The Use of Optimization
Techniques in Parking Facility
Siting at Stanford University
I
BY DENNIS G PERKINSON
S
tanford University’s extensive acreage
affords a luxury rare to most university campuses — parking for all faculty, staff,
students, and visitors who wish to drive to
the campus. As in any community, however,
parking at Stanford is a complex and
sometimes volatile issue.
Parking is essentially an infrastructure
element, serving the needs of academic and
residential facilities. Like any infrastructure
system, parking must be responsive to
facility plans, and parking concerns are
sometimes dwarfed by more important
considerations.
Parking, however, differs from most
infrastructure systems, such as underground
utilities, in one important respect: The
decisions that are made about parking are
perceptible to all members of the community.
The supply, location, design, and operation
of parking facilities affect the convenience
of daily users, the safety of drivers and
pedestrians, and the ambiance of the campus
environment.
Regional planning, a relatively new approach to planning at Stanford, provides a
context in which parking can be coherently
planned (Figure 1). Through the regional
planning process, long-range parking issues
can be addressed in their institutional
perspective – serving academic needs while
also attempting to strike a balance among a
variety of potentially conflicting concerns.
Until the 1960s, surface parking lots had
been interspersed among academic buildings
throughout the campus. Since then, this
pattern has changed. Interior spaces in the
central campus have been converted to
pedestrian malls and courts, sometimes
displacing parking areas. Simultaneously, the
need for academic facilities has grown and
building sites have become scarce. As a
result, many of the new buildings are located
on former parking lots. The resulting
shortage of land that can be used for parking
in and near the central campus has led the
university
to plan multilevel
parking
structures that will maintain or increase
parking supply while minimizing
site
coverage.
Parking is
essentially an
infrastructure
element, serving
academic and
residential
facilities.
As a result of the new constraints and
costs, parking questions have recently
become increasingly
complicated
and
critical. Parking planning has thus become
more sophisticated and more formalized.
Whenever possible, parking plans are now
developed in conjunction with regional
plans; formal funding sources for parking
facilities have been adopted, and greater
expertise has been brought in-house to
enhance the university’s planning and
management capabilities in these areas.
Model Methodology
Data
and
The university’s Office of Transportation
Programs has developed a computer-based
optimization model to examine the distribution of current and projected parking
spaces on campus and to determine the level
of service for each planning region. Because
the program goal is to meet the complex
needs of employees, commuting students,
and visitors, the model focuses on those
users. Other parking categories (e.g.,
handicapped, student resident, and service
vehicle) represent local needs and are
addressed based on local demand and actual
use.
The Stanford parking model assesses the
adequacy of existing and proposed parking
supply by analyzing the parking supply in
each planning subregion, the employee
population within the subregion, and the
walking distances between parking lots and
buildings across subregional and regional
boundaries. The model improves regional
planning by allowing planners to examine
hypothetical future scenarios (e.g., the
effects of parking demand that might result
from regional population changes or the
parking impacts of a proposal to site a
building or parking facility at a specific
location).
Technically, the model is a general linear
optimization model that takes advantage of
certain characteristics of the “transportation
problem.” This problem consists of m origins
(with origin i possessing a, items), n
destinations (with destination j requiring b,
items), and the sum of the a, values equal
to the sum of the b, values. The costs
associated with moving a single item from
any origin to any destination are given.
The objective of the model is to empty the
origins and fill the destinations in such a way
that the total cost is minimized. The problem
ITE JOURNAL
. APRIL 1989029
can be stated and solved as a linear programming problem whose variables are the mn
individual allocations, with the summed cost
as the objective function and with rn+n-1
independent constraints.
A program to establish the feasibility of
conceptualizing campus parking in this way
was developed by a team of graduate students
as a project for the course Operations
Research 280 (under the guidance of the
Office of Transportation Programs). The
Office of Transportation Programs then
reformulated the program to better reflect
real world parking problems, as well as to
make it more capable of analyzing various
scenarios.
In the application,
the origins are
analogous to supply (parking spaces in 25
supply regions),
the destinations
are
analogous to demand (people wanting to park
as near as possible to one of the 25
population
subregions),
and cost is
analogous to distance walked to a parker’s
destination. No monetary value is assigned
to distance walked or to walking time. The
Stanford parking pricing and allocation
policy is the same for faculty, staff, and
commuting students. Thus, the assigned
value of time is the same for all parkers in
the aggregate and is not included in the
model. The benefits of this formulation,
aside from the computational
benefits
already noted, are conceptual clarity and
utility of the output. The solution algorithms
also produce whole-unit answers. Thus, we
do not have to deal with fractional parkers
or parking spaces.
Specifically, the model provides measures
of the marginal cost (in distance walked), of
changes in supply in any subregion and the
Al
.4
FIGURE
1.
Figure 1. Map of Stanford University regions.
30.
ITE JOURNAL
. APRIL
1989
marginal cost (in distance walked), and of
changes in demand in any subregion of
campus. The model assumes that parking
behavior in the aggregate is rational and the
dominant goal is to minimize the total
distance walked. Individuals,
however,
attempt to optimize their own situation,
rather than the campus-wide situation.
Two constraints are sufficient to model
these undesirable conditions in the a~regate.
For regions where parking demand is less
than or equal to 100 spaces, all of that
demand is assigned to that region, up to the
available supply in the region. For regions
where parking demand is greater than 100
spaces, 50% of that demand is assigned to
the region, up to the available supply in the
region. No adjustments are made for
regional variation in the mix of permit type
or for the proportion of the population of a
region (faculty, staff, students, and visitors)
requiring parking. Campuswide averages are
assumed in both cases. The mix of permit
type is based on actual sales. The ratio of
parking demand to total population is based
on the observed ratio of actual parking use
to population.
The parking supply of each region is taken
from a university parking inventory created
and maintained for this purpose. Data on use
are based on the surveys conducted by the
university’s Public Safety Department and the
Office of Transportation Programs. Subregional population figures are taken from
Stanford
University
Facilities
and
Engineering Database (SUFED), maintained
by Facilities Project Management.
The output of the model is a universitywide distribution of parkers under current
conditions and for any specified future
scenario, which includes potential changes
in population and parking supply. This
formulation provides a campuswide perspective in that it allows the planners to
minimize the total walking distance of all
campus parkers and to rank subregions by
the average walking distance.
The ratio of
parking demand
to total population
is based on the
observed ratio of
actual parking
use tO pOpUldiOflm
Stanford’s parking program, based on this
procedure, helps to prioritize future parking
needs and benefits by subregion. It can also
determine the number of spaces needed to
meet those needs, while identifying the most
efficient parking configuration from the
perspective of the entire campus. Where
other land uses conflict with preferred
parking locations, the cost of these conflicts
in extra walking distance is available to
decision makers.
An Example
Following
the development
of the
optimization model, Stanford University
began construction of an administrative
office complex on an existing parking lot.
This facility, located in the Serra Triangle
region of campus (see Figure 1), displaced
390 parking spaces during construction;
however, the project resulted in a net increase
in the number of parking spaces in the region
and throughout the campus. Our surveys
showed that the users of this parking area
had destinations in several other regions. The
impact of this facility, during construction
and at completion, was forecast using the
techniques described in this report.
The case during construction
was
relatively
because
several
simple
underutilized lots were available near the
construction site. The model allowed us to
identify the “best” alternate sites (least
walking distance) for a given office location
for those displaced by construction. Region-
specitic notices, naming specific alternative
parking locations,
were prepared and
distributed. This was one of the university’s
least disruptive major construction projects.
Of more interest is the use of optimization
to predict parking behavior upon completion
of the administrative office complex. The
region-by-region cost matrix for the entire
central campus, listing walking distances in
hundreds of feet, is shown in Figure 2. The
matrix is not symmetrical because parking
supply centroids and population centroids
are often at different points within a region.
The row and column of interest in this
example is labeled SER for Serra Triangle
region.
Table 1 is a portion of the allocation matrix
STAFF,FACIJLTY
AIIDVISITDAPARKING
BY REGIcIN
COSTMATRIX
(IN HUNDREDS
OF FEET TO DESTINATION)
AA
PO
Occ
AVU
II
LA
AVVCC
ML0121z:0
R
E
G
1
8
NNNJ
UWUOMMEEE
RCC
PALM
ARB
OVAL
CIV1
NuC1
NUC2
WC3
JORD
sLmcl
3LMC5
NEC1
NEC2
NEC3
NEC4
FRO
ATHE1
ATHE2
ATw3
BON
RESU
RESE
COilL
$
10
20
19 30 26
28 40 36
9 21 16
;:
2! 12
1
6
22 15 12 18 13
221181585
12
8 12 23 18
2622222620914161
18 19 24 32 28
8162131261919919
22 13 10 14 14
30 22 14 10 12
15 10 12 20 20
25 17 16 20 20
12 13 19 28 26
18 16 18 24 23
22 23 29 36 36
3021151510891813
35 33 37 40 42
38 30 24 23 20
40 34 28 26 30
44 32 26 21 25
z524242#a9%3tt
Uc
32
35
27
32
26
32
32
36
IJUNNNNTT
22
30
15
18
1
10
22 12
30 22
11
8
15 23
5109
1 10
10
1
16
18
10
12
22
24
24
28
29
30
41
18 21
20 27
18 18
23 25
25 22
24 25
36 34
30
34
31
36
36
37
68
48 44
15$18
41 36
38 32
42
25
41
39
26
36
22
26
14
14
56
13
49
46
3043
26
32
15
20
19
24
19
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6
12
RRc
EEOSS
Ssui?vw
UEL
U2C
EFHHB
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CCC
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32 60 14
16 48 22
18 48 18
10 38 21
12 48 30
1
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1
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33501108
39 34 10
29228181
37307138
31 24 !5
35 28 10
43 36 23
24 24 27
50 45 28
27 31 33
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49 45 18
+f % 15
13 20 36
16 26 42
30
38
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20
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34
39
34
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20
10
20
24
1.S
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233235
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364048
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32 & 2732
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44 42 46444750642450565441
..
Figure 2. Cost matrix: staff, faculty, and visitor parking by region (in hundreds of !eet
to destination).
Table
1. Base Case
Allocation
Matrix
(Partial)
supply
(No.
Lot
Use
Lot
Utl
–
–
–
–
-lo
-12
-13
-5
–
–
1.00
1.00
1.00
1.00
Dual
Spaces)
ATHEI
NECI
NEC3
NE(2I
—
—
90
251
20
861
187
1400
86
0
0
101
560
2000
4
11
1
219
290
1300
0
240
0
0
1200
0
0
19
541
●
●
●
●
●
●
● ☛☛☛☛
●
●
●
●
9
●
●
999**
●
●
●
●
9
9
●
● ****
●
Demand
Dual (ft]
ATHEI
NEC3
NEC4
SER
TOTAL
560
●
00
**
. . .
9**
●
●
●
**
**
90
251
20
861
8,623
10,307
ITE JOURNAL
oAPRIL 1989.31
that shows the distribution of parking origins
and building destinations before construction. This is part of the output of the base
case optimization model. The row labeled
demand represents the demand for parking
within each region. This demand is
estimated
from parking
origin
and
destination surveys conducted periodically
by Stanford’s Office of Transportation
Programs. The row labeled dual represents
the improvement (reduction in total walking
distance) wrought by adding a parking space
in the region represented by that column.
The remaining rows represent the various
parking regions.
The first column represents each region.
The second column gives parking supply (in
number of spaces); a 5 % vacancy factor is
included in that number. Actual supply is 5 %
higher than shown, because in terms of
parker behavior and perception, a lot is
functionally full when 95% of the spaces are
occupied. The next group of columns
represent the various demand or destination
regions. The last three columns are the
change in the solution for adding a unit of
demand to the corresponding parking region
row (dual), lot use in spaces occupied (lot
use), and lot utilization as a percentage of
spaces filled (lot utl). The cells of the matrix
represent numbers of parkers. Note that because the Serra Triangle Region (SER) had
no buildings before construction and was
therefore not a destination from a parking
lot, it is not represented by a column. We
can see from Table 1 that before construction, the Serra parking region was fully
utilized by three destination regions: Near
East Campus
1 (NEC1), NEC4, and
Athletics East 1 (ATHE1).
Table 2 predicts the situation in these
selected
regions after completion
of
Table
2. Post Construction
Aiiocation
construction and occupancy. The Serra
(SER) region is now a demand region with
destinations, as well as a supply region, as
shown by the addition of the column labeled
SER. The parking capacity of the region has
also increased from 861 to 915, as shown by
the row labeled SER. The region is now fully
utilized by NEC1, NEC4, and itself. The
increase in the dual column for NEC4 shows
that the benefit of an added space in NEC4
has increased considerably. Comparison of
the values in the dual row shows that, of the
regions shown, additional demand in the
Serra region carries the least negative
impact, 700 ft of additional total walking
distance, as opposed to 1,200 to 2,100 ft. Of
the regions shown, additional growth in
Serra would have the least impact on parking
campuswide.
Changes in demand caused by the
relocation
of personnel
to the new
administrative
office complex are also
reflected in the corresponding columns. This
analysis allowed the Office of Transportation
Programs to anticipate the impact of this new
administrative office complex on campus
parking during construction,
and more
importantly, it allowed us to predict the
combined impact of this project and other
speculative future projects. Finally, the
anafysis confirmed that the SER region more
than adjacent
regions,
could support
additional growth in terms of impact on
campuswide parking.
This method of forecasting parking behavior
has successfully predicted the aggregate
behavior of parkers for two major changes
in parking supply on the Stanford campus:
the opening of a major parking structure of
Matrix
NEC4
(Partiai)
Dual
SER
ATHEI
NECI
NEC3
Demand
Dual (ft)
ATHEI
NEC3
NEC4
–
–
55
251
20
20
1200
20
0
0
530
2100
35
67
1
200
500
3t)t)
● *O
1400
0
184
0
915
0
134
0
700
0
0
t)
300
●
SER
1300
0
0
19
481
●
●
●
●
●
●
●
9
●
.
●
●
●
●
●
●
●
●
●
●
●
●
*O
00
..*
● 0.
OO
● ***
● ***
9***
●
Lot
Use
32. ITE JOURNAL
–
–
–
55
251
–
1.00
1.00
-55
20
1.00
.6
915
_
1.00
●
●
●
●
●
●
8,766
. APRIL 1989
Lot
Utl
–
-11
-13
_
10,419
Acknowledgments
The author wishes to thank Professor Alan
Manne, of Stanford University’s Operations
Research Department, and the six students
in his OR 280 class of 1985-1986 who helped
establish the feasibility of this approach to
university parking.
Bibliography
Hillier, Frederick S., and Gerald J. Lieberman.
Introduction to Operations Research, 3rd ed.
Oakland, CA: Holden-Day, 1980.
IBM. An Introduction to Linear Programming.
White Plains, NY International Business
Machines Corporation, t964.
Marine, Alan S. GAMS/MINOS:
Three Eramples.
Stanford, CA: StanfordUniversity, December
1986.
SAS Institute, Inc. SA.!VOR User’s Guide: 1983
Edition. Cary, NC: SASInstitute, Inc. 1983.■
Summary
SupPly
TOTAL
over 1,000 spaces and the displacement of
almost 400 spaces because of the construction
of an administrative
office
complex. This approach now forms the basis
of Stanford University’s campuswide parking
program that will guide the planning for all
future parking facilities at the university. As
with most quantitative tools, calibration and
adjustment are ongoing. Model results are
not used blindly, but help guide the planners’
thinking about the problem.
Lknrds G. Avkin.son
is currently director
of planning for VIA
Metropolitan Transit
in San Antonio,
Texas. At the time
this article
was
written, he was managing director of
transportion
programs
at Stanford
University.
In that capacity,
he was
responsible for Stanford’s campus transit
system, which carries over 420,000 riders
per year, the 15,0G9space parking program,
and the university’s campuswide commute
alternatives
effort.
Perkinson
holds
undergraduate and graduate degrees in
sociology fi-om the University of South
Florida and an M. S. in transportation from
Northwestern University He is an Associate
Member of ITE.