# An Integrated Method for Locating Logistic Centers in a Rural Area

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Rural Logistics

#### 2.2. Facility Location Problems

- (1)
- PMP is a “MinSum” problem, which aims to select P facilities from a given set to serve all demand points while minimizing the total weighted distance from demand points to their nearest facilities [26]. PMP is proven to be a NP-hard problem [27]. Both heuristic and optimal algorithms are provided [28]. PMP is still a research hotspot, with various extensions studied by modern researchers, including capacitated PMP [29], simplified PMP [30], and uncertain PMP [31].
- (2)
- (3)
- CP, including set covering problem (SCP) and maximal covering problem (MCP), introduces the constraint of service radius, which means a facility cannot serve a demand point beyond a given distance. First raised by Toregas, SCP is a “Min” problem, aiming to serve all demand points with as few facilities as possible [33]. MCP is a “Max” problem, aiming to serve as many demand points as possible with a given number of facilities, and was first proposed by Church and ReVelle [34]. The problem is further discussed by Daskin, Hogan, Berman, Krass, and many other researchers [35,36,37].

- (4)
- In addition to the above methods, a number of other locating methods have emerged in recent studies, considering facility capacity, road capacity, dynamic decision process, competitive situation, and many other factors. Kulakova described a locating model based on geographic coordinates [41]. Muravev used the Dematel–Marica method and applied the multicriteria decision model to locate China Railway Express International Logistics Centers [42]. Stienen developed a single deterministic optimization model for locating disaster relief warehouses [43]. Rabe combined the system dynamics simulation model with the multicycle capacity-limited facility locating problem to locate automated parcel lockers [44].

#### 2.3. Literature Summary

## 3. Study Area and Data

## 4. Methods

#### 4.1. Demand Prediction

#### 4.2. Demand Allocation

- (1)
- Demand allocation from Lhasa to each county. Specifically, allocation of sending packages is based on gross regional product, as manufacturers and commercial enterprises are main express package senders. Allocation of receiving packages is based on population, as local residents constitute the main express parcel recipient. In Lhasa, Chengguan district has a relatively high proportion of urban residents, and is assigned 1.25 times the population weights of other counties [45]. Allocation results in this stage are shown in Table 2.
- (2)
- Demand allocation from counties to towns. In this step, demand allocation for both sending and receiving packages are based on population, number of industrial enterprises, and number of supermarkets in each town. Specifically, each industrial enterprise or supermarket is roughly considered to have 100 times the logistic demand of a resident. An industrial enterprise above designated size is considered to have 500 times that. These proportions are decided after consulting local logistic practitioners. Take Qushui county as an example. Allocation results are shown in Table 3, while allocation results of all 64 towns in Lhasa are visualized in Figure 4.

#### 4.3. Maximal Covering Model for Locating Logistic Centers

#### 4.3.1. Maximal Covering Model

- ${W}_{i}$
- Importance of demand point $i$ to target function $Z.$
- ${d}_{ij}$
- Distance from demand point $i$ to logistic center $j.$
- ${D}_{i}$
- Service radius, i.e., maximum service distance accepted by demand point $i.$
- $K$
- Number of logistic centers to be located.

- $I$
- Set of demand points.
- $J$
- Set of candidate logistic centers.
- $N\left(i\right)$
- Set of logistic centers that can cover demand point $i$, $N\left(i\right)=\left\{j|{d}_{ij}\le {D}_{i}\right\}$.

#### 4.3.2. Marginal Efficiency Analysis on Service Radius and Number of Logistic Centers

^{2}in Caina town). The number of sending and receiving packages in the neighborhood area of each logistic center is then calculated accordingly.

#### 4.4. Revenue Evaluation on the Selected Logistic Centers

- (1)
- Regular income

- (2)
- Extra income

- (3)
- One-time initial investment cost

- (4)
- Operating cost

## 5. Discussion

#### 5.1. Adopting Joint Distribution Mode

#### 5.2. Making Full Use of Local Transportation Resources

#### 5.3. Pricing Strategies for Long-Distance Logistic Service and Government Supervision

#### 5.4. Model Comparison

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- George, B.; Henry, G.; John, R. Rural Transport: Improving Its Contribution to Growth and Poverty Reduction in Sub-Saharan Africa; Sub-Saharan Africa Transport Policy Program (SSATP) Working Paper no. 93; World Bank: Washington, DC, USA, 2012; Available online: https://openknowledge.worldbank.org/handle/10986/17807 (accessed on 1 May 2022).
- Paul, S.; Simon, E.; John, H.; Anna, T. Improving Rural Mobility: Options for Developing Motorized and Nonmotorized Transport in Rural Areas; World Bank Technical Paper No. 525; World Bank: Washington, DC, USA, 2002; Available online: https://openknowledge.worldbank.org/handle/10986/15230 (accessed on 1 May 2022).
- Peter, R.; Shyam, K.C.; Cordula, R. Rural Access Index: A Key Development Indicator; Transport Paper Series; No. TP-10; World Bank: Washington, DC, USA, 2006; Available online: https://openknowledge.worldbank.org/handle/10986/17414 (accessed on 1 May 2022).
- American Public Transportation Association. Rural Communities Expanding Horizons: The Benefits of Public Transportation; American Public Transportation Association: Washington, DC, USA, 2012. [Google Scholar]
- Enoch, M.P.; Cross, R.; Potter, N.; Davidson, C.; Taylor, S.; Brown, R.; Huang, H.; Parsons, J.; Tucker, S.; Wynne, E.; et al. Future local passenger transport system scenarios and implications for policy and practice. Transp. Policy
**2020**, 90, 52–67. [Google Scholar] [CrossRef] - Donnges, C. Rural Transport and Local Government Units: How to Improve Rural Transport for the Rural Poor; Transport and Communications Bulletin for Asia and the Pacific, No.71; Economic and Social Commission for Asia and the Pacific: Bangkok, Thailand, 2001. [Google Scholar]
- Vitale Brovarone, E.; Cotella, G. Improving rural accessibility: A multilayer approach. Sustainability
**2022**, 12, 2876. [Google Scholar] [CrossRef] [Green Version] - Fu, H.; Li, H. Research on the Optimization of Rural Logistics Development in Henan Province. Int. J. Soc. Sci. Educ. Res.
**2020**, 3, 181–185. [Google Scholar] - Jin, E.T. Research on Innovation of Agricultural Products Circulation System under Digital Rural Strategy; Nanchang University: Nanchang, China, 2020. [Google Scholar]
- Wang, M.; Chen, X. Analysis of influencing factors of urban and rural logistics distribution in Hainan province based on AHP. China Tequ Econ.
**2020**, 11, 81–86. [Google Scholar] - Li, X.; Ramshani, M.; Huang, Y. Cooperative maximal covering models for humanitarian relief chain management. Comput. Ind. Eng.
**2018**, 119, 301–308. [Google Scholar] [CrossRef] - Song, G.; Zhao, Z.; Tian, C.; Yi, Y.; Song, T. Research on Joint Distribution of Rural Logistics. In IOP Conference Series: Materials Science and Engineering; IOP Publishing: Bristol, UK, 2019; Volume 631, p. 052003. [Google Scholar] [CrossRef]
- Xie, L.; Zhou, L. Regional differentiation of service quality of rural E-commerce logistics terminal distribution: A case study of four districts and counties in Chongqing. Logist. Technol.
**2020**, 39, 73–77. [Google Scholar] - Ren, X.; Shi, X. Research on Milk Run Model of Rural Logistics Based on “Internet +”; International Informatization and Engineering Associations: Qinhuangdao, China, 2019. [Google Scholar]
- Jiang, L.J. Research on LRP Optimization of Urban and Rural Joint Distribution Network Based on Two-Way Logistics; Beijing Jiaotong University: Beijing, China, 2019. [Google Scholar]
- Liu, Y.H. Study on the Join Distribution Mode Design and Vehicle Route Planning of Urban Trade Logistics; Chongqing Technology and Business University: Chongqing, China, 2020. [Google Scholar]
- Xiahou, J. Study on Site Selection and Distribution Optimization of Joint Distribution Network at the End of E-Commerce Logistics; Beijing Jiaotong University: Beijing, China, 2020. [Google Scholar]
- Wang, Y.; Zhou, X. Optimization of multi-center joint distribution alliance based on vehicle sharing. Comput. Integr. Manuf. Syst.
**2021**, 27, 1820–1832. [Google Scholar] - Chen, X. Study on Location Selection of Urban Distribution Center Using Multi-Level Inventory Management; Changsha University of Science and Technology: Changsha, China, 2007. [Google Scholar]
- Özcan, O.; Reeves, K.A. The Impact of Sustainability-Focused Strategies on Sourcing Decisions. In Green Finance and Sustainability: Environmentally-Aware Business Models and Technologies 2011; IGI Global: Hershey, PA, USA, 2011; pp. 358–386. [Google Scholar] [CrossRef]
- Berman, O.; Drezner, Z. The multiple server location problem. J. Oper. Res. Soc.
**2007**, 58, 91–99. [Google Scholar] [CrossRef] - Church, R.L.; Murray, A.T. Business Site Selection, location Analysis and GIS; John Wiley & Sons Incorporated: Hoboken, NJ, USA, 2009. [Google Scholar]
- Farahani, R.Z.; Hekmatfar, M. (Eds.) Facility Location: Concepts, Models, Algorithms and Case Studies; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2009. [Google Scholar]
- Yu, R. The Capacitated Reliable Fixed-Charge Location Problem: Model and Algorithm. Dissertations Thesis, Lehigh University, Bethlehem, PA, USA, 2015. [Google Scholar]
- Weber, A. Theory of the Location of Industries; University of Chicago Press: Chicago, IL, USA, 1957. [Google Scholar]
- Hakimi, S.L. P-median theorems for competitive location. Ann. Oper. Res.
**1986**, 6, 75–98. [Google Scholar] [CrossRef] - Garey, M.R.; Johnson, D.S. Computers and Intractability: A Guide to NP-Completeness; W. H. Freeman: New York, NY, USA, 1979. [Google Scholar]
- Rosing, K.E.; Hillsman, E.L.; Rosing-Vogelaar, H. A note comparing optimal and heuristic solutions to the p-median problem. Geogr. Anal.
**2010**, 11, 86–89. [Google Scholar] [CrossRef] - Lorena, L.A.N.; Senne, E.L.F. Local search heuristics for capacitated p-median problems. Netw. Spat. Econ.
**2003**, 3, 407–441. [Google Scholar] [CrossRef] - Church, R.L. Cobra: A new formulation of the classic p-median location problem. Ann. Oper. Res.
**2003**, 122, 103–120. [Google Scholar] [CrossRef] - Berman, O.; Drezner, Z. The p-median problem under uncertainty. Eur. J. Oper. Res.
**2008**, 189, 19–30. [Google Scholar] [CrossRef] - Levin, Y.; Ben-Israel, A. A Heuristic Method for Multifacility Location Problems. Comput. Oper. Res.
**2004**, 31, 257–272. [Google Scholar] [CrossRef] [Green Version] - Toregas, C.; Revelle, C.; Bergman, L. The location of emergency services. Oper. Res.
**1971**, 19, 93–95. [Google Scholar] [CrossRef] - Church, R.L.; Revelle, C. The Maximal Covering Location Problem. Pap. Reg. Sci. Assoc.
**1974**, 32, 101–118. [Google Scholar] [CrossRef] - Daskin, M.S. A maximum expected covering location model: Formulation, properties and heuristic solution. Transp. Sci.
**1983**, 17, 48–70. [Google Scholar] [CrossRef] [Green Version] - ReVelle, C.; Hogan, K. The maximum availability location problem. Transp. Sci.
**1989**, 23, 192–200. [Google Scholar] [CrossRef] - Berman, O.; Krass, D. The generalized maximal covering location problem. Comput. Oper. Res.
**2002**, 29, 563–581. [Google Scholar] [CrossRef] - Tian, S.; Hua, G.; Cheng, T.C.E. Optimal Deployment of Charging Piles for Electric Vehicles Under the Indirect Network Effects. Asia-Pac. J. Oper. Res.
**2019**, 36, 1950007. [Google Scholar] [CrossRef] - He, S.; Kuo, Y.H.; Wu, D. Incorporating institutional and spatial factors in the selection of the optimal locations of public electric vehicle charging facilities: A case study of Beijing, China. Transp. Res. Part C
**2016**, 67, 131–148. [Google Scholar] [CrossRef] - Xue, Y.; Wen, Z.; Ji, X.; Bressers, H.T.A.; Zhang, C. Location optimization of urban mining facilities with maximal covering model in GIS: A case of China. J. Ind. Ecol.
**2017**, 21, 913–923. [Google Scholar] [CrossRef] - Kulakova, I.M.; Lebedeva, O.A.; Poltavskaya, J.O. Solving the problem of determining the optimal location of the logistics center, taking into account cost minimization. In IOP Conference Series: Materials Science and Engineering; IOP Publishing: Bristol, UK, 2020; Volume 971, p. 052009. [Google Scholar]
- Muravev, D.; Hu, H.; Zhou, H.; Pamucar, D. Location optimization of CR express international logistics centers. Symmetry
**2020**, 12, 143. [Google Scholar] [CrossRef] [Green Version] - Stienen, V.F.; Wagenaar, J.C.; den Hertog, D.; Fleuren, H.A. Optimal depot locations for humanitarian logistics service providers using robust optimization. Omega
**2021**, 104, 102494. [Google Scholar] [CrossRef] - Rabe, M.; Gonzalez-Feliu, J.; Chicaiza-Vaca, J.; Tordecilla, R.D. Simulation-Optimization Approach for Multi-Period Facility Location Problems with Forecasted and Random Demands in a Last-Mile Logistics Application. Algorithms
**2021**, 14, 41. [Google Scholar] [CrossRef] - Lasa Bureau of Statistics. Lhasa Statistical Yearbook 2016–2020. Available online: www.lasa.gov.cn (accessed on 3 May 2022).
- Lasa Municipal Postal Administration. Monthly Operation Report on Postal Industry in Lhasa (2016–2020). Available online: Xz.spb.gov.cn/xzyzglj/c104416/indexshi.shtml (accessed on 3 May 2022).
- Koehler, A.B.; Snyder, R.D.; Ord, J.K. Forecasting models and prediction intervals for the multiplicative Holt–Winters method. Int. J. Forecast.
**2001**, 17, 269–286. [Google Scholar] [CrossRef] [Green Version] - Ripley, B.D. Pattern Recognition and Neural Networks; Cambridge University Press: Cambridge, UK, 2009. [Google Scholar]

**Figure 3.**Forecasting logistic demand with the Holt–Winters method. (The Holt–Winters multiplicative model fits real data well in the testing period and provides a relatively high prediction in the future).

**Figure 4.**(

**a**). Allocated number of receiving packages in each town. (

**b**). Allocated number of sending packages in each town. (As shown in the figure, towns around downtown Lhasa are predicted to have relatively high demand for sending and receiving express packages in 2025. The demand varies greatly between different towns).

**Figure 5.**Number of covered villages under different service radius and center numbers. (Due to cost considerations, total number of logistic centers is limited, as well as the service radius. We have to choose a feasible plan that can cover as many villages as possible with limited cost).

**Figure 6.**Spatial distribution of the selected logistic centers and covered demand points. (This figure shows how the 22 logistic centers cover 294 villages in Lhasa).

**Figure 7.**Results of maximal covering model, p-median model, and set covering model. (This figure shows 3 locating plans produced from 3 models. Although the maximal covering model cannot cover all villages, it is still considered the most feasible plan.).

**Table 1.**Overview of the Holt–Winters model testing results. (The Multiplicative model performed better with lower RMSE).

Holt–Winters Method | Adjusted R^{2} of Training Data | RMSE of Training Data | RMSE of Testing Data |
---|---|---|---|

Additive | 0.786 | 6.13 | 17.056 |

Multiplicative | 0.851 | 4.91 | 9.66 |

**Table 2.**Logistic demand allocation from city to counties. (Total prediction of Lhasa is allocated to its subregions based on economy and population).

County | Gross Regional Product (million CNY) | Population | Sending Packages (thousand pkgs) | Receiving Packages (thousand pkgs) |
---|---|---|---|---|

Duilong | 7410 | 63,626 | 1979 | 11,663 |

Dazi | 2112 | 35,430 | 564 | 6495 |

Linzhou | 2292 | 73,128 | 612 | 13,405 |

Dangxiong | 2281 | 62,344 | 609 | 11,428 |

Nimu | 1029 | 35,125 | 275 | 6439 |

Qushui | 1932 | 41,999 | 516 | 7699 |

Mozhu | 3955 | 56,689 | 1056 | 10,391 |

Chengguan | 31,287 | 186,060 | 10,388 | 76,480 |

Total | 52,297 | 554,400 | 16,000 | 144,000 |

**Table 3.**Demand allocation from county to towns in Qushui county. (Prediction of a subregion in Lhasa is further allocated to towns based on economy and population. This table shows the secondary allocation results in 1 of 8 counties).

Town | Population | Number of Industrial Enterprises | Number of Supermarkets | Sending Packages (thousand pkgs) | Receiving Packages (thousand pkgs) |
---|---|---|---|---|---|

Nanmu | 3438 | 1 | 6 | 57.9 | 714.6 |

Daga | 8767 | - | 3 | 113.2 | 1822.4 |

Chabala | 4666 | - | 6 | 65.8 | 969.9 |

Qushui | 9354 | - | - | 116.8 | 1944.4 |

Niedang | 5138 | - | 10 | 76.6 | 1068.0 |

Caina | 5674 | - | 12 | 85.8 | 1179.4 |

Total | 37,037 | 1 | 37 | 516.1 | 7698.7 |

Service Radius (Meter) | No. of Logistic Centers | No. of Covered Demand Points | Service Radius (Meter) | No. of Logistic Centers | No. of Covered Demand Points |
---|---|---|---|---|---|

25,000 | 12 | 305 | 12,000 | 36 | 301 |

11 | 299 | 33 | 296 | ||

10 | 293 | 30 | 290 | ||

9 | 285 | 27 | 281 | ||

8 | 275 | 24 | 272 | ||

7 | 265 | 21 | 260 | ||

6 | 242 | 18 | 246 | ||

20,000 | 16 | 300 | 10,000 | 50 | 306 |

15 | 294 | 46 | 302 | ||

14 | 288 | 42 | 296 | ||

13 | 282 | 38 | 288 | ||

12 | 276 | 34 | 280 | ||

11 | 269 | 30 | 268 | ||

10 | 260 | 26 | 255 | ||

15,000 | 26 | 306 | 8000 | 65 | 301 |

24 | 299 | 60 | 295 | ||

22 | 294 | 55 | 291 | ||

20 | 286 | 50 | 285 | ||

18 | 276 | 45 | 277 | ||

16 | 265 | 30 | 268 | ||

14 | 251 | 26 | 255 |

Service Radius (Meter) | No. of Logistic Centers | No. of Covered Demand Points | Marginal Efficiency |
---|---|---|---|

25,000 | 12 | 305 | 6 |

20,000 | 16 | 300 | 6 |

15,000 | 22 | 294 | 3 |

12,000 | 27 | 281 | 3 |

10,000 | 26 | 255 | 3 |

8000 | 35 | 255 | 2.4 |

Location of Logistic Center | Number of Covered Demand Points | Receiving Packages (×10,000 pkgs) | Sending Packages (×10,000 pkgs) |
---|---|---|---|

Qushui | 7 | 76.39 | 8.49 |

Deqing | 10 | 92.53 | 10.28 |

Banjuelin | 25 | 53.57 | 5.95 |

Tanggu | 7 | 73.27 | 8.14 |

Daqiong | 4 | 35.98 | 4.00 |

Changmu | 11 | 59.90 | 6.66 |

Chaduo | 9 | 59.48 | 6.61 |

Jiagen | 8 | 79.41 | 8.82 |

Xin | 25 | 52.61 | 5.85 |

Jiba | 11 | 15.80 | 1.76 |

Jiangre | 4 | 24.51 | 2.72 |

Jiaru | 12 | 94.79 | 10.53 |

Zhongsa | 44 | 153.82 | 17.09 |

Zhujie | 21 | 83.59 | 9.29 |

Songchan | 29 | 50.19 | 5.58 |

Zimoze | 13 | 50.11 | 5.57 |

Kaduo | 11 | 45.33 | 5.04 |

Tajie | 6 | 100.90 | 11.21 |

Danan | 5 | 49.41 | 5.49 |

Qiareduo | 9 | 86.48 | 9.61 |

Bangda | 9 | 39.23 | 4.36 |

Nietang | 14 | 62.66 | 6.96 |

Total | 294 | 1439.96 | 160.01 |

**Table 7.**Cost components for revenue evaluation. (This figure shows how costs and incomes are calculated for each logistic center.).

Item | Equation | Parameters | Values |
---|---|---|---|

One-Time Initial Investment Cost$TNC={\sum}_{i=1}^{4}N{C}_{i}$ | |||

Decoration | $N{C}_{1}={k}_{dc}A$ | ${k}_{dc}$: decoration cost per unit area $A$: logistic center area | ${k}_{dc}=280$ $A=330$ |

Equipment purchase | $N{C}_{2}={k}_{ec}A+{b}_{ec}$ | ${k}_{ec}$: equipment cost per unit area ${b}_{ec}$: constant equipment cost | ${k}_{ec}=180$ $A=330$ ${b}_{ec}=\mathrm{20,000}$ |

Vehicle purchase | $N{C}_{3}=\frac{{X}_{1}}{{k}_{ta}}{P}_{t}+\frac{{X}_{2}}{{k}_{ma}}{P}_{m}$ | ${X}_{1}$: number of packages with short delivery distance per day ${k}_{ta}$: tricycle delivery efficiency (packages/tricycle·day) ${P}_{t}$: tricycle price ${X}_{2}$: number of packages with long delivery distance per day ${k}_{ma}$: microvan delivery efficiency (packages/tricycle·day) ${P}_{m}$: microvan price | ${X}_{1}/{k}_{ta}=2$ ${X}_{2}/{k}_{ma}=4$ ${P}_{t}=2800$ ${P}_{m}=\mathrm{65,000}$ |

Franchise fee | $N{C}_{4}={k}_{f}{N}_{4}$ | ${k}_{f}$: franchise fee for one express brand $N$: number of brands | ${k}_{f}=\mathrm{10,000}$ $N=9$ |

Operating cost$TOC={\sum}_{j=1}^{5}O{C}_{j}$ | |||

Land rent | $O{C}_{1}={k}_{lr}A$ | ${k}_{lr}$: land rent per unit area | ${k}_{lr}=15$ $A=330$ |

Personnel salary | $O{C}_{2}=\frac{({X}_{1}+{X}_{2})}{{k}_{cd}}{P}_{s1}+{k}_{oa}A{P}_{s2}$ | ${k}_{cd}$: courier delivery ability (packages/tricycle·day) ${P}_{s1}$: courier salary ${k}_{oa}$: operator needed per unit area ${P}_{s2}$: operator salary | ${X}_{1}+{X}_{2}/{k}_{cd}=7$ ${k}_{oa}A=3$ ${P}_{s1s2}=4000$ |

Personnel training | $O{C}_{3}=\left[\frac{({X}_{1}+{X}_{2})}{{k}_{cd}}+{k}_{oa}A\right]{k}_{rr}{P}_{tc}$ | ${k}_{rr}$: personnel replace ratio within a fixed time period ${P}_{tc}$: training cost for one personnel | ${k}_{rr}=10\%$ ${P}_{tc}=2000$ |

Gasoline expenses | $O{C}_{4}={k}_{te}\frac{{X}_{1}}{{k}_{ta}}{S}_{t}+{k}_{me}\frac{{X}_{2}}{{k}_{ma}}{S}_{m}$ | ${k}_{te}$: (energy consumption of a tricycle) multiplies (unit price of energy) ${S}_{t}$: average number of miles traveled per tricycle in a period of time ${k}_{me}$ and ${S}_{m}$ for microvans | ${k}_{te}=0.05,$ ${S}_{t}=1000,$ ${k}_{me}=0.45$ ${S}_{m}=4000$ |

Other expenses | $O{C}_{5}=({k}_{s1}+{k}_{s2})({X}_{1}+{X}_{2})+{b}_{o}$ | ${k}_{s1}$: shared penalty cost (=penalty possibility × amount) ${k}_{s2}$: shared compensation cost (=compensation possibility × amount) ${b}_{o}$: daily water and electricity fee | ${k}_{s1}+{k}_{s2}=0.15$ ${b}_{o}=500$ |

Center Location | Yearly Income (CNY) | Area (m ^{2}) | Staff | Vehicle | Yearly Cost (CNY) | Yearly Profit (CNY) |
---|---|---|---|---|---|---|

Qushui | 1,485,372 | 191 | 19 | 11 | 1,320,267 | 165,105 |

Deqing | 1,799,166 | 231 | 22 | 13 | 1,534,960 | 264,206 |

Tanggu | 1,424,604 | 183 | 18 | 11 | 1,278,691 | 145,913 |

Changmu | 1,164,814 | 150 | 16 | 9 | 1,100,947 | 63,867 |

Chaduo | 1,156,596 | 149 | 16 | 9 | 1,095,324 | 61,272 |

Jiagen | 1,544,163 | 199 | 19 | 11 | 1,360,491 | 183,672 |

Jiaru | 1,843,202 | 237 | 22 | 13 | 1,565,089 | 278,113 |

Zhongsa | 2,991,001 | 385 | 32 | 19 | 2,350,394 | 640,607 |

Zhujie | 1,625,430 | 209 | 20 | 12 | 1,416,093 | 209,337 |

Tajie | 1,962,006 | 252 | 23 | 14 | 1,646,372 | 315,634 |

Qiareduo | 1,681,648 | 216 | 20 | 12 | 1,454,556 | 227,092 |

Nietang | 1,218,314 | 157 | 16 | 10 | 1,137,550 | 80,763 |

Banjuelin | 1,041,721 | 134 | 15 | 9 | 1,016,729 | 24,993 |

Songchan | 976,012 | 125 | 14 | 8 | 971,771 | 4240 |

Zimoze | 974,426 | 125 | 14 | 8 | 970,687 | 3740 |

Kaduo | 881,383 | 113 | 13 | 8 | 907,028 | −25,645 |

Danan | 960,839 | 124 | 14 | 8 | 961,390 | −551 |

Daqiong | 699,605 | 90 | 11 | 7 | 782,658 | −83,053 |

Jiba | 307,167 | 39 | 8 | 5 | 514,159 | −206,992 |

Jiangre | 476,614 | 61 | 9 | 6 | 630,091 | −153,478 |

Bangda | 762,864 | 98 | 12 | 7 | 825,939 | −63,075 |

Model | Number of Logistic Centers | Service Radius (Meter) | Coverage Rate |
---|---|---|---|

P-median | 46 | 15,000 | 100% |

Set Covering | 22 | unlimited | 100% |

Maximal Covering (this study) | 22 | 15,000 | 89% |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, Q.; Mao, H.
An Integrated Method for Locating Logistic Centers in a Rural Area. *Sustainability* **2022**, *14*, 5563.
https://doi.org/10.3390/su14095563

**AMA Style**

Zhang Q, Mao H.
An Integrated Method for Locating Logistic Centers in a Rural Area. *Sustainability*. 2022; 14(9):5563.
https://doi.org/10.3390/su14095563

**Chicago/Turabian Style**

Zhang, Qianli, and Haijun Mao.
2022. "An Integrated Method for Locating Logistic Centers in a Rural Area" *Sustainability* 14, no. 9: 5563.
https://doi.org/10.3390/su14095563