Impact of Last Mile Parking Availability on Commercial Vehicle Costs and Operations

Portland State University Portland State University

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Civil and Environmental Engineering

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Impact of Last Mile Parking Availability on Impact of Last Mile Parking Availability on

Commercial Vehicle Costs and Operations Commercial Vehicle Costs and Operations

Miguel Figliozzi

Portland State University

, ;[email protected]

Chawalit Tipagornwong

Portland State University

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Published as: Figliozzi, M., & Tipagornwong, C. (2017, April). Impact of last mile parking availability on

commercial vehicle costs and operations. In Supply Chain Forum: An International Journal (Vol. 18, No. 2,

pp. 60-68). Taylor & Francis.

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Impact of Last Mile Parking Availability on

Commercial Vehicle Costs and Operations

Miguel Figliozzi

and Chawalit Tipagornwong

Department of Civil and Environmental Engineering, Portland State University. P.O. Box 751,

Portland, Oregon 97207-0751, USA. [email protected]

Abstract:

This research analyses how parking availability levels affect commercial vehicle

parking costs and operations in congested urban areas. Unlike passenger vehicles,

parking availability has an impact on route characteristics and commercial vehicle fleet

sizes. Hence, commercial vehicles parking costs cannot be captured solely by estimating

delays and/or the cost of parking fines. This research combines logistics, queuing, and

optimization models to study the impact of last mile parking availability on commercial

vehicle costs and operations. Scenarios are built to study the impact of parking

availability on typical less-than-truckload (LTL) and courier service costs. Results

indicate that parking availability levels do affect commercial vehicle costs and

operations significantly. The magnitude of the impacts is a function of customer and

route characteristics. The analysis of elasticity values indicates that a few variables

have a significant impact on commercial vehicle parking behaviour. In some cases,

productivity improvements like service time reductions may result in undesirable

changes in commercial vehicle parking behaviour.

Keywords: commercial vehicles; last mile; parking costs; economic analysis; elasticity

Journal Reference

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Introduction

There is a growing awareness regarding problems associated with commercial vehicles

in congested urban areas. Efforts to increase downtown or neighbourhood livability can

result in costly restrictions. Typical restrictions include commercial vehicle bans at

certain times of the day, limited parking and/or loading and/or unloading zones for

commercial vehicles, commercial vehicle noise level limits (when loading and

unloading), commercial vehicles pollution constraints, and commercial vehicles size

limits. For example, in New York City commercial vehicle size, routes, and parking areas

are restricted for urban freight distributors and service providers (City of New York,

2013).

On-street parking spaces and freight loading zones (FLZs) are typically

insufficient during certain periods of the day in most dense and congested urban areas,

for example in the USA these urban areas include New York City, San Francisco, Los

Angeles, Boston, Chicago, and Washington D.C. News organizations frequently report

on the problems caused by double-parked commercial vehicles or the high parking fines

that delivery companies must pay (NBC News, 2006; Gordon, 2007; Halsey, 2013;

Hawkins, 2013; Berezin, 2014).

Although anyone that lives in a dense and congested city is familiar with the

problems associated to commercial vehicle parking there is limited research in this area.

In particular, there is scant research related to models that attempt to understand the

impacts of FLZ availability on commercial vehicles costs and behaviour. This study

addresses the following research questions: how does parking availability affect

distribution companies’ parking behaviour? and (ii) what are the key variables that

affect parking costs?

Next section discusses key aspects of the problem under study and presents a brief

literature review. Later sections present a modelling framework that includes queueing,

logistics, and cost optimization models. A case study that includes different delivery

services types is analysed and cost elasticity and break-even values are discussed. The

final sections discuss policy and managerial implications and summarize the main

conclusions that can be derived from this research effort.

Background and Brief Literature Review

When all parking spaces near delivery destinations are occupied, commercial drivers

prefer not to park away from the delivery destination (Pluvinet et al., 2012). Several

factors explain this preference. It is difficult to move bulky or heavy products over long

distances or across intersections even if the driver or delivery person is utilizing a hand

truck (Allen et al. 2000). In some cities or neighbourhoods, drivers may prefer to see their

vehicles to prevent theft and/or vandalism (Morris, Kornhauser and Kay, 1999). In

addition, parking away from the delivery points adds time per delivery and small delays

quickly become significant for drivers or companies that have to serve many customers

along the route (Figliozzi, 2007, Figliozzi & Tipagornwong, 2016).

When there is no parking available nearby the delivery point commercial drivers

may double park. If commercial drivers double park frequently, the cost of parking fines

can be substantial. For example in New York City, large delivery fleets including FedEx,

UPS, and the U.S. Postal Service paid $550 million in 2013 (Hawkins, 2013). Since

repeated double parking fines increase the final delivery cost, urban freight distributors

and service providers may raise service fees to customers in areas where deliveries or

pick-ups are more difficult. For example, UPS charges a surcharge in some congested or

difficult delivery areas (such as zip codes 10000 – 10292) of Manhattan, New York City

(United Parcel Service of America, 2015).

Previous research efforts have modelled parking availability by analysing a

parking demand-to-supply ratio that is defined as the ratio between parking demand and

parking supply rates. Some publications define the parking demand rate as a freight trip

generation rate multiplied by the average parking time; for example, Jaller et al. (2013)

studied off-peak-hour deliveries and evaluated commercial parking availability with the

parking demand-to-supply ratio at different times of day in New York City. The freight

trip generation rate has been traditionally estimated as a function of the number of

employees by type of industry, commercial sector, or land use (Fischer and Han, 2001).

The parking supply is defined as the number of parking spaces or FLZs. The literature

based on the analysis of empirical demand/supply data largely agree that at peak times

there is insufficient parking capacity in commercial districts and along urban arterials

(Wenneman, Habib, and Roorda, 2015) and even in neighbourhoods (Chen and Conway,

2016).

Another line of research has utilized simulation models (for example, Aiura and

Taniguchi, 2006 and McLeod and Cherrett, 2011) to study commercial vehicle parking

in urban areas. These models can accurately represent transportation networks and FLZs,

generate commercial vehicle trips and their parking time, and estimate commercial

vehicles delays. A recent model to analyse parking policies in specific locations combines

parking choice models and a traffic simulation models (Nourinejad, et al., 2014).

The third approach is a statistical model. For example, a statistical model (based

on queuing theory) has been used to study how personal or passenger parking demand

responds to pricing and parking availability in San Francisco (Millard-Ball, Weinberger,

& Hampshire, 2014). This type of modeling effort can be used to investigate the impact

of pricing on parking arrival rate, parking duration, and parking availability.

Unfortunately, there is no similar dataset that can be utilized to study the impacts of

pricing and parking availability on commercial vehicles. A previous paper by the same

authors was preliminary (conference proceedings) and did not include a discussion of

elasticity values and policy/managerial implications (Figliozzi & Tipagornwong, 2016).

Unlike previous research efforts, this research focuses on modelling parking

availability combining queuing models and logistical models based on continuous

approximations. Unique contributions of this research are the addition of real-world

routing constraints such as load capacity or route time durations, the analysis and

comparison of courier and less-than-truckload (LTL), and ranking the impact of logistics

and policy variables as a function of their elasticity values. Next section presents the

modelling framework integrating queuing and continuous approximations for long-term

logistic costs.

Modelling Commercial Parking

This research models parking availability utilizing queuing models. Routing constraints

are modelled utilizing continuous approximations. Service costs includes all the relevant

long-term (vehicle and driver) costs. Finally, all the models are integrated within an

optimization framework that can be utilized to determine the optimal number of

vehicles, vehicle type, and parking behaviour.

Parking availability

Convenient access is important for both consumers and carriers (Duran & Gonzales-

Feliu, 2012) hence the number of available parking spots is usually limited. Assuming

that there are (S) freight loading zones available on a first-come-first-serve basis and

that inter-arrival times and FLZ occupation times follow exponential distributions, a

M/M/S queuing model can be utilized. The expected probability of double parking

$ % &'

(

)

can be estimated as follows:

"#$ % &'( * +,"#&$ - ',+( * +,

#/01(

"#$ * 4(

567

289

"#$ * 4( *

#/01(

;

#/01(

+,/0'1

567

289

Where

"#$ % &'(

: probability that all FLZs are occupied

N : number of commercial vehicles in the system

S : number of FLZs

: commercial vehicle arrival rate (vehicles per hour)

: commercial vehicle service rate (vehicles per hour)

P( N=0 ) = probability that all FLZs are empty

If a commercial driver waits when FLZs are fully occupied, the expected waiting

time of the driver can be estimated as follows:

#/01(

#/0'1(

'3#+,/0'1(

When a commercial driver waits until a FLZ is available, it is assumed that the driver

waits inside the vehicle and since the vehicle is never left unattended, the “waiting”

driver will not receive a parking fine.

When the driver double-parks a parking enforcement officer can issue a parking

fine. However, an illegally parked vehicle does not always receive parking fines. This

study models the expected probability of receiving a parking ticket or fine given that all

FLZs are occupied

as a function of service time (

) and the parking enforcement

cycle duration (

). The inverse of

is the duration of the average parking zone

utilization or

* &HIJKLKMNMDO

DMPQRD

$ % '

(

( *

An average parking utilization level (

) is defined as the ratio of parking

demand to parking supply

&#T * &/0'1(

. Parking utilization and parking availability are

inversely related, low parking utilization

&#NJU&T(

is associated with high parking

availability or easiness to find empty loading zones.

Routing Constraints

Continuous approximations have been successfully used by many research efforts to

model urban distribution systems (Langevin, A., Mbaraga, P., and Cambell, J. 1996;

Daganzo C. 2005). This study utilizes a continuous approximation model successfully

used in the past (Figliozzi M. 2008; Figliozzi M. 2010) to estimate the average route

distance of commercial vehicles.

VW"&

(

* Q

Y,Z

[

Y\;]I

where VRP (V) = average distance travelled for a fleet of m vehicles (miles)

= local service area coefficients

n = number of customers

m = number of routes

A = the size of a service area (km

)

^ = average distance between customers and a depot (km)

The following parameters are utilized to formulate long-term service costs.

aJbI&cMdDLYPR&Je&fRgMPNR&DOHR&M&#ZMNRd0DJbI(

* aJbI&cbILDMJY&Je&fRgMPNR&DOHR&M&#gJbId(

hij

* kLlMZbZ&DJbI&cbILDMJY#gJbId(

* \fRILnR&PbdDJZRI&cRZLYc&#NKo0dDJH(

* \fRILnR&dRIfMPR&DMZR&#ZMYbDR0dDJH(

* \fRILnR&dHRRc&Je&fRgMPNR&M&nJMYn&eIJZ&L&cRHJD&DJ&DgR&dRIfMPR&LIRL&#ZHg(

* \fRILnR&dHRRc&Je&fRgMPNR&M&IbYYMYn&MYdMcR&DgR&dRIfMPR&LIRL&#ZHg(

* \fRILnR&dHRRc&Je&fRgMPNR&M&IRDbIYMYn&DJ&DgR&cRHJD&#ZHg(

* _JLc&PLHLPMDO&Je&fRgMPNR&DOHR&M&#NKd(

Route duration and vehicle capacity constraints can be expressed as follows:

* I

;

{

}

•

€

•

;

[

€

‚

;

•

€

;&Y

;#+,O

(

#T(

)

% Y

&&&&&&&&&&„M … †‡ „ˆ … ‰

hij

% a

&&&&&&&&&&&

&&&&&&&&&&„M … †‡ „ˆ … ‰

The binary variable

indicates whether the vehicle double-parks (

* +(

or waits for

parking (

* 4(

. These equations estimate the length of a delivery tour that starts from

a depot, serves customers, and returns to the depot as well as tour duration. Average

parking utilization levels

and parking behaviour affect waiting time

and can

indirectly also affect fleet size when

increases over the maximum tour duration.

Service Costs

Long-term service cost includes vehicle depreciation cost, energy/fuel cost, vehicle

maintenance cost, driver wage, driver annual costs, truck annual costs, and double-

parking fines. In the USA drivers’ annual costs include driver health insurance, social

security tax, Medicare tax, and pension/retirement; the truck annual costs include

vehicle registration and insurance. The following indices are utilized to formulate long-

term service costs.

Š …

‹

dRD&Je&fRgMPNR&DOHRd

* †&

• …

‹

dRD&Je&HLIQMYn&KRgLfMJId

* ‰&&

j = 1 for double parking and j = 0 for waiting or

cruising for parking

Ž …

‹

dRD&Je&ORLId&Je&DgR&HNLYYMYn&gJIM•JY

* ‹+‡]‡•‡‘&Œ&

The following parameters are utilized to formulate long-term service costs.

’

* “YMD&HbIPgLdR&PJdD&eJI&fRgMPNR&DOHR&M&#cJNNLI0fRgMPNR(

* “YMD&IRdLNR&PJdD&eJI&fRgMPNR&DOHR&M&

”

cJNNLI

fRgMPNR

•

MY&ORLI&‘&

* “YMD&RYRInO&PJdD&eJI&fRgMPNR&DOHR&M&#cJNNLI0nLNNJY&JI&cJNNLI0Q=g(

* RYRInO&PJYdbZHDMJY&ILDR&Je&fRgMPNR&DOHR&M&#nLNNJY0ZMNR&JI&Q=g0ZMNR(

* “YMD&ZLMYDRYLYPR&PJdD&eJI&fRgMPNR&DOHR&M&#cJNNLI0ZMNR(

* –JbINO&cIMfRI&ULnR&eJI&fRgMPNR&DOHR&M&#cJNNLI0gJbI(

—

* &HLIQMYn&eMYR&#cJNNLId(

—

* "IJKLKMNMDO&Je&IRPRMfMYn&L&HLIQMYn&eJI&fRgMPNR&DOHR&M&LYc&KRgLfMJbI&DOHR&ˆ

* “YMD&LYYbLN&PJdD&eJI&fRgMPNR&DOHR&M&#cJNNLI0fRgMPNR(

* ˜MdPJbYD&eLPDJI&#™(&

* WLDR&Je&MYeNLDMJY&eJI&cMRdRN&ebRN&&#™(

c * ˜LOd&Je&dRIfMPR&HRI&ORLI

‘ * šRLId&MY&HNLYYMYn&gJIM•JY

= fleet size

`‡s

(integer) of vehicles type

following parking behaviour j

The sum of purchasing, resale, energy/fuel, maintenance, driver wages, parking tickets,

and vehicle fixed annual costs can be expressed as follows:

› *

: :

+;e

(

,‘

)

Mˆ

;

: #

+;e

(

+;e

(

•

Mˆ

‘

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Mˆ

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: #

+;e

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Mˆ

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Q*+

;

: #

+;e

(

Mˆ

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Optimization Problem

The optimization problem minimizes long-term vehicle costs by selecting the best

vehicle type

and parking behavior j. The decision variable is the fleet size

`‡s

(integer)

of vehicles type

following parking behavior j and the number of customers

assigned to vehicle type

following parking behavior j. The binary variable

is 1

when the vehicle double parks (

ˆ * +(

and zero otherwise (

ˆ * 4(

when the driver waits

until a parking space is available.

› *

Total cost over the planning horizon (dollars)

Minimize

›

(1)

Subject to:

% Y

&&&&&&&&&&&&&&&&&&&&&&&„M … †‡ „ˆ … ‰

(2)

hij

% a

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&„M … †‡„ˆ … ‰

(3)

—

* O

—

&- +&&

&„M … †‡„ˆ … ‰

(4)

‡Z

% 4&&&&&&&Y

‡Z

… 'RD&Je&†YDRnRId&&&&&&&&„M … †‡ „ˆ … ‰

(5)

- &YO

&„M … †‡ ˆ * +

(6)

- &Y#+,O

(

&„M … †‡ ˆ * 4

(7)

Y -&

: :

s87

(8)

Equation (1) is the objective function, minimization of total cost. Equation (2) is a

weight/capacity constraint and equation (3) is a route duration constraint. Equation (4)

estimates the probability of receiving a fine. Equation (5) is an integer non-negativity

constraint. Equations (6) and (7) are logical constraints that link parking behaviour and

fleet size. Equation (8) ensures that all customers are served.

The reader should note that the threshold for waiting or double parking is purely

monetary. The model attempts to explain what factors may support a waiting or double-

parking strategy. It is assumed that loading zones are convenient for commercial vehicle

drivers; another dimension of the problem is the situation when commercial drivers stop

in the closest place (double-park) even when loading zones are free but not close

enough to the final delivery location (a trade-off that is not analysed in this research).

Case Study

It is hypothesized that logistics constraints and route characteristics have an impact on

parking costs, operations and behaviour. Two types of delivery services are analyzed:

less-than-truckload (LTL) and courier deliveries. LTL deliveries are heavier and require

more time per delivery than courier deliveries. LTL shipments can range between 600

and 1,200 lbs. (Morris and Kornhauser 2000) with service times ranging between 15

and 25 minutes per stop (Muñuzuri, Cortés, Guadix, and Onieva 2012). Courier services

are lighter, ranging from less than 1 to 170 lbs. (Morris and Kornhauser 2000). Courier

service time ranges from 1 to 5 minutes (Muñuzuri, Cortés, Guadix, and Onieva 2012).

Four route types are studied in this is research but due to space constraints, only one

vehicle type (a typical small delivery truck) is utilized in this research.

LTL and courier deliveries are classified into two groups: A and B; “A” types

have heavier shipment sizes, longer service times, and longer tour durations than “B”

types. The characteristics of customers LTL A, LTL B, Courier A and Courier B are

summarised in Table 1. The characteristics of the vehicle, a typical small delivery

vehicle in the USA, are shown in Table 2.

The model presented in Section 3 is utilized to minimize long-term service costs as a

function of fleet size and changing demand and supply

&#T * &/0'1(

ratios but

conditional on utilizing one strategy (waiting or double-parking). Scenarios LTL A and

LTL B are weight-constrained whereas Courier A and Courier B scenarios are time-

constrained.

Impacts of Parking Availability on Costs

Long-term costs are estimated for each scenario as a function of parking availability.

The results show that the impacts of parking availability are different for the double

parking and waiting strategies. Figure 1 shows the expected probability of no parking

and the expected waiting time as a function of parking utilization levels

. The rate of

increase of the probability of no parking is steady and comparable across different

service types. However, expected waiting time varies significantly across delivery

types. For the sake of simplicity, only LTL A and Courier B graphs are shown in Figure

1; the other two scenarios (LTL B and Courier A) fall in between LTL A and Courier B

scenarios and are not included for the sake of brevity.

For LTL A routes, with longer service times, the increase of expected wait times

as a function of ρ starts to show high values – more than 5 minutes per customer – for

parking utilization values ρ > 0.60. On the other hand, for Courier B routes, the increase

of expected wait time as a function of parking utilization values starts to show high

values – more than 5 minutes per customer – for values ρ > 0.90. In the latter scenario,

the increase is very sharp when ρ > 0.90.

Costs per customer (per stop) are shown in Figure 2. For the sake of simplicity,

only the LTL A and Courier B curves are shown. In terms of absolute costs, as

expected, courier deliveries are several times more economical than LTL deliveries.

This is expected because it is more difficult to deliver heavier loads that have longer

service times; more routes, drivers, and vehicles are necessary to accommodate fewer

LTL customers per route. Courier routes are several times more efficient in terms of

utilization of resources such as vehicles and drivers.

The comparison of the costs of double parking and waiting strategies are less

straightforward. For LTL A deliveries, it is better to “wait” than to double park until ρ

0.90; for Courier B deliveries, it is better to “wait” than to double park until ρ

0.70.

The results indicate that for Courier B double parking is a nearly optimal strategy for

any ρ value, since the difference between the cost of double parking and waiting can be

barely perceived in the interval 0 < ρ

¤&

0.70. In other words, Couriers are nearly

indifferent between double parking and waiting in the interval 0 < ρ

¤&

0.70. On the

other hand, for LTL A services the difference between the cost of double parking and

waiting is noticeable in the range 0.40 < ρ

¤&

0.90.

These results indicate that the impact of parking availability on LTL and Courier

operations and behaviour are likely different. In areas with a reduced number of loading

zones and high parking demand it is expected that Courier vehicles will show a

tendency to double-park more than LTL vehicles. For LTL vehicles, waiting is a more

attractive option. LTL vehicles have longer service times and hence the probability of

parking fines are high when the vehicles are not legally parked. The parking utilization

must be high (ρ

¥&

0.90) and waiting times must be very long to outweigh the expected

parking fine costs.

Per-Stop Elasticity Analysis

Previous results are useful to highlight general trends regarding occupancy, waiting

times, cost per customer, route type, and parking demand/supply ratios. Elasticity values

are calculated in this section to get an estimate of the relative importance of service,

routing, and parking variables on long-term cost per stop or customer.

The elasticity analysis was conducted at break-even values (

) of ρ where the

service cost of the double-parking behaviour equals the service cost of the waiting

behaviour. The breakeven points were chosen because at these points small changes

may result in behaviour reversals, e.g. from waiting to double parking or vice versa. The

elasticities were obtained using numerical approximations of this function:

§#›0¨‡©( *

ª#›

©‡¦

(

0¨(

ª©

&›#©‡¦(0¨

where:

§#›0¨‡©( *

variable

long-term service cost per stop elasticity

›

©‡¦

(

0¨ *&

per customer or stop long-term service cost

¦ *

breakeven point

Table 3 provides the elasticity values for the LTL B scenario. To facilitate a

comparison, elasticity values are sorted from highest to lowest value when j = 1

(double-park). A positive sign must be interpreted as an increase in per stop cost, for

example, if the value of the parking fine increases 1% the per stop cost is going to

increase 0.6% if the driver decides to double park and 0.0 % if the driver decides to

wait for an available parking space.

As expected, when ρ increases there is a major increase in service costs but at

the breakeven point the increase is three times higher if the driver decides to wait

instead of double park. The ratio between

§#›0¨‡T(

and

§#›0¨‡P

—

(

indicates that at

the breakeven point fines must increase more than 2.3 (1.37/0.6 ≈ 2.3) times faster than

the demand/supply ratio (ρ) to make double parking less appealing.

Service time has a high elasticity in the double parking scenario, almost four

times higher than in the wait scenario. This is may be explained by the fact that a

service time increase also increases the probability of receiving a parking fine while

double parking. Hence, in the double parking scenario a longer service time creates an

indirect cost increase related to parking fines and a direct cost increase related to longer

route durations. The reverse, a reduction of service time leads to a decrease in service

costs but because the decrease is much faster for companies that double park, a decrease

in service time moves the breakeven point between double-parking and waiting to the

left or a smaller demand/supply ratio (ρ). Driver hourly wage is the other variable that

has a high impact on costs, especially in the waiting time scenario.

Variables related to route length such as service area size and distance depot-

service area have a relatively small elasticity; the same can be said about the travel

speeds. Vehicle purchase cost elasticity is more important in the wait scenario but it is

five times smaller than the elasticity value for driver wages,

§#›0¨‡P

(

= 0.65 and

§#›0¨‡P

’

(

= 0.13. Other costs such as energy or the value of money (discount rate)

have low elasticity values.

Table 4 provides the elasticity values for the Courier-A scenario. Overall, the

same trends are maintained. However, a major jump is observed in the elasticity value

for ρ if the vehicle waits. At the breakeven point, for any given increase in ρ the

resulting increase in service costs per stop is 5.2 times higher if the driver decides to

wait instead of double parking.

The ratio between

§#›0¨‡T(

and

§#›0¨‡P

—

(

indicates that at the breakeven

point fines must increase more than 2.3 (1.17/0.5 ≈ 2.34) times faster than the

demand/supply ratio (ρ) to make double parking less appealing. The value of this ratio

is similar to the value found in the LTL scenario.

Discussion

Two key policy insights can be derived from the results: (a) double parking is unlikely

to disappear from urban areas unless more dedicated freight and service parking spaces

are available at peak times and (b) increasing parking fines and parking enforcement

can discourage double parking but it will not eradicate the problem for sufficiently high

values of demand/supply ratios (

. In the long-term, urban policy may be more

productive when the focus is on requiring enough on-street and off-street parking spaces

for freight and service vehicles. These conclusions roughly agree with previous studies

(Wenneman, A., Habib, K. and Roorda, M. 2015; Chen, Q. and Conway, A. 2016).

For managers at delivery or service companies the options seem limited as well.

Large package delivery companies such as FedEx or UPS understand that parking fine

costs are just another element of the cost of doing business in congested urban areas.

Pricing policies can reflect this additional cost (as in the cited case for UPS in

Manhattan) which means that parking costs are eventually transferred to consumers in

the forms of extra costs such as service or delivery fees. Alternatively, companies can

try to lower service times or delivery costs. Some costs are not transferred to direct

consumers of freight or commercial services, for example double parking severely

restricts needed roadway capacity during peak hours which causes congestion and

emissions; congestion impacts are mainly a function of service times or double-parking

duration (Lopez et al., 2016).

For companies that double park when parking is not available the largest cost

reduction is obtained when service times are reduced. For example, delivering packages

to a package dropbox at the ground level entrance of a building can save valuable

minutes otherwise spent at the elevator or carrying a hand truck through long hallways.

For companies that usually wait or cruise until parking is available the largest cost

reduction is obtained when driver wages are reduced. Significant driver wage cuts aan

option in a competitive labour market and long-term cost reductions are usually

achieved by decreasing service times or increasing driver productivity.

Managers have an incentive to increase productivity by reducing service times,

but a reduction in service times makes (ceteris paribus) double-parking a rational

response for a wider range demand/supply ratios (ρ). On the other hand, a reduction of

driver wages makes (ceteris paribus) waiting a rational response for a wider range

demand/supply ratios (ρ). Finally, it is worth noting that increasing passenger parking

fees and assigning just a small percentage of parking to commercial vehicles produces a

significant social surplus (Amer & Chow, 2016). However, in practice it also important

to monitor that commercial vehicle zones are not taken by passenger vehicles; increased

monitoring may increase (government) costs if parking fines do not cover the cost of

enforcement.

Conclusions

This study addressed the following research questions: how does parking availability

affect distribution companies’ parking behaviour? and (ii) what are the key variables

that affect parking costs? A model where long-term service costs and fleet size are

affected by changes in parking demand/supply ratios was formulated. The model also

accounts for different parking strategies such as double-park when necessary or

wait/cruise until parking is available.

Results show that as parking availability decreases, costs increase more rapidly

for LTL services than for Courier services. The difference in cost changes is related to

customer service times and route structures. It is also observed that LTL services are

more likely to cruise or wait until parking becomes available than Courier services. LTL

vehicles have longer service times and hence the probability of parking fines are higher

if the vehicles are not legally parked. The parking utilization must be high and waiting

times long to outweigh expected parking fine costs for LTL deliveries.

The results also indicate that double parking can be a company’s rational

response, especially for Courier type services, in urban environments with high parking

demand/supply ratios. Parking policy options to tackle commercial vehicle double

parking are limited and perhaps bound to fail in the long-term unless development codes

require enough on-street and off-street parking spaces for freight and service vehicles.

A novel result is that increases in logistics or service productivity achieved through a

reduction in service times makes (ceteris paribus) double-parking a rational response for

a wider range of demand/supply ratios (ρ). This demonstrates the intricacy of the

commercial vehicle parking problem, changes at the route or customer level (that are

hard to observe for a public transportation agency) may result in undesirable (but

rational from a private company perspective) changes in commercial vehicle parking

behaviour.

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ACKNOWLEDEGEMENTS

Financial support for this research was provided by the Freight Mobility Research

Institute (Transportation Center) and the Transportation Technology and People lab at

Portland State University. Any omissions or mistakes are the sole responsibility of the

authors.

Table 1. Route and Service Characteristics

Parameter

Scenario

LTL A

LTL B

Courier A

Courier B

Number of daily stops

400

Service area size (sq. mile.)

8.5

Distance between a depot and a service

area (miles)

4.5

Customer demand (lb./stop)

450

Service time (minutes)

Time window (hours)

Planning horizon (years)

Average speed (mph)

- Inside service area

- Outside service area

Delivery days per year

260

Discount factor

6.5%

Fuel/energy inflation

2.5%

Table 2. Characteristics of a Single Unit Truck

Parameter

Truck

Make

Isuzu N-series

Fuel tank / battery size

25 gallon

Fuel / electricity consumption rate

10 mpg

Gross vehicle weight

12,000 lbs.

Tare

5,672 lbs.

Payload

6,328 lbs.

Lifetime

12 years

Purchase cost

$ 50,000

Maintenance cost

$ 0.20 / mile

Vehicle insurance

$ 2,336 /year

Vehicle registration

$ 391 /year

Diesel / electricity cost

$ 2.689 / gal

Driver wage

$ 16.28 / hour

Driver health insurance

$ 7,000 / year

Driver Social Security/Medicare taxes

7.65% of driver compensation

Driver pension/retirement

25% of driver compensation

Table 3. Elasticity Values for the LTL-B Scenario

Variable

j = 1

(double-park)

j = 0

(wait)

Demand/supply ratio (ρ)

1.37

3.85

Service time, D

0.80

0.21

Parking fine, P

—

0.60

0.00

Driver wage

‡P

0.25

0.65

Purchase cost, P

’

0.06

0.13

Discount factor, e

0.02

0.04

Service Area (SA) Size, A

0.02

0.03

Distance depot to SA, r

0.02

0.05

Energy cost, P

0.01

0.02

Speed outside SA, «

-0.02

-0.03

Speed inside SA, «

-0.04

Table 4. Elasticity Values for the Courier-A Scenario

Variable

j = 1

(double-park)

j = 0

(wait)

Demand/supply ratio (ρ)

1.17

6.13

Service time, D

0.68

0.18

Parking fine, P

—

0.50

0.00

Driver wage‡P

0.27

0.57

Purchase cost,

’

0.08

0.16

Discount factor, e

0.04

0.05

Service Area (SA) Size, A

0.03

Distance depot to SA, r

0.03

0.07

Energy cost, P

0.02

0.03

Speed outside SA, «

-0.02

-0.03

Speed inside SA, «

-0.07

Figure 1. Occupancy and Average Waiting Time vs. parking utilization (ρ)

LTL A (service time = 20 min)

Courier B (service time = 3 min)

Figure 2. Long-term per-stop costs vs. parking utilization (ρ)

LTL A

Courier B

0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.50 1.00

Av. Wait time (min)

Prob. of FLZs occupied

Parking Utilization Factor (ρ)

Probability of All FLZs occupied

Expected waiting time (minute)

0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.50 1.00

Av. Wait time (minute)

Prob. of FLZs occupied

Parking Utilization Factor (ρ)

Probability of All FLZs occupied

Expected waiting time (minute)

0 0.2 0.4 0.6 0.8 1

Per-stop cost (dollar)

Parking utilization factor (ρ)

Double parking Waiting

0 0.2 0.4 0.6 0.8 1

Per-stop cost (dollar)

Parking utilization factor (ρ)

Double parking Waiting