Uncertainty analysis of autonomous delivery robot operations for last-mile logistics in European cities

Figures & data

Table 1. Comparative summary of related literature on ADR operation optimization problem.

Reference	Operation type	Problem setup	Modeling technique
Daganzo (1984)	Delivery vehicles from DC	TSP	CA
del Castillo (1999)	Delivery vehicles from DC	TSP	CA
Estrada and Roca-Riu (2017)	Urban consolidation center	Two-echelon VRP	CA
Figliozzi (2020)	Truck-launched ADRs	TSP with Robot	CA
Jennings and Figliozzi (2019)	Truck-launched ADRs	TSP with Robot	CA
Balcik et al. (2008)	Delivery trucks from DC	Inventory and VRP	Mixed-integer programming
Boysen et al. (2018)	Truck-launched ADRs with micro depots	TSP with Robot	Mixed-integer programming
Simoni et al. (2020)	Truck-launched ADRs	TSP with Robot	Integer programming
Ulmer and Streng (2019)	Pickup stations and ADRs	Dynamic dispatching problem for same-day delivery	Markov decision process

TSP: traveling salesman problem; VRP: vehicle routing problem.

Figure 1. Business-as-usual delivery scheme.

Figure 2. Two-echelon delivery scheme.

Table 2. Logistics key performance indicator notations.

Notation	Description
$L\left(N,R\right)$	Optimized length of a traveling salesman tour visiting $N$ customers in a disk of radius $R,$ considering a ring-radial metrics and demand decreasing with distance to city center (del Castillo, 1999)
$S(N)$	Number of subsectors of a traveling salesman tour visiting $N$ customers in a disk, considering a ring-radial metrics and demand decreasing with distance to city center (del Castillo, 1999)
$\rho (N)$	Optimum partition ratio of a traveling salesman tour visiting $N$ customers in a disk, considering a ring-radial metrics and demand decreasing with distance to city center (del Castillo, 1999)
$N_i^{\mathit{\text{veh}}}$	Total daily number of recipients visited by vehicle fleet $\mathit{\text{veh}}$ in distribution scheme $i$
$N_{t,c}$	Total daily number of visited recipients visited by carrier $c$ in a given city
${\overline{r}}_{\mathit{\text{BAU}}}$	Expected distance between the city center and final receivers in the BAU distribution scheme
$r_0$	Radius of Zone A in the two-echelon delivery scheme
${\rho }_h$	ADR access distance between the logistics micro-hub and final recipients in Zone A in the two-echelon distribution scheme
$r_h$	Distance between the city center and the urban micro-hub in the two-echelon delivery scheme
${\overline{r}}_z$	Expected distance between the city center and final receivers in Zone $z$ of the two-echelon delivery scheme
$d_{\mathit{\text{BAU}}}^{\mathit{\text{LH}}}$	Expected line-haul distance between the carrier’s DC and final receivers in the BAU distribution scheme
$d_B^{\mathit{\text{LH}}}$	Expected line-haul distance between the carrier’s DC and final receivers located in Zone B of the two-echelon distribution scheme
$l_d^{\mathit{\text{ADR}}}$	Expected distance between two consecutive recipients visited by an ADR in the two-echelon distribution scheme
$t_d^{\mathit{\text{ADR}}}$	Expected ADR total delivery time in the two-echelon distribution scheme, including travel time between two consecutive recipients and parcel hand-over process to recipient
${\mathrm{\Psi }}_{t,i}^{\mathit{\text{veh}}}$	Expected capacity, i.e., total number of recipients visited along a delivery route of vehicle $\mathit{\text{veh}},$ considering time restriction, in distribution scheme $i$
${\mathrm{\Psi }}_{b,i}^{\mathit{\text{veh}}}$	Expected capacity, i.e., total number of recipients visited along a delivery route, considering battery restriction (if applicable) of vehicle $\mathit{\text{veh}}$ in distribution scheme $i$
${\mathrm{\Psi }}_i^{\mathit{\text{veh}}}$	Expected capacity, i.e., total number of recipients visited along a delivery route of vehicle $\mathit{\text{veh}}$ in distribution scheme $i$
$n^{\mathit{\text{ADR}}}$	Expected size of ADR fleet in the two-echelon distribution scheme
$D_i^{\mathit{\text{veh}}}$	Expected total distance traveled daily by vehicle fleet $\mathit{\text{veh}}$ in distribution scheme $i$
$D_B^{\mathit{\text{LCV}}}$	Expected distance traveled daily by the LCV fleet in Zone B of the two-echelon distribution scheme
$T_i^{\mathit{\text{veh}}}$	Expected total daily working time of vehicle fleet $\mathit{\text{veh}}$ in distribution scheme $i$
$E_i^{\mathit{\text{veh}}}$	Expected total daily energy consumption of vehicle fleet $\mathit{\text{veh}}$ in distribution scheme $i$
$Z_i^{\mathit{\text{veh}}}$	Expected total daily operation costs of vehicle fleet $\mathit{\text{veh}}$ in distribution scheme $i$
${\mathrm{\Omega }}_h$	Expected total daily costs of micro-hub in the two-echelon distribution scheme, including infrastructure and personnel costs
$Z_i$	Expected total daily operation costs of delivery scheme $i$

Figure 3. Small and medium European cities considered in the sample.

Figure 4. (a) City population PDF and (b) city area PDF, per country.

Figure 5. Carrier demand spatial PDF. Examples in different European cities.

Figure 6. Micro-hub unit area daily infrastructure cost as a function of distance to city center. Examples in different European cities.

Table 3. Parameter and cost assumptions.

Parameter	Value assumption	Reference
Carrier daily demand density ${\delta }_c(r)$ [receivers/km^2/day]	Follows a negative exponential PDF which depends on the considered city and carrier	(European Commission et al., 2018; Eurostat, 2021, 2022b; von Bergmann, 2019)
City radius $r_c$ [km]	Depends on the considered city	(OECD, 2019)
Line-haul distance between the carrier’s DC and city center $l_{\mathit{\text{DC}}}$ [km]	Follows a uniform PDF between 10 and 30	(Heitz & Dablanc, 2015)
Operation time window $H$ [h]	8	(Allen et al., 2018)
Micro-hub daily unit area infrastructure cost ${\omega }_{\mathit{\text{inf}}}$ [€/m^2/day]	Follows a negative exponential PDF which depends on the considered city	(Ackland & Wargentin, 2014; d'Acci, 2019; Lukavec & Kadeřábková, 2017; Numbeo, 2022; Rosenthal et al., 2022)
Unit time personnel cost ${\omega }_p$ [€/h]	Depends on the considered city	(Numbeo, 2022; Observatory of road freight transport in Catalonia, 2019)
Unit area $a^p$ occupied by one parcel at the logistics micro-hub [m^2/parcel]	1	(Navarro et al., 2016)
LCV volume capacity $C^{\mathit{\text{LCV}}}$ [parcels]	150	(Perboli & Rosano, 2019; Renault Renault, 2023)
LCV line-haul speed $v_{\mathit{\text{LH}}}^{\mathit{\text{LCV}}}$ [km/h]	50	(DieselNet, 2023; NREL, 2023)
LCV local speed $v_L^{\mathit{\text{LCV}}}$ [km/h]	20	(DieselNet, 2023; NREL, 2023)
LCV stop time per delivery ${\tau }_d^{\mathit{\text{LCV}}}$ [min]	4	(Allen et al., 2018; Perboli & Rosano, 2019)
LCV unit distance operation cost $c_d^{\mathit{\text{LCV}}}$ [€/veh-km]	Depends on the considered city	(Numbeo, 2022; Observatory of road freight transport in Catalonia, 2019)
LCV unit time operation cost $c_t^{\mathit{\text{LCV}}}$ [€/veh-h]	Depends on the considered city	(Numbeo, 2022; Observatory of road freight transport in Catalonia, 2019)
ADR volume capacity $C^{\mathit{\text{ADR}}}$ [parcels]	15	Own prototype of road ADR
ADR commercial speed $v^{\mathit{\text{ADR}}}$ [km/h]	10	(Lemardelé et al., 2023)
ADR stop time per delivery ${\tau }_d^{\mathit{\text{ADR}}}$ [min]	2	(Perboli & Rosano, 2019)
ADR unit time depreciation cost ${\epsilon }^{\mathit{\text{ADR}}}$ [€/veh-h]	1	Variable value used for sensitivity analysis
ADR insurance costs ${\gamma }_{\mathit{\text{insurance}}}^{\mathit{\text{ADR}}}$ [€/veh-h]	Assumed to be equal to LCV insurance costs in the considered city	(Numbeo, 2022; Observatory of road freight transport in Catalonia, 2019)
ADR maintenance costs ${\gamma }_{\mathit{\text{maintenance}}}^{\mathit{\text{ADR}}}$ [€/veh-km]	Assumed to be equal to LCV maintenance costs in the considered city	(Numbeo, 2022; Observatory of road freight transport in Catalonia, 2019)
ADR structure costs ${\gamma }_{\mathit{\text{structure}}}^{\mathit{\text{ADR}}}$ [€/veh-h]	Assumed to be equal to LCV structure costs in the considered city	(Numbeo, 2022; Observatory of road freight transport in Catalonia, 2019)
ADR unit distance energy consumption rate for mechanical propulsion ${\beta }_{\mathit{\text{mech}}}^{\mathit{\text{ADR}}}$ [Wh/km]	20	(Lemardelé et al., 2023)
ADR electronics and sensor power $P_e^{\mathit{\text{ADR}}}$ [W]	500	(Lemardelé et al., 2023)
ADR battery capacity ${\mathit{\text{BC}}}^{\mathit{\text{ADR}}}$ [kWh]	3.75 (assuming a rate of discharge of 80%)	(Lemardelé et al., 2023)
Number of ADRs an operator is able to monitor and supervise ${\kappa }^{\mathit{\text{ADR}}}$ [ADRs]	5	(National Academies of Sciences, Engineering, and Medicine, 2023)
HDV volume capacity $C^{\mathit{\text{HDV}}}$ [parcels]	1,000	(Perboli & Rosano, 2019; StreetScooter, 2023)
HDV line-haul speed $v_{\mathit{\text{LH}}}^{\mathit{\text{HDV}}}$ [km/h]	50	(DieselNet, 2023; NREL, 2023)
HDV loading/unloading time per parcel ${\tau }_{\mathit{\text{LU}}}^{\mathit{\text{HDV}}}$ [s]	45	(Dell’Amico & Hadjidimitriou, 2012; Hofmann et al., 2017)
HDV unit distance operation cost $c_d^{\mathit{\text{HDV}}}$ [€/veh-km]	Depends on the considered city	(Numbeo, 2022; Observatory of road freight transport in Catalonia, 2019)
HDV unit time operation cost $c_t^{\mathit{\text{HDV}}}$ [€/veh-h]	Depends on the considered city	(Numbeo, 2022; Observatory of road freight transport in Catalonia, 2019)
Price of electricity ${\$}_e$ [€/kWh]	Depends on the country where the city is located	(Eurostat, 2022a)

Table 4. Line-haul and local driving cycles.

Driving cycle name	Driving cycle type	Average speed (km/h)
CADC line-haul	Line-haul	57.5
EPA UDDS line-haul	Line-haul	41.3
NEDC line-haul	Line-haul	66.4
NREL parcel delivery truck	Line-haul	30.7
WLTC line-haul	Line-haul	56.7
Braunschweig city driving cycle	Local	30.1
CADC urban	Local	17.6
CSHVC	Local	22.2
EPA UDDS urban	Local	25.8
NEDC urban	Local	18.1
NREL Class 6 EV	Local	25.1
NYCC	Local	11.4
WLTC urban	Local	18.9

Figure 7. Operation delivery cost ratio $Z_{\mathit{\text{ech}}}/Z_{\mathit{\text{BAU}}}$ as a function of micro-hub delivery zone radius $r_0$ and distance $r_h$ between the logistics micro-hub and city center in Roanne.

Figure 8. Operation delivery cost ratio $Z_{\mathit{\text{ech}}}/Z_{\mathit{\text{BAU}}}$ as a function of micro-hub delivery zone radius $r_0$ and distance $r_h$ between the logistics micro-hub and city center in Legnica.

Figure 9. Operation delivery cost ratio $Z_{\mathit{\text{ech}}}/Z_{\mathit{\text{BAU}}}$ as a function of micro-hub delivery zone radius $r_0$ and distance $r_h$ between the logistics micro-hub and city center in Potenza.

Figure 10. Decomposition of the optimized delivery cost ratio $z_{\mathit{\text{ech}}}^{*}/z_{\mathit{\text{BAU}}}$ per vehicle type and micro-hub contribution for several cities.

Figure 11. Optimized delivery cost ratio $z_{\mathit{\text{ech}}}^{*}/z_{\mathit{\text{BAU}}}$ as a function of the line-haul distance $l_{\mathit{\text{DC}}}$ for several cities.

Figure 12. Histogram of cost ratio $z_{\mathit{\text{ech}}}^{*}/z_{\mathit{\text{BAU}}}$ as a function of (a) micro-hub infrastructure/personnel cost ratio ${\omega }_{\mathit{\text{inf}}}\left(r_h=0\right)/{\omega }_p,$ (b) demand density $\delta =N_{t,c}/A_c,$ (c) distribution center distance/city radius ratio $l_{\mathit{\text{DC}}}/r_c,$ (d) city area $A_c,$ (e) personnel cost/ADR depreciation ratio ${\omega }_p/{\epsilon }^{\mathit{\text{ADR}}},$ and (f) total number of deliveries $N_{t,c}.$

Figure 13. (a) Two-echelon mean operation costs per parcel delivery, (b) operation costs variation when implementing two-echelon delivery scheme, and (c) probability of obtaining lower two-echelon operations costs $P\left(z_{\mathit{\text{ech}}}^{*}\le z_{\mathit{\text{BAU}}}\right).$

Figure 14. Hypothetical two-echelon operation PDFs.

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