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Carbon emissions comparison of last
mile delivery versus customer pickup
Jay R. Browna & Alfred L. Guiffridab
a Department of Information Systems and Operations Management,
Loyola University Maryland, Baltimore, MD 21210, USA
b Department of Management and Information Systems, Kent State
University, Kent, OH 44242, USA
Published online: 10 Apr 2014.
To cite this article: Jay R. Brown & Alfred L. Guiffrida (2014): Carbon emissions comparison of last
mile delivery versus customer pickup, International Journal of Logistics Research and Applications: A
Leading Journal of Supply Chain Management, DOI: 10.1080/13675567.2014.907397
To link to this article: http://dx.doi.org/10.1080/13675567.2014.907397
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International Journal of Logistics: Research and Applications, 2014
http://dx.doi.org/10.1080/13675567.2014.907397
Carbon emissions comparison of last mile delivery versus
customer pickup
Jay R. Browna∗and Alfred L. Guiffridab
aDepartment of Information Systems and Operations Management, Loyola University Maryland,
Baltimore, MD 21210, USA; bDepartment of Management and Information Systems, Kent State University,
Kent, OH 44242, USA
(Received 24 July 2013; accepted 18 March 2014)
The last mile problem comprises one of the most costly and highest polluting segments of the supply
chain in which companies deliver goods to end customers. The recent trend towards green supply chains
and social and environmental responsibility has led to many new green initiatives. One business strat-
egy gaining popularity involves retailers offering home delivery. This paper performs a comprehensive
comparison of carbon emissions resulting from conventional shopping involving customer pickup with
trip chaining versus e-commerce-based online retailing involving last mile delivery to customers’ homes.
The break-even number of customers for carbon emissions equivalence is determined and analysed for
the feasibility of last mile delivery at a desired service level based on the radius of the demand region
and the delivery time available. A methodology for calculating the difference in expected carbon emis-
sions is formulated and demonstrated to quantify which method has the least harmful impact on the
environment.
Keywords: supply chain management; last mile problem; carbon emissions; sustainable logistics
1. Introduction
Environmental sustainability is well recognised in the operations and supply chain literature as a
key current and future concern for organisations competing in the global marketplace (Kleindorfer,
Singhal, and Van Wassenhove 2005;Linton, Klassen, and Jayaraman 2007;Kim and Kim 2011;
Sarkis 2012;Seuring 2013). Sustainability in an organisation is often driven along the three
core dimensions of economic, environmental, or social development (Seuring and Müller 2008).
Whether driven by social responsibility, compliance to pending and future governmental legis-
lation, or attraction to new consumer markets, organisations are addressing the impact of their
operational decisions on greenhouse gas (GHG) emissions as a part of their overall sustainability
efforts. In this climate of enhanced awareness of environmentally sustainable business practices,
the issue of GHG emissions that result from freight transportation in the product delivery process
is becoming a key concern for operations and supply chain managers (Piecyk and McKinnon
2010;Ubeda, Arcelus, and Faulin 2011).
Consumers have two basic options when making a retail purchase. E-commerce channels
allow the customer to initiate the purchase electronically without visiting the physical location
∗Corresponding author. Email: jbrown11@loyola.edu
© 2014 Taylor & Francis
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2J.R. Brown and A.L. Guiffrida
of the item to be purchased while conventional shopping methods involve visiting the phys-
ical location of the item. In conventional shopping for retail items, the customer themselves
pick up the purchased item from the retailer and self-delivers the item to their home using
their own vehicle. In e-commerce, the item is delivered to the customer by the retail seller or
by an agent contracted by the seller to provide a home delivery service. Each of these deliv-
ery options impacts the environment through the generation of GHG emissions during the
delivery of the purchased item. As identified by Ericsson, Larsson, and Brundell-Freij (2006),
CO2generated by transport trucks burning carbon-based fuel represents a serious threat to the
environment.
Several researchers have investigated the GHG emissions and carbon footprint implications
resulting from conventional shopping (customer pickup) versus delivery of the product to the cus-
tomers’ residence for e-commerce transactions (see, for example, Siikavirta et al. 2003;Edwards,
McKinnon, and Cullinane 2010). The aforementioned studies provide a baseline for investigating
the trade-off in the carbon footprint associated with product delivery under conventional shopping
and e-commerce-based online retailing and report the amount of carbon dioxide (CO2) generated
by each shopping option for retail purchases. These studies are limited in that they do not integrate
the carbon footprint burden of the two delivery options into the logistical decision-making process
under varying levels of customer demand. This limitation represents a research gap in the litera-
ture and suggests the need for a more comprehensive analysis of the environmental impact of the
logistical component of the supply chain under the alternative delivery methods for conventional
shopping and home delivery under online retailing.
In this paper, we model the carbon footprint resulting from delivery of products to customers
under conventional shopping and e-commerce-based online retailing. Our research objectives are
to: (i) integrate customer demand-based measures of carbon emissions into the decision-making
process for delivery of products to consumers, and (ii) provide a decision-making framework that
can be used to assist organisations in making decisions involving the choice of delivery options
under a policy where sustainable logistical performance is evaluated.The research contribution of
this paper is twofold. First, we integrate carbon emissions that are generated by customer demand
for the delivery of products into the logistical decision process thereby offering a more comprehen-
sive modelling environment for evaluating logistical performance. Better model development of
the environmental aspects of the logistics function in making deliveries may help to overcome the
potential negative effects to the economy of making suboptimal logistics decisions (Van Woensel,
Creten, and Vandaele 2001). Second, using break-even analysis, we provide a decision framework
that can be used by an organisation to identify a delivery option that has the least harm-
ful impact on the environment in terms of the carbon footprint under the competing delivery
options. The research herein is topical with current trends in the marketplace as retail and
online organisations such as Walmart and Amazon.com are beginning to consider or are in
the process of beta testing same-day delivery of selected products to their customers (Banjo
2012).
The remaining sections of this paper are organised as follows. In Section 2, we present a
review of the literature on sustainable aspects of delivery, which provides the foundation for
the development of our research modelling. In Section 3, we formulate our model for last mile
delivery whereby product delivery is made to the customer’s home by the seller or an agent
providing delivery service for the seller. In Section 4, we formulate a methodology for quanti-
fying expected travel distances and carbon emissions for conventional shopping involving self
deliveries of a purchased product. In Section 5, we introduce empirical data on customer travel
distances and destinations to parameterise the delivery formulations defined in Sections 4and 5.
In Section 6, we do break-even analyses and quantify the carbon emission trade-off between
conventional shopping and last mile delivery. Conclusions and future research are summarised in
Section 7.
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International Journal of Logistics: Research and Applications 3
2. Literature review
In this section, we present a general overview of the importance that delivery performance plays
in the integration and coordination of a supply chain. Following this overview, we summarise
research on the ‘last mile problem (LMP)’ in supply chain management, which represents a class
of delivery models pertaining to our stated research objective.
The importance of the delivery and the supporting logistical process is well recognised in the
operations and supply chain literature (see, for example, Chopra 2003;Stank et al. 2003). In the
early 1980s, researchers established the link between competitive performance and time-based
measures of performance (see, for example, Porter 1980;Stalk 1988). Rao, Rao, and Muniswamy
(2011) and Gunasekaran, Patel, and McGaughey (2004) identify delivery performance as a key
metric that serves to integrate performance measurement throughout a supply chain. As a time-
based performance measure, delivery timeliness has been linked to customer satisfaction (Tan,
Lyman, andWisner 2002;Forslund, Jonsson, and Mattsson 2009), the selection of suppliers (Ernst,
Kamrad, and Ord 2007;Shin, Benton, and Jun 2009;Anderson et al. 2011), production planning
and control (Lane and Szwejczewski 2000), and the interrelationship between sales globalisation
and supply chain investment (Golini and Kalchschmidt, 2010).
Of particular concern to operations and supply chain managers is the LMP which is defined
as optimising the last-leg of the business-to-consumer delivery service (Boyer, Prud’homme, and
Chung 2009). The LMP implies delivery to the physical address of the end customer from the
location (depot) where the purchased item is maintained and is acknowledged as a key element
of the order fulfilment process (Bromage 2001;Lee and Whang 2001). The logistical burden
of the LMP is considered to be one of the most costly and highest polluting segments of the
supply chain (Gevaers, Van de Voorde, and Vanelslander 2011;Ülkü 2012). While costs vary
with population density, product type, package size, and package weight, last mile delivery has
proven to incur the highest transportation costs in the supply chain (Chopra 2003). Goodman
(2005) notes that up to 28% of all transportation costs are incurred in last mile delivery. Naturally
these high costs provide an opportunity for companies to achieve substantial efficiencies through
optimal planning and proper execution of a delivery plan which may involve analyses to redesign
the overall distribution network, establishing more efficient routings, changing delivery zonings,
or upgrading to a more fuel-efficient transportation fleet.
The LMP has been investigated along several research dimensions. Huang, Smilowitz, and
Balcik (2011),Stapleton, Pedraza Martinez, and Van Wassenhove (2009), and Balcik, Beamon,
and Smilowitz (2008) have adopted a last mile framework in modelling the delivery of relief
supplies from local distribution centres to demand locations requiring aid due to natural disasters.
Boyer, Prud’homme, and Chung (2009) investigated the effect that factors such as customer den-
sity and duration of the delivery window have on delivery efficiency. Kull, Boyer, and Calantone
(2007) studied how websites influence the efficiency of the supply chain last mile via differ-
ing learning rates within the order cycle. Esper, Jensen, and Turnipseed (2003) examined the
effects of the disclosure and promotion of carrier information by online merchants on customers’
purchasing behaviour and perceptions of the delivery process. Punakivi, Yrjölä, and Holmström
(2001) examined the cost and operating efficiencies for home delivery service under conditions
of attended and unattended receipt of the delivered items.
The research cited above demonstrates the importance of the LMP in operations and supply
chain management. Of particular importance to our research herein are treatments of the LMP that
capture how the LMP interacts with environmental sustainability. McIntyre et al. (1998) identified
that traditional time and cost-based logistic performance metrics which tend to support short-term
managerial decision-making are incapable of supporting the longer term logistical decisions that
are required under a sustainable and environmentally compatible green logistics strategy. Golicic,
Boerstler, and Ellram (2010) identify that developing a sustainable supply chain transportation
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4J.R. Brown and A.L. Guiffrida
strategy is a key concern of organisations yet as reported in Supply Chain and Logistics (2009),
only 10% of companies are actively modelling their supply chain carbon footprints and have
implemented successful sustainability initiatives. According to a survey by Carbone and Moatti
(2011), 83% of companies claim to take environmental concerns into account in their strategic
decisions, yet only 35% of companies have established a green supply chain. The inclusion of
environment consideration seems to be increasing with time.
Siikavirta et al. (2003) examined the GHG emissions of alternative home delivery strategies
for the e-grocery industry and compared these findings to GHG emissions that would result
from customer pickup. Based on a case study of e-grocery customers in Helsinki Finland, the
GHG emissions were measured as a function of the travel distance incurred under the competing
delivery methods. The travel distance resulting from home delivery was analysed under a set of
conditions in which differing lengths of a promised delivery window and differing frequencies of
home delivery to a household delivery reception box were offered. Point of sales information and
the road infrastructure were used to determine the travel distances that would be incurred under
customer pickup. The results of the simulation experiments conducted suggest that home delivery
service offers the potential for significant traffic reduction over customer self pickup. Depending
on the home delivery methods used, reductions in GHG emissions in the range of 18–87% can
be achieved over customer pickup.
Edwards, McKinnon, and Cullinane (2010) contribute a comparativestudy of the CO2emissions
resulting from home delivery from online shopping and customer pickup (conventional shopping)
in the non-food retail sector. Using established secondary data sources which define the emission
factors for carbon-fuel-based vehicles, the CO2per kilometre travelled under each type of delivery
(online shopping versus conventional shopping) was estimated. Delivery failure rates for home
delivery ranging from 2% to 25% were considered and a subjective estimate of the degree of trip
chaining (picking up multiple items from multiple locations in one trip) was considered under
the conventional shopping option. Given a set of modelling assumptions and acknowledging that
numerous factors influence emissions from home deliveries, when customers buy less than 24
items per shopping trip, it is likely that the CO2per item purchased will be lower under home
delivery.
Failed home deliveries also have security and customer service implications. McKinnon and
Tallam (2003) examined the security implications associated with unattended home delivery and
presented a classification of the main types of unattended home delivery and their relative security.
Post offices, grocery stores, and petrol stations have been investigated as possible outlets for the
use as local collection and delivery points (CDPs) for customers to retrieve their missed home
deliveries. The environmental and transportation impacts of using CDPs have been investigated
by McLeod, Cherrett, and Song (2006),Song et al. (2009),Edwards, McKinnon, and Cullinane
(2010), and Song et al. (2013).
In summary, the literature indicates that attempts have been made to introduce CO2emis-
sions into the logistical delivery component of the supply chain. The studies reviewed have
provided a starting point for comparing the CO2emissions generated under the alternatives
of home delivery and customer pickup. In the study herein, we extend this type of research
through the incorporation of factors which improve the robustness of the comparison of delivery
options.
3. Stochastic last mile model development
Last mile delivery involves the final leg of delivering to end customers in the supply chain.
Generally, trucks depart from a central depot to deliver goods. In order to model this delivery
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International Journal of Logistics: Research and Applications 5
Figure 1. Demand region with last mile delivery for N=10 and T=1.
in the general case, a circular demand region with a radius of Rsurrounding a centrally located
depot is the starting point. The following assumptions are adopted:
(a) Demand is considered to be uniformly and randomly distributed, which is supported in a
review of continuous approximation models in freight distribution by Langevin, Mbaraga,
and Campbell (1996).
(b) Travel distance is measured in miles using the Manhattan (L1) distance metric.
(c) Time available for delivery is a feasibility constraint. For example, in Walmart’s beta testing
of same-day delivery, the available hours for delivery are 4–10 pm or 6 hours available for
delivery.
(d) Automobiles are the primary means for customer shopping trips.
In the development of this delivery model, demand points were uniformly and randomly generated
within a circular demand region of radius Rwith a single depot located at the circle centre (see
Figure 1for an illustration). We note that using a circular demand region is a limitation to the
model as customers may have pre-established preferences for retail shopping locations which
may not necessarily be contained in a given circular demand region. Details on how the demand
points within the assumed circular demand region were generated can be found in Appendix 1.
Truck tour distances were evaluated using the Manhattan distance (L1) metric, which implies
that only north, south, east, and west travel is allowed. Truck tour distances at each level of
customer demand were evaluated for 120 random trials. The minimum tour distance travelled
in each trial was determined based on the minimum tour distance resulting from four built-in
travelling salesman problem (TSP) solution algorithms found in Mathematica. Details on the TSP
algorithms employed to determine the minimum tour distance can be found in Appendices 2 and 3.
This methodology was previously used by Brown and Guiffrida (2012).
While total truck capacity is not considered in the numerical example, this could easily be added
as a feasibility constraint if the distribution of the customer demand volume (or perhaps weight)
was known. If the probability of exceeding available capacity exceeded a predefined threshold,
then more trucks would be required and the comparison would be based on this number of delivery
trucks.
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6J.R. Brown and A.L. Guiffrida
Figure 2. Demand sub regions with last mile delivery for N=10 and T=2.
Figure 3. Distribution of single truck expected optimal tour distances for N=50.
Similar to the trials conducted for single truck tours, additional trials were performed for T=2,
3, 4, and 5 trucks. For multiple trucks (T>1), the circular demand region of the radius Rwas
subdivided into Tequally sized and shaped sub regions. Each sub region was assigned one truck;
hence, the number of sub regions equates directly to the number of individual truck delivery tours.
Figure 2illustrates the demand sub regions for T=2 trucks.
For each level of Nand T, the minimum tour distances resulting from each of the 120 trials
conducted were aggregated and analysed using the statistical analysis system (SAS) statistical
package John’s Macintosh Program (JMP). Goodness-of-fit testing of the aggregated trial data
using the Shapiro–Wilk test supports the use of the Gaussian probability density function for
defining the distribution of the minimum tour distance travelled in satisfying ncustomers. Figure 3
illustrates the distribution of expected optimal tour travel distances for N=50 nodes (includes
the depot) and T=1 truck. This analysis was done at periodic levels of Nand Tand the Gaussian
fit held 91% of the time.
For a given radius of the demand region, R, the expected distance travelled per day, μT,isa
function of the number of trucks Tand the number of nodes (customer delivery points plus the
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International Journal of Logistics: Research and Applications 7
Table 1. Statistical information of model equations.
Mean Standard deviation
T=Equation μTR2Sig. Equation σTR2Sig.
1(0.017 +1.871√N)(R).998 <.0001∗(0.990 −0.064 ln(N))(R).528 .0075∗
2(1.862 +1.744√N)(R).999 <.0001∗(1.591 −0.199 ln(N))(R).832 .0308∗
3(2.776 +1.770√N)(R).999 <.0001∗(1.864 −0.245 ln(N))(R).871 .0206∗
4(3.721 +1.706√N)(R).998 <.0001∗(2.336 −0.367 ln(N))(R).861 .0229∗
5(4.666 +1.794√N)(R).989 .0005∗(2.789 −0.434 ln(N))(R).940 .0063∗
∗Statistically significant (p<.05).
depot), N. Based on numerical analyses where the number of nodes Nvaried from 2 to 160 and
the number of trucks Tvaried from 1 to 5 (T=1, all nodes within the demand region serviced
by one truck; T=2, two identical sub regions with one truck serving each sub region;…; and
T=5, five identical sub regions with one truck serving each sub region), the following general
form for the expected tour distance for T=1, 2,…, 5 was fit
μT=(b1T+b2T√N)R, (1)
where
b1T=y-intercept coefficient for T=1, 2,…, 5,
b2T=slope coefficient for T=1, 2,…, 5.
Fitting Equation (1)∀Tfrom the trial data yielded statistically significant results (p<0.001)
with R2in the range of 0.989–0.999. The standard deviation of Equation (1)is
σT=(c1T+c2Tln(N))R,(2)
where
c1T=y-intercept coefficient for T=1, 2, ...,5,
c2T=slope coefficient for T=1, 2, ...,5.
As illustrated in Table 1, statistical significance was achieved for the fitted distance equations
for the means and standard deviations of the tour distances across all values of T. The strengths
of the fits for the mean tour distance were very strong with slightly weaker (but acceptable) fits
for the standard deviations.
Using the fitted equations for the mean and standard deviation of the tour distance found in
Table 1, we can construct probabilistic estimates of tour distances. For example, by introducing
an average truck speed, a 95% service level for the delivery time could be created. Calculating
expected carbon emissions is a function of total tour mileage and will be discussed further in
Section 6.
4. Expected distance travelled for customer pickup
In this section, we depart from last mile delivery and look at the alternative of customers driving
to the primary or delivering store (depot) to pick up goods and return home. Figure 4illustrates
customer pickup from a depot with a circular demand region with radius, R.
In the development of the equations in this section, a depot is located at the centre of the circular
demand region with a radius of R. The following assumptions are adopted.
(a) Demand is considered to be uniformly and randomly distributed.
(b) Distance is measured in miles using the Manhattan (L1) distance metric for travel distances
and Euclidean (L2) for radius estimation (shown at the end of Section 5).
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8J.R. Brown and A.L. Guiffrida
Figure 4. Demand region with customer pickup for n=9 customers.
The expected roundtrip distance that a customer travels in order to purchase goods (without trip
chaining) can be defined mathematically. Using Euclidean distances (L2distance metric) with
uniformly and randomly distributed customers around the depot with a radius of R, the Euclidean
mean distance, ¯
DE, of a customer from the depot can be defined mathematically as follows (Stone
1991):
¯
DE=2
3R. (3)
The mean Euclidean distance as defined by Equation (3) can be converted to a mean Manhattan
distance through the integration found in Equation (4). For example, when the depot lies exactly
south from the customer (angle is 0 degrees), the L2and L1distances are both 2
3R. However,
when the depot lies perfectly southwest from the customer (angle is 45 degrees), the L1distance
is DM=r2
3sin 45◦+2
3cos 45◦=(2√2/3)R. Hence, the expected Manhattan distance, ¯
DM,
where xequals the angle in radians from 0 to 2π(equivalent to 0 to 360 degrees) is
¯
DM=2π
o2
3|sin(x)|+2
3|cos(x)|dx
2πR=8R
3π.(4)
The expected Manhattan round trip distance is 2 ¯
DM.
In order to find the proportion of customer travel distance that should be applied to the depot
due to trip chaining, a distance proportion, P(0 ≤P≤1), is used to account for trip chaining.
For example, if a customer leaves home, stops at Walmart, then the bank, then the local grocery
store, and then returns home, only a portion of that trip can be attributed to the stop at Walmart.
The distance proportion, P, is defined as
P=n
i=1(di,X−di,Z/2di,O)
n, (5)
where iis the index for each customer from 1 to n;di,Xis the total distance of the trip, including
other stops, di,Zis the distance that would have been travelled had the customer not visited the
depot, but made the other stops, di,Ois the distance from the trip origin to the depot and nis the
number of customers.
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International Journal of Logistics: Research and Applications 9
The difference, di,X−di,Z, can be thought of as the marginal distance saved due to last mile
delivery. In the event that the customer made additional stops, but would not have made the trip
at all if the depot had delivered the goods, then P=1. The expected total mileage, D, travelled
for ncustomers is
D=16nPR
3π. (6)
The distance proportion, P, can be estimated using empirical data. This proportion would be P=1
if every customer only went directly to the depot and returned home. However, many customers
will be trip chaining, making other stops at other stores or may be stopping at the depot on the
way to or from work (McLeod, Cherrett, and Song 2006). In these cases, the marginal distance
that the stop at the depot adds is the true distance that would not have occurred if the customer
had the goods delivered. Empirical data on trip chaining were collected and will be discussed in
Section 5.
Given Equation (6), fuel consumption, F, and total kilos of CO2emissions, C, can be determined
using
F=D
f=16nPR
3πf, (7)
where Fis the total gallons of fuel consumed, fis the average fuel economy in miles per gallon
(MPG), Dis the expected total mileage for ncustomers, nis the number of customers, Pis the
proportion of customer travel distance that is devoted to the depot, and Ris the radius of the
demand region around the depot.
C=cF =cD
f=16cn PR
3πf, (8)
where Cis the carbon footprint defined as total kilos of CO2emitted and cis the average CO2
emitted per gallon of fuel.
The EPA (2011) estimates that the average gasoline vehicle on the road in 2011 has a fuel
economy of around 21 MPG. Kodjak (2004) states vehicles typically used in delivery (platform
trucks, delivery vans, super-duty pickups, etc) average 7.8 MPG, which is generally diesel, and
estimates fuel economy in 2015 could rise to 10.1 MPG. However, 7.8 MPG may be a better
estimate for all delivery vehicles on the road today with an understanding that fuel economies
of both passenger vehicles and delivery vehicles are on the rise due to the introduction of more
fuel-efficient vehicles and the retiring of older vehicles.
5. Empirical data on customer travel distances
As mentioned in Section 4, one of the biggest issues in assessing the reduction of carbon emissions
resulting from last mile delivery is determining P, the proportion of distance that a customer travels
that is devoted to the depot. In a questionnaire on customer collection from a depot, McLeod,
Cherrett, and Song (2006) found that around half of respondents would engage in trip chaining,
but collected no data on the proportion of distance attributable to the depot collection for those
people. In order to gather data on P, a survey was conducted on customer stops when engaging
in conventional shopping involving a Walmart or Target in the Midwest USA with a focus on
suburban Ohio and Pennsylvania. These two stores, considered the depot, were chosen since
they are both representative of conventional shopping retail outlets. Respondents, who used only
automobiles for transportation, were asked for all addresses involved in the last trip to either
Walmart or Target.
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10 J.R. Brown and A.L. Guiffrida
Figure 5. Regression results of google map miles by L1distance.
In all, 80 responses (out of 140 possible) were received of which 55 were useable. Responses
that contained incomplete or duplicate information were discarded. Responses were analysed as
follows:
•Determining P, the proportion of customer travel distance that is devoted to the depot.
•Comparing L1distances to real-world road distances.
•Estimating the average vehicle speed of customers.
•Finding the average distance from customers to the depot and using this to determine the
estimated radius of the demand region.
As discussed, determining Pwas the primary motivation for collecting these data. Employing
Equation (5), P=0.6368. The data comprise 42% of respondents who would not have made the
trip to the other locations if home delivery had been provided. Only 5% of respondents did not
engage in trip chaining. The remaining 53% of respondents would still have made the trip to visit
the other stops had the depot delivered.
Another use of these data is comparing L1distances to road distances. All the addresses for
each response were converted to a point of latitude and longitude. From there, the great-circle
distance formula was used to calculate L1distances. For the road distances, Google Maps was
used to route the quickest trip between the addresses. Figure 5shows that the correlation between
road distance and L1distance for these observations is quite strong with an R2of 0.97647 and
a statistical significance of p<.0001. While we use L1distances throughout our estimations,
the equation (Google Map Miles =0.437 +1.026 ∗L1distance) can be used to convert these
L1distances into expected road distances. Naturally, since these data were mostly from Ohio
suburban areas, the correlation may differ in more rural or more urban areas, particularly if there
are extensive barriers such as rivers or mountains.
Road distances and travel times were obtained from Google Maps in order to establish the
average vehicle speed, which is needed for determining the radius of the demand region that can
be serviced for a given number of trucks. Figure 6shows a mean vehicle speed of 27.68 miles per
hour (MPH) with a 95% confidence interval of 27.68 ±1.55 MPH (26.13, 29.23). Interestingly
enough, this correlates almost exactly to the 27.6 MPH national average traffic speed as represented
by the EPA (EPA 2008).
In Section 6, the average distance to the depot becomes important. Using Walmart as an example,
Holmes (2005) found that the average distance of a customer to the nearest Walmart varied by the
region’s population density, but the average distance, weighted by population was 6.7 miles. The
range of this distance estimate runs from a minimum of 3.7 miles in medium density (1273–3183
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International Journal of Logistics: Research and Applications 11
Figure 6. Vehicle speeds returned by google maps for customer trips.
Figure 7. Distribution of L1distance from origin of trip to depot.
Figure 8. Distribution of L2distance from origin of trip to depot.
people per square mile) regions to 24.2 miles in sparsely populated regions. Using our survey
data, the average distances to the depot under the Manhattan and Euclidean distance metrics are
reported in Figures 7and 8, respectively.
Although these average distances can be converted to an expected delivery radius using Equa-
tions (3)or(4), we opt to use Euclidean distances (3) because it offers more precision in the
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12 J.R. Brown and A.L. Guiffrida
Table 2. Estimated delivery region radius based on mean distance to depot.
Population density Mean distance Calculated delivery
Source (1000 in 5 mile radius) to depot (miles) radius (miles)
Holmes (2005) 5–10 11.3 16.96
10–20 7.2 10.80
20–40 5.1 7.65
40–100 4.0 6.00
100–250 3.7 5.55
250–500 4.2 6.30
500 and above 6.9 10.35
Population weighted average 6.7 10.05
Our data 20–250 (estimated) 4.3 6.40
estimate of the delivery radius. Table 2lists possible mean distances to depots based on our
survey data and from Holmes (2005).
6. Break-even analyses and findings supported by empirical data
This section will analyse break-even points for the number of nodes, N(which can be converted to
nbased on the successful delivery rate) and the distance proportion, P, in terms of CO2emissions
for last mile delivery versus customer pickup. The break-even points for the number of customers
are analysed for delivery feasibility based on the results and our empirical data.
Setting Equation (8) equal to Equation (1) yields the break-even points for CO2emissions for
Nand P
16cGS(N−1)PR
3πfG=cD(b1T+b2T√N)R
fD
, (9)
where cGis the average kilos of CO2emitted per gallon of gasoline, cDis the average kilos of CO2
emitted per gallon of diesel, fGis the average fuel economy for a passenger vehicle in MPG, fDis
the average fuel economy for a delivery vehicle in MPG and S=is the percentage of deliveries
that are successful.
Examining Equation (9), we note that the demand region radius Rdoes not impact the break-
even point for Nor P. However, Rdoes impact how many customers can be serviced through last
mile delivery in a given time period. Also, the number of successfully serviced customers, n,is
equivalent to S(N– 1). The break-even equation for P(10) and the break-even equation for N
(11) are
P=3πfGcD(b1T+b2T√N)
16fDcGS(N−1)(10)
and
N=3πb2TcDfG+9(πb2TcDfG)2+64cGfDP(16cGfDP+3πb1TcDfG)
32cGfDPS 2
. (11)
While the break-even Pis not illustrated in the example, it could be useful for determining
feasibility.
The expected break-even point for the number of customers, n=S(N– 1), can be established
by parameterising Equation (11) using the following values found in the literature and through our
empirical analysis: (i) average fuel economy for a passenger vehicle is fG=21 MPG of gasoline
(EPA 2011), (ii) average fuel economy for a delivery vehicle is fD=7.8MPG of diesel (Kodjak
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International Journal of Logistics: Research and Applications 13
Table 3. Break-even points for CO2emissions.
Customers, n
Number of trucks, TS=1.00 S=0.98 S=0.88 S=0.75
T=1 truck n=29.6 n=30.2 n=33.8 n=40.0
T=2 trucks n=35.3 n=36.0 n=40.3 n=47.6
T=3 trucks n=40.4 n=41.3 n=46.2 n=54.5
T=4 trucks n=42.8 n=43.8 n=48.9 n=57.7
T=5 trucks n=49.8 n=50.8 n=56.8 n=67.0
2004), (iii) the EPA estimated the average CO2emitted per gallon of gasoline as cG=8.887 kilos,
and (iv) for diesel cD=10.180 kilos (EPA 2011). From Section 2,b1Tand b2Tvary depending on
how many trucks are doing deliveries. For T=1 truck, b1T=0.017 and b2T=1.871. Finally, as
stated previously, Pwas estimated to be 0.6368 from our empirical data.
Employing the parameterised Equation (11), Table 3gives the break-even points involving the
number of customers for CO2emissions for 1–5 trucks, T, with the rates of successful deliveries
as defined by Edwards, McKinnon, and Cullinane (2010). As the number of trucks increases, the
break-even number of customers rises because fewer trucks will always cover less distance to
service the same number of customers. The way in which a circular region divides for different
numbers of trucks explains why the gap between the break-even point for different numbers of
delivery trucks is irregular. If the average daily number of new customers requiring delivery is
less than the break-even point, then last mile delivery is not reducing the overall carbon footprint.
In order to test the feasibility of the break-even points for number of customers, we need to
address the average time a delivery truck spends at each stop and the average vehicle speed. Both
of these attributes are addressed in Equation (12), which gives the distance a vehicle can travel
given an average vehicle speed (V), hours available for delivery (H), and an average time (a)
spent at each stop
Dmax =VTH −(N−1)a
60, (12)
where Dmax is the distance in miles, Vis the average vehicle speed in MPH, Tis the number of
trucks being used for delivery, His the number of hours available for delivery per truck, Nis the
number of nodes, and ais the average minutes spent at each stop or customer location.
Using Equations (1) and (2), the service level (C), which determines the percentage of time
that the delivery route(s) will be completed within the available delivery hours, is
−1(C)=Dmax −μT
σT
, (13)
where Cis the the service level or confidence level percentage and −1(C)is the z-score that is
returned from C.
Introducing Equations (12), (1), and (2) into Equation (13)gives
−1(C)=V(TH −(N−1)(a/60)) −(b1T+b2T√N)R
(c1T+c2Tln(N))R. (14)
Solving Equation (14) for Ryields the radius of the delivery region
R=V(TH −(N−1)(a/60))
−1(C)(c1T+c2Tln(N))+b1T+b2T√N. (15)
To evaluate the maximum delivery radius (R) for a given number of trucks (T) at their correspond-
ing break-even point for the number of customers, we need to parameterise V,H, and a. Using
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14 J.R. Brown and A.L. Guiffrida
Table 4. Maximum serviceable delivery radius.
Maximum delivery radius, R
Number of trucks, TS=1.00 S=0.98 S=0.88 S=0.75
T=1 truck R=11.4 miles R=11.0 miles R=9.4 miles R=7.0 miles
T=2 trucks R=21.1 miles R=20.7 miles R=18.4 miles R=15.1 miles
T=3 trucks R=28.7 miles R=28.2 miles R=25.5 miles R=21.5 miles
T=4 trucks R=37.1 miles R=36.5 miles R=33.4 miles R=28.8 miles
T=5 trucks R=40.2 miles R=39.6 miles R=36.4 miles R=31.5 miles
Table 5. Maximum new customers per day.
Customers, n
Number of trucks, TS=1.00 S=0.98 S=0.88 S=0.75
T=1 truck n=57.7 n=56.5 n=50.8 n=43.3
T=2 trucks n=152.4 n=149.4 n=134.1 n=114.3
T=3 trucks n=254.9 n=249.8 n=224.3 n=191.2
T=4 trucks n=371.2 n=363.8 n=326.7 n=278.4
T=5 trucks n=475.7 n=466.2 n=418.6 n=356.8
V=27.68 MPH from our empirical findings, H=6 available delivery hours as per the Walmart
same-day delivery beta testing, and a=2.5 minutes.Average minutes spent at each stop, a=2.5,
was estimated from data on the average daily mileage, planned hours, and numbers of deliveries
and pickups from 33 UPS drivers (UPS 2006).Applying these values return a maximum delivery
radius with a 95% service level as shown in Table 4.
The above values of R, which represent the maximum serviceable delivery radius at the
break-even point for the number of customers, are reasonable since they exceed the empiri-
cally established R=6.4 miles. Exceeding the empirically established baseline of R=6.4 miles
insures that it is possible to service more customers than the break-even point number of cus-
tomers. Failure to exceed R=6.4 miles would have meant that last mile delivery could not have
serviced the break-even number of customers and thus would produce more carbon emissions
than customer pickup. This baseline radius of R=6.4 miles, which was established from our
empirical data is compatible with the research of Holmes (2005).
Using Equation (14), the maximum daily demand (daily new customers) that can be serviced
in a radius of R=6.4 miles at a service level of C=95% is shown in Table 5.
In order to assure that the depot is reducing the overall carbon footprint while maintaining its
95% service level, the number of customers requiring delivery needs to be between the break-even
point and the maximum number of serviceable customers. For example, when using one truck with
no failed deliveries, daily customers need to be between the break-even point of approximately
30 and the maximum number of serviceable customers, 58.
Continuing the example, in Figure 9a comparison of carbon emissions from last mile delivery
(with the best case of no failed deliveries) and customer pickup is illustrated. The illustration in
Figure 9follows directly from Equation (9). The two notches in the last mile delivery line indicate
the customer level at which the number of trucks increased by one. While Pwas found to be
0.6368 from the data, the other two levels of Prepresent the upper and lower limits of Pfrom a
90% confidence interval (0.5397 and 0.7338) on the data.
A general form for quantifying the difference in the kilos of CO2emissions produced by the
alternative delivery strategies of last mile delivery and customer pickup is defined by
CS=16cGS(N−1)PR
3πfG−cD(b1T+b2T√N)R
fD
. (16)
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International Journal of Logistics: Research and Applications 15
Figure 9. Example CO2emissions of customer pickup versus last mile delivery.
Figure 10. Example CO2emissions saved through last mile delivery.
When CS>0, last mile delivery produced lower CO2emissions than customer pickup; CS<0,
customer pickup produced lower CO2emissions than last mile delivery.
Figure 10 illustrates the trade-off defined by Equation (16) for the previously defined parameters
in which P=0.6368, R=6.4 miles, S=1, and the minimum number of trucks that can service
ncustomers are used at a service level of 95%. Again, the three levels of Prepresent the mean
and the upper and lower limits of Pfrom a 90% confidence interval (0.5397 and 0.7338) on the
data. The break-even point of 30 customers moves to 23 using the upper limit of Pand 41 using
the lower limit of P.
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16 J.R. Brown and A.L. Guiffrida
7. Conclusions
In this paper, we compared the carbon emissions resulting from the delivery of products to
customers under conventional shopping involving customer pickup and e-commerce-based online
retailing involving last mile delivery. We integrated customer demand-based measures of carbon
emissions into the decision-making process for delivery of products to consumers and provided a
decision-making framework that can be used to assist organisations in making decisions involving
the choice of delivery options under a policy where sustainable logistical performance is evaluated.
In addition, we integrated carbon emissions that are generated by customer demand for the delivery
of products into the logistical decision process thereby offering a more comprehensive modelling
environment for evaluating logistical performance. Using break-even analysis, we provided a
decision framework that can be used by an organisation to identify whether last mile delivery or
customer pickup has the least harmful impact on the environment in terms of carbon emissions.
Providing delivery to fewer customers than the break-even number of customers results in higher
carbon emissions than if the customers had picked up their purchases themselves (conventional
shopping). Finally, we provided a method to quantify the difference in CO2emissions resulting
from customer pickup versus last mile delivery as demonstrated in the numerical example and
illustrated in Figures 9and 10.
The model presented herein is limited along the following dimensions. First, automobiles were
used in the model as the only mode of transportation for customer shopping trips. The use of
automobiles for shopping trips is more common in the USA than Europe; however, other modes
of travel such as public transportation, cycling, or walking are possible (Edwards, McKinnon, and
Cullinane 2010, 109). Second, a circular customer demand region was assumed which may not
totally accommodate customer shopping preferences for specific retail locations or retail locations
selected as a part of trip chaining.
There are several aspects of this research that could be extended. Since the marginal distance
applied to the depot impacts the break-even number of customers, additional research on customer
trip chaining could be conducted. In addition, alternative delivery scenarios not originating from
the central depot could be explored. For example, if delivery is farmed out to a third party that is
not located at the central depot, the break-even point would change based on how the expected
tour distances change and what proportion of these distances should be applied to the depot due
to delivery carrier trip chaining. Finally, the break-even methodology employed herein could be
extended to include stochastic input parameters.
Acknowledgement
The authors thank the anonymous referees for their positive reviews and helpful comments.
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Appendix 1: Demand generation
In order to achieve uniformly distributed points with a single central depot located at the centre of the circular demand
region the following procedures were performed.
Let:
R=radius of the demand region
h=a distance (or new radius) from origin used in generating a node, 0 <h<R
Rand() =a generator that gives a uniform random number between 0 and 1
RADIANS() =converts a number within the parentheses from 0 to 360 into radians
A=area of the demand region =π∗R2
angle =angle (out of 360) that the generated node is from the depot
i=the number of nodes
Xi=the x coordinate of the ith node
Yi=the y coordinate of the ith node
N=number of nodes
Demand point (X, Y) generation:
Set (X1,Y1)=(0, 0)for the central depot
h=[Rand () ∗(A/π)]1/2=[Rand() ∗R2]1/2=Rand ()1/2∗R
angle =RADIANS(Rand() ∗360)
For all ifrom 2 to N,Xi=COS(angle)∗h
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International Journal of Logistics: Research and Applications 19
For all ifrom 2 to N,Yi=SIN(angle)∗h
For example, if the areas of the regions chosen are all equal to 10,000, then the radius is equal to approximately 56.42.
However, the resulting optimal tours based on these sizes are easily transferrable to different sized regions.
When changing the size of a circular region, the expected optimal tour length changes by the same factor as the change
in the radius of the region. So the optimal tour of the same distribution of points (coordinates change) in a region with a
radius of 20 miles is 2 times longer than this same representation in a region with a radius of 10 miles. In addition to the
mean doubling, the standard deviation will also double in this scenario.
Appendix 2: Travelling salesman solution algorithms employed
TwoOpt or 2-opt (Croes 1958) is a tour improvement heuristic that works by taking a complete tour and removing two
edges currently in the tour and replacing them with two edges that reconnect the tour and decrease its length. When all
edges around the tour are broken and no improvement is found, the heuristic is done.
OrOpt (Or 1976) is very similar to TwoOpt and works by removing substrings of one, two, or three nodes and reinserting
elsewhere (perhaps in a reversed order).
OrZweig (Zweig 1995) is actually a modification of the OrOpt procedure that uses neighbour lists based on the
Delaunay triangulation in order to try and improve the insertion effectiveness.
CCA stands for convex hull, cheapest insertion, angle selection and is a tour construction algorithm (Golden and
Stewart 1985). CCA works by constructing the convex hull, which can be thought of as stretching a rubber band around
the nodes as though they were thumbtacks on a bulletin board. From there, the algorithm determines where each point not
touching the rubber band should be inserted to increase the tour length the least. Among all those possibilities, the node
making the largest angle is inserted and the process repeats.
Using the minimum of these four allows for results closer to the true global minimum compared to using any one
heuristic or algorithm alone, especially as the problem size increases. There are more heuristics that could be employed,
even built-in algorithms in Mathematica like IntegerLinearProgramming, but computation time becomes unmanageable
at high node levels.
Appendix 3: Sample mathematica code
Sample code generated for Mathematica with associated output using the random node generating method described in a
previous appendix.
For a given trial where T =1, N =10, A =10000 (R =56.42):
In[1]:=FindShortestTour[{{0,0}, {6.601, −19.567}, {8.25, 40.652}, {43.122, 43.755}, {−11.085, 47.991}, {51.792,
22.197}, {−8.359, −4.464}, {−27.494, −8.565}, {−7.954, −32.486}, {5.068, −21.792}}, DistanceFunction- >
ManhattanDistance, Method- >"OrOpt"]
FindShortestTour[{{0,0}, {6.601, −19.567}, {8.25, 40.652}, {43.122, 43.755}, {−11.085, 47.991}, {51.792,22.197},
{−8.359, −4.464}, {−27.494, −8.565}, {−7.954, −32.486}, {5.068, −21.792}}, DistanceFunction- >
ManhattanDistance, Method- >"CCA"]
FindShortestTour[{{0,0},{6.601, −19.567}, {8.25, 40.652}, {43.122, 43.755}, {−11.085, 47.991}, {51.792,
22.197}, {−8.359, −4.464}, {−27.494, −8.565}, {−7.954, −32.486}, {5.068, −21.792}}, DistanceFunction- >
ManhattanDistance, Method- >"TwoOpt"]
FindShortestTour[{{0,0},{6.601, −19.567}, {8.25, 40.652}, {43.122, 43.755}, {−11.085, 47.991}, {51.792,
22.197}, {−8.359, −4.464}, {−27.494, −8.565}, {−7.954, −32.486}, {5.068, −21.792}}, DistanceFunction- >
ManhattanDistance, Method- >"OrZweig"]
Out[1]={344.386, {1, 6, 4, 3, 5, 7, 8, 9, 10, 2}} (OrOpt Algorithm)
Out[2]={347.902, {1, 7, 8, 9, 10, 2, 6, 4, 3, 5}} (CCA Algorithm)
Out[3]={347.902, {1, 7, 8, 9, 10, 2, 6, 4, 3, 5}} (TwoOpt Algorithm)
Out[4]={344.386, {1, 6, 4, 3, 5, 7, 8, 9, 10, 2}} (OrZweig Algorithm)
Minimum tour distance for this trial =344.386 (Tie between OrOpt and OrZweig)
Downloaded by [Loyola Notre Dame], [Jay Brown] at 10:38 23 April 2014
