

${t}^{hand2}$ | Total order handling time at node l |

${v}_{nkl}$ | Quantity moving from supplier point to destination point. |

Decision variables | |

${\tau}_{nk}^{proc}$ | Order processing time per unit order at node k |

${\tau}_{nk}^{packaging}$ | Order packaging time per unit demand at node k |

${\tau}_{nk}^{hand1}$ | Order handling time per unit demand at node k |

${\tau}_{nkl}^{ma\mathrm{int}}$ | Vehicle maintenance time when vehicle moving from node k to node l with order n |

${\tau}_{nk}^{hand2}$ | Order handling time per unit demand at node l |

${s}_{nkl}$ | Optimum speed of the vehicle when vehicle moving from node k to node l with order n |

${y}_{nkl}$ | Binary decision variable, if s_{nkl} > 70 then 1, otherwise, 0 |

${x}_{nkl}$ | Binary decision variable, if order n pickup from node k and deliver at node l, then 1, otherwise, 0 |

Availability | S1 | S2 |
---|---|---|

1000 | 5000 |

Demand | R1 | R2 | R3 |
---|---|---|---|

10 | 20 | 10 |

Dist. | R1 | R2 | R3 |
---|---|---|---|

S1 | 100 | 110 | 120 |

S2 | 150 | 155 | 121 |

Instances | Number of Suppliers | Number of Retailers | Number of Constraints | Number of Variables | Branch-and-Bound (in LINGO 18) | Genetic Algorithm | ||
---|---|---|---|---|---|---|---|---|

Obj Func. (hrs.) | Comp. Time (sec.) | Obj Func. (hrs.) | Comp. Time (sec.) | |||||

1. | 2 | 3 | 19 | 123 | 37.129 | 0.30 | 42.019 | 0.21 |

2. | 3 | 5 | 32 | 451 | 63.305 | 2.99 | 72.121 | 2.01 |

3. | 4 | 8 | 55 | 1446 | 191.146 | 84.99 | 228.354 | 64.29 |

4. | 5 | 12 | 91 | 3930 | 264.044 | 1614.24 | 297.547 | 104.94 |

5. | 6 | 15 | 127 | 7251 | 366.353 | 8769.44 | 399.024 | 106.57 |

6 | 6 | 18 | 151 | 10,374 | 416.122 | 26,231.56 | 432.985 | 131.48 |

7 | 8 | 25 | 217 | 15,523 | - | - | 587.394 | 135.61 |

8 | 10 | 30 | 339 | 20,145 | - | - | 629.380 | 149.34 |

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**MDPI and ACS Style**

Prajapati, D.; Kumar, M.M.; Pratap, S.; Chelladurai, H.; Zuhair, M.
Sustainable Logistics Network Design for Delivery Operations with Time Horizons in B2B E-Commerce Platform. *Logistics* **2021**, *5*, 61.
https://doi.org/10.3390/logistics5030061

**AMA Style**

Prajapati D, Kumar MM, Pratap S, Chelladurai H, Zuhair M.
Sustainable Logistics Network Design for Delivery Operations with Time Horizons in B2B E-Commerce Platform. *Logistics*. 2021; 5(3):61.
https://doi.org/10.3390/logistics5030061

**Chicago/Turabian Style**

Prajapati, Dhirendra, M. Manoj Kumar, Saurabh Pratap, H. Chelladurai, and Mohd Zuhair.
2021. "Sustainable Logistics Network Design for Delivery Operations with Time Horizons in B2B E-Commerce Platform" *Logistics* 5, no. 3: 61.
https://doi.org/10.3390/logistics5030061