日本オペレーションズ・リサーチ学会
2021年 秋季研究発表会

2-B-9

Hub Location Model of Platoon Formation Center for Truck Platooning
05001456
01900990

Tokyo Univ. of Marine Science and Technology
Tokyo Univ. of Marine Science and Technology

1. Introduction
Truck platooning is a grouping of freightvehicles into connected vehicle convoys using
electronic coupling as an application in automateddriving technology for saving fuel, reducing travel
cost and improving infrastructure efficiency.
Therefore, it is critical to locate platoon
formation centers (PFCs) for (de)forming
platoons[1]. In this study, we will apply the hublocation model to find the optimal location of PFCs.
The objective is to minimize the total travel costfor each origin-destination pair via two PFCs.
2. Formulation
Most hub location models consider the discountfactor due to the economies of scales. In this study,
we will consider the discount factor thanks to thetruck platooning for optimized location of PFC.
Two different assignment systems are used for
PFCs formation — single assignment and multiple
assignment. Single assignment is that trucks from acertain origin must (de)form a platoon only at asingle PFC, while platoons can be created more thanat a single PFC in multiple assignment. The
optimization model by Skorin-Kapov et al.(1996) isused for single allocation, which is a LP relaxationof Campbell(1994b). For multiple allocation, acompact formulation of the model, known as theHUBLOC by Skorin-Kapov et al.(1997) is applied.
Discount Factor(𝑎𝑎)Discount factor estimation due to truck
platooning by Watanabe et al. (2021) is applied asfollows.
(1)
𝑇𝑇𝑠𝑠 = 𝑠𝑠𝑠𝑠
(2)
𝑇𝑇𝑝𝑝 = 𝑎𝑎 + (𝑛𝑛 − 1)𝑏𝑏
𝑇𝑇𝛼𝛼 = 𝑇𝑇𝑝𝑝 =𝑠𝑠𝑎𝑎+(𝑛𝑛−1)𝑏𝑏𝑠𝑠𝑠𝑠(3)

where,
𝑇𝑇𝑠𝑠 = travel cost of trucks without platoon*SAW Aung
WATANABE Daisukes = travel cost per truckn= number of trucks

𝑇𝑇𝑝𝑝 = travel costs of trucks with platooning
𝑎𝑎 = leading truck travel costb = following trucks travel cost

3. Numerical experiments
The ratio of the labor costs in the trucking
industry is around 40% and this is related to thecost reduction for unmanned driving against manneddriving. As for the reduction of fuel consumption,
the leading vehicle is around 10% and that of thefollowing vehicles is around 20%. The number oftrucks (n) is hypothetically varied from 3 to 10 toallow a wider range of α value. Therefore, thefollowing discount values as shown in Table 1 areused for platooning hub optimization.
We test our linearization using dataset with 20cities, which is extracted from Turkish network
dataset of 81 cities by Kara[4]. Travel demand ofeach node is shown in Table 2. We solve the model
via XpressIVE 8.11 on an Intel Xeron Bronze 1.9 GHz
computer with 32768 MB RAM, and 1 MB Cache.
Table 1. Discount factor 𝛼𝛼 for truck platooning

4. Findings
These are the following general characteristics
found from our optimization. Figure 1 shows thetotal travel cost in each scenario. Increasing thenumber of platooning trucks cannot significantly
reduce the inter-PFC travel cost. Semi or complete
unmanned platooning and multiple allocation canreduce the cost dramatically. Multiple allocation
can also bring down the cost significantly rather

than single allocation.
Figure 2 shows the optimal location for single

Table 2. Travel demand of each node and PFC
location in optimization instances with theassignment with discount factor when the number of PFCs
is 5. Lower discount factor means that truck

number of PFCs from 1 to 7

platoons can enjoy more of the platooning benefit.
Therefore, lower inter-PFC discount factor cangenerally lead to larger inter-PFC distance. This
characteristic can be found more for single
assignment and uniformly distributed data. In otherwords, optimal PFC location in multiple assignmentis less sensitive to discount factor variation.

City

ANKARAADANAANTALYABALIKESİR
AYDIN

AFYON

ADAPAZARISİVAS

3,000

Total Travel Cost(Million km)

Locatio

ADIYAMAN

2,500

AĞRI

2,000

BATMAN1,500BİTLİSAKSARAYAMASYA

1,000BİNGÖLBİLECİK500-ARTVİN

1234

567

Number of PFCs

BARTIN

ARDAHANBAYBURT

Single(α=0.8)

Multi(α=0.8)

Single(α=0.6)

Multi(α=0.6)

Single(α=0.4)

Multi(α=0.4)

Figure 1. Objective cost values for single
allocation and multiple allocation with different
discount factor and number of PFCs

nof PFCs Outflow○737202○364921

○
○
○
○
○
○
○
○
○

389583236571210361181059169016168785140386119571
103664

90174

88521

○83279
58180

44689

44144

42377

30852

22497

Inflow

Total

7040851441286365405

730326389236239346213233183908171817171585142986121949105833

92138

90458

85129
59563

45788

45231

43425

31636

23080

778819475917423594364967340833340369283372241520209497182312

178979168408117744

90477

89375

85801

62488

45576

Nodes with the larger flows appear as hubs
repeatedly in almost all instances of linearization
as shown in Table 2. This is more correct for
uniformly distributed dataset.
References

α=0.4-0.6

α=0.8

Figure 2. Hub Location for single assignment withdiscount factor(number of PFCs=5)[1] Watanabe, D., Kenmochi, T. and Sasa, K.: An
Analytical Approach for Facility Location for Truck
Platooning-A Case Study of Unmanned Following Truck
Platooning System in Japan-, Logistics, 5(2), 27,
https://doi.org/10.3390/logistics5020027, 2021.
[2] O’Kelly, M.E., Bryan, D., Skorin-Kapov, D. andSkorin-Kapov, J.:Hub network design with single andmultiple allocation: a computational study. Location
Science 4, 125–138, 1997[3] Skorin-Kapov, D., Skorin-Kapov, J. and O’Kelly,M.E.: Tight linear programming relaxations of
uncapacitated phub median problems. European Journalof Operational Research 94, 582–593, 1997
[4]
KaraB.Y.:
Turkishnetworkdataset,https://ie.bilkent.edu.tr/~bkara/dataset.php