A multiobjective land development optimization model

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A multiobjective land development optimization model: the case of New Castle County, Delaware a

b

c

d

Reza Taromi , Michael DuRoss , Bintong Chen , Ardeshir Faghri , d

e

Mingxin Li & Tracy DeLiberty a

ARCADIS US, 2410 Paces Ferry Road, Suite 400, Atlanta, GA, USA

b

Delaware Department of Transportation, 800 Bay Road, Dover, DE, USA c

Department of Business Administration, Lerner College of Business and Economics, University of Delaware, Newark, DE, USA

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d

Department of Civil & Environmental Engineering, University of Delaware, Newark, DE, USA e

Department of Geography, University of Delaware, Newark, DE, USA Published online: 19 Jan 2015.

To cite this article: Reza Taromi, Michael DuRoss, Bintong Chen, Ardeshir Faghri, Mingxin Li & Tracy DeLiberty (2015) A multiobjective land development optimization model: the case of New Castle County, Delaware, Transportation Planning and Technology, 38:3, 277-304, DOI: 10.1080/03081060.2014.997450 To link to this article: http://dx.doi.org/10.1080/03081060.2014.997450

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Transportation Planning and Technology, 2015 Vol. 38, No. 3, 277–304, http://dx.doi.org/10.1080/03081060.2014.997450

A multiobjective land development optimization model: the case of New Castle County, Delaware


Reza Taromia*, Michael DuRossb, Bintong Chenc, Ardeshir Faghrid, Mingxin Lid and Tracy DeLibertye a ARCADIS US, 2410 Paces Ferry Road, Suite 400, Atlanta, GA, USA; bDelaware Department of Transportation, 800 Bay Road, Dover, DE, USA; cDepartment of Business Administration, Lerner College of Business and Economics, University of Delaware, Newark, DE, USA; dDepartment of Civil & Environmental Engineering, University of Delaware, Newark, DE, USA; eDepartment of Geography, University of Delaware, Newark, DE, USA

(Received 26 October 2012; accepted 29 September 2014) This paper develops a multiobjective optimization model to consider transportation impacts of the future development of land. The output of the model is the best location and type of land use that has minimal negative transportation effects and uses the maximum available public transportation infrastructure. It provides tools for both planners and transportation engineers and enables them to consider different scenarios of possible policies and land development. Since multiple objectives and their nonlinear structures are considered, the model is solved using mixed integer nonlinear programming. The final results are shown in both tabular and graphical format. The effectiveness of the model is applied to the northern part of New Castle County, Delaware. The results show that the model successfully finds the best locations for both residential and commercial land uses in order to meet several criteria discussed in the paper. Keywords: multiobjective optimization model; land use; nonlinear programming; application

1. Introduction An integrated land use/transportation model is in general composed of a land use submodel and a transportation network submodel, with the outputs of one submodel transformed into inputs for the other. While the transportation models are quite standard, there are a wide variety of land use models with distinct structures. The objective of a land use model is the allocation of economic activities over a geographic space, usually a network, with economic and transportation formulations on the relationships among the activities (Ying 2007). Land use/transportation models provide a systematic methodology to evaluate policies that are designed in advance by the decision makers as inputs to the models and are usually used to compare the impacts of several alternative policies. Land use/transportation optimization is a location-allocation problem that allocates different land uses (such as residential, commercial, industrial, recreational, etc.) to specific units of land in an area using transportation related variables. Since land use planning decisions are made based on not only activities but also internal interactions between units *Corresponding author. Email: [email protected] © 2015 Taylor & Francis


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(transportation, environmental, political, etc.), solving this location-allocation problem is very complex. Love and Juel have developed a heuristic approach which employs the alternate location-allocation procedure (Love and Juel 1982). Exact solution procedures for the minimization problem, which is neither convex nor concave, have been developed by applying a branch-and-bound algorithm and a similar algorithm has been programmed by researchers (Cooper 1967; Ostresh 1978). Kuenne and Soland’s branch-and-bound algorithm derives an exact solution to this problem (Kuenne and Soland 1972). In fact, in most cases, the optimum solution may not be the best answer due to major considerations (e.g., political considerations). Depending on the size of the region and the spatial, transportation, and environmental considerations required, an enormous increase in the number of decision variables can easily result. This complexity makes the problem very hard to solve (if not impossible) in most cases. Older land use/transportation optimization techniques select optimal locations for a single land use and most of them are not able to consider different land uses within an area (Wright, Revelle, and Cohon 1983; Williams and ReVelle 1998; Cova and Church 2000). Some of these older techniques have attempted to use heuristic algorithms to solve single-site allocation problems especially when the number of variables is high (e.g., Lockwood and Moore 1993; Murray and Church 1995; Brookes 1997; Boston and Bettinger 1999; Carver 1991; Malczewski 1996; Pereira and Duckstein 1993). Therefore, sometimes it is necessary to use heuristic algorithms capable of achieving near-best solutions in a reasonable time where exact answers are not achievable or applicable due to the size of the problem (Aerts and Heuvelink 2002; Aerts et al. 2003). Recent trends in land use planning are more comprehensive in terms of applying use of geographical information systems (GIS) as well as sustainable development principles (Shaw and Xin 2003; Santé-Riveira, Crecente-Maseda, and Miranda-Barrós 2008; Gabriel, Faria, and Moglen 2006; Leccese, McCormick, and Congress 2000; Silberstein and Maser 2000; Ward, Murray, and Phinn 2003; Jenks, Williams, and Burton 2000). Current advances in technology – including faster computers and more efficient computational packages – have allowed researchers to model more realistic and comprehensive land use/ transportation optimization problems. Other advantages of current approaches are multiobjective optimizations compared to the single-objective optimizations of the past. The contribution of this research will be a multiobjective optimization considering the most important transportation effects of land use allocation instead of single or weighted optimization. Unlike most previous research, the proposed approach will optimize the combination of different types of land uses at the same time. Since transportation criteria are considered, the transportation effects of land use changes will be calculated accurately. The paper is organized as follows: Section 2 presents the location-allocation models; Section 3 is devoted to the model evaluation; Section 4 presents the description of the real world study area; Section 5 presents model application and the interpretation of the results; Section 6 provides the summary and conclusions and offers some recommendations on the future expansion of the model. 2. Location-allocation models 2.1. Location-allocation problems Location theory was first formally introduced in 1909 when Alfred Weber investigated the problem of locating a single warehouse to minimize the total travel distance between the warehouse and a set of spatially distributed customers (Brandeau and Chiu 1989).


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Location-allocation problems jointly optimize the location of facilities and the allocation of consumers to them. Simply stated, the rationale underlying location-allocation problems is optimizing (either maximizing or minimizing) the value of an objective function subject to a set of specified constraints. One attraction of location-allocation models is that they do not require much information. Basically, given the demand attributes and either facility costs or the desired number of facilities, it is possible to solve a simple problem. If it is assumed that facilities can locate anywhere on a plane, the necessary distances are calculated internally using the coordinate system. The most famous location-allocation models are p-median models. This family of median location problems involves the optimum location of a supply facility which minimizes the aggregate weighted travel distance contracted in satisfying demand. Alternate distance metrics, such as Euclidean and rectilinear, can be incorporated. The problem of optimally locating a set of p uncapacitated, supply facilities, which minimizes the total weighted distance (or transport costs) between them and then exogenously given demand points, may be expressed as (Beaumont 1981): Min Dðd; sÞ;

ð1Þ

where d and s are the vectors denoting the location of n demand points, (xi, yi), and the p supply points, (xi, yi), respectively. This optimization problem, the so-called p-median problem, equals to

Min D ¼

p n P P

Oi kij C ij

ð2Þ

ði ¼ 1; …; nÞ

ð3Þ

ði ¼ 1; …; nÞ ð j ¼ 1; …; pÞ

ð4Þ

i¼1 j¼1

subject to p P

kij ¼ 1

j¼1

kij ¼

1 0

where Oi is the quantity demanded at location (xi, yi), and the distance (or the generalized transport cost which is assumed proportional to distance between the demand point i and the supply point j is represented by Cij (i = 1,…, n; j = 1,…, p). It can be assumed that Cij is the Euclidean distance, that is rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi 2 xi xj þ yi y j C ij ¼

ð5Þ

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or rectilinear distance that is C ij ¼ xi xj þ yi yj

ð6Þ

λij is a binary variable, having the value 1 if the demand point i is allocated to supply facility j, and 0 otherwise. It is noted that consumers are allocated to their nearest facility; constraints (3 and 4) ensure the all-or-nothing allocation procedure.


2.2. Model notations In order to structure the optimization model, four objectives suitable for model formulation are chosen: (1) Minimization of open space development that encourages efficient urban land utilization; (2) Minimization of incompatibility of adjacent land uses that might prevent environmental deterioration; (3) Minimization of distance to other areas, which acts as a coarse-equivalent to accessibility; and (4) Minimization of the length of transportation network access within the study area. The following notations are considered: Ai ¼ land area at location i m ¼ land use types ð1 ¼ Commercial; 2 ¼ ResidentialÞ Transiti ¼ distance to closest transit facility at location i Highwayi ¼ distance to closest major highway at location i LUIi ¼ land use index at location i ða real number between 1 ¼ Commercial and 2 ¼ ResidentialÞ MaxDensityim ¼ maximum allowed density for land use m at location i Demandm ¼ deamand area for land use m where Ai is the total available area of the land at location i and m is the different land use types considered in this paper. In this model all the different land uses have been categorized into residential and commercial land uses. Transiti is the distance between the closest transit bus line and the closest corner of the vacant land. Highwayi is the distance between the closest major numbered highway and the closest corner of the vacant land. LUIi is the weighted average number between 1 (commercial land use) and 2 (residential land use) to show the suitability of land for future development. Figure 1 illustrates how the LUI can be calculated based on the neighbor land use types. MaxDensityim is the maximum allowed density for development for land use m at location i. The maximum density can be different for different land uses for the same location i. Demandm is the total demand area for land use m.

Transportation Planning and Technology C

C

C

R C

R

C

R C

C

R

R

C

LUI=1

281

R R

LUI=(3*1+2*2)/5=1.4

LUI=2


Figure 1. Land use index calculation.

2.3. Decision variables The model considers three decision variables: 1; if location i is picked for development 0; otherwise 1; if location i is picked for land use m Blockim ¼ 0; otherwise Xi ¼

Dim ¼ development density at location i for land use m where Xi determines if the location is picked for future development or not. If this variable is set to 0 by the optimization model, obviously Blockim and Dim will be 0. If Xi is set to 1 by the optimization model, the Blockim can have a value of 1. Blockim determines if the land that was previously selected for development becomes residential or commercial. Obviously, the same block cannot become partially residential and partially commercial as one of the settings of the model. Finally, Dim dictates the density for the future development at location i if it is already picked for development (Xi = 1) and picked for land use m (Blockim = 1). 2.4. Objective function Given the previous discussion about the model notations and decision variables, the optimization model of this paper can be written as: Minimize XX m

Ai Dim Transiti þ

XX

i

i

j

Xi Xj Distij þ

XX m

Ai Dim Highwayi

ð7Þ

i

Subject to: XX m

i

Ai Dim Demandm ; 8m

ð8Þ

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R. Taromi et al. Dim Blockim MaxDensityim ; 8i; 8m

ð9Þ

Blocki2 ¼ 0; 8LUIi ¼ 1 ðcommercialÞ

ð10Þ

Blocki1 ¼ 0; 8LUIi ¼ 2 ðresidentialÞ

ð11Þ

Blockim 2 f0; 1g; 81 < LUIi < 2ðmixÞ

ð12Þ

P

Blockim Xi ; 8i

ð13Þ

Blockim 2 f0; 1g; 8i

ð14Þ


m

P m

Xi 2 f0; 1g; 8i

ð15Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Distij ¼ ðxi xj Þ2 þ ðyi yj Þ2 ; 8i; 8j

ð16Þ

where

Through minimizing development, the model seeks to minimize the change of urban land use and therefore only reasonable development is encouraged. Objective function (7) minimizes the following: . The sum of the transit distance for all of the locations picked for development; . The distance of new developments to other under development sites; and . The sum of the major numbered highway distances for all locations picked for development. Constraint (8) ensures that the total demand for land use m is satisfied by the already picked locations for each land use. Constraint (9) checks that the allocated density for land use m at location i must be less than or equal to the maximum density for land use m at location i. Constraint (10) guarantees that Blocki is not picked for residential development if all of the surrounding neighbors are commercial (LUIi = 1). Constraint (11) guarantees that Blocki is not selected for commercial development if all of the surrounding neighbors are residential (LUIi = 2). Constraint (12) allows the blocks with LUI between 1 and 2 to be picked for either residential or commercial land uses. Constraint (13) ensures that we can allocate maximally one land use to each Blocki indicating that each piece of land can be picked for only one development. Finally, constraints (14) and (15) guarantee that the decision variables are binary. Equation (16) shows how the model calculates the aerial (Euclidean) distance between each pair of available land centroids. In the case of mixed land use, where the adjacent lands are not


283

playing a role to determine the land use for location i, constraints (11), (12), and (13) are omitted.


3. Model evaluation 3.1. Data preparation The model is tested against a hypothetical example that covers a small geographic area in the State of Delaware. A GIS is used to prepare the data for the model analysis. Environmental Systems Research Institute, Inc. ArcGIS software is chosen because it is one of the most advanced in terms of tools available for data management. Delaware Centerline (a digital, spatial representation of the State of Delaware’s statewide transportation network), Delaware Transit Corporation’s bus lines and the latest land use land cover GIS files, along with transportation analysis zone shape files, were the basic data in the GIS. The first step in preparing the data is changing the layer’s spatial reference into a selected spatial reference appropriate for the analysis. The second step is clip out the spatial extent of the study area (Northern New Castle County). The next step is to calculate the center of each land unit (polygon layer) to its closest transit and highway facility (polyline layers) using ‘Generate Near Table’ command in ArcGIS. It should be noted that only major numbered highways are considered in this research and local roads are omitted. The last step categorizes all of the land uses into different groups. The set of land uses under consideration comprises commercial (all nonresidential developments) and residential (only residential developments). The ‘Near’ and ‘Generate Near Table’ tools have been used to calculate the distance between land units to the transit bus lines and highways. During calculation process some issues and errors were found in the software and the data had to be converted into different formats or different computers or ArcGIS versions had to be used to overcome these problems. Finally, by converting all of the shape files into geodatabase format, and using ArcGIS 10, the distance tables were generated. ArcGIS is also used to calculate the centroid location (X,Y) for every land unit (block) using ‘Calculate Geometry’ tool. With this information, the model calculates the distance between blocks. In order to find out the LUI for each block, all of the neighbors that share a border with every block is located in the GIS, then using a weighted average, the LUI is calculated. In order to minimize the environmental damages, all of the vacant blocks that are adjacent to wetland or forest are not considered by the model. In other words, the model only makes decisions for those vacant lands that are not adjacent to wetland or forests. All of the data calculated in ArcGIS is then transferred into MS Excel and MS Access databases. Due to the nature of the model, LINGO proprietary optimization software has been determined as the mathematical tool to perform the optimization part. Results of the LINGO application, optimum answers, are stored in Excel files and then transferred back to the GIS environment. Using the powerful cartographic tools in GIS, maps are then generated. The answers then can be exported to Google Earth software to better visualize the optimum answer to the general public since Google Earth is more popular among the general public. Using


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Figure 2. Database and optimization process flowchart.

Movie Maker software, the GIS maps can be put together to make visually pleasing movies to show the changes during the optimization process. The process described above is shown in Figure 2. Figure 3 illustrates the study area selected for model evaluation displaying the intersection of State Route 896 and US 40 in New Castle County, Delaware. The area is sufficient for model evaluation with 59 selected vacant land units that meet all of the criteria for selection. The map also shows the LUI which determines the suitability of land for possible future developments. Figure 4 illustrates the same location in Google Earth software to show how powerful the model is in terms of visual presentation (mixed areas are colored yellow, residential areas are in red, and commercial areas are colored green). 3.2. Evaluation and validation The easiest way to evaluate and also validate the model is to check if the model picks the best locations or not. To achieve this goal, the distances calculated in ArcGIS to both transit and highway network are used. Figure 5 illustrates the map of distances between each of 59 locations to the closest transit bus line. The legend is intentionally in meters in this map while all of the other maps are in feet. This is because these data will be added to highway distance data and therefore need to be consistent. In this figure, the closest locations to the transit system are shown together with the farthest locations. So in terms of transit accessibility it is possible to see which locations are better. Figure 6 illustrates the map of distances between each of the 59 locations to the closest numbered highway. In this figure, the closest locations to the numbered highways



285

Figure 3. Vacant land map in GIS.

are shown together with the farthest locations. So, as with transit accessibility, in terms of highway accessibility it is possible to see which locations are better. Finally, Figure 7 illustrates the map of total distances between each of 59 locations to both transit and highway network. In this map the legend shows total distance. In this map, the closest locations to the highway and transit networks are shown together with the farthest locations. So in terms of total accessibility it is possible to see which locations are better. Figure 7 is thus the base map used to validate the model. The data shown in Figures 5, 6, and 7 are illustrated in Table 1. Table 1 illustrates the original land use of each of the 59 locations, and the value of the LUI calculated based on the neighborhood land use of these locations. The LUI is another way to demonstrate proposed land use. The LUI of 1 is ‘Commercial,’ 2 is ‘Residential’ and any number between 1 and 2 is ‘Mixed’. Transit, highway, and total distance shows the same numbers calculated in Figures 5, 6, and 7, respectively. Now if these numbers are ranked in ascending format, a list of best locations to develop can be generated.


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Figure 4. Vacant land map in Google Earth.

Transit distance rank is the ranking of these 59 locations based on their distances to the transit system. According to this field, Blocks 6, 33, 38, 56, 55, and 58 have the minimum distance to the transit system, so they are the best locations to develop in terms of transit accessibility. This field also reveals that Blocks 30, 35, 34, and 29 have the highest distance to the transit system and therefore they are the least desirable locations to develop in terms of transit accessibility. Highway distance rank is the ranking of these 59 locations based on their distances to the numbered highways. According to this field, Blocks 4, 37, 54, 53, and 51 have the minimum distance to the highway system so they are the best ideal locations to develop in terms of highway accessibility. This field also reveals that Blocks 15, 14, 13, 35, and 34 have the highest distance to the highway system and therefore they are the least favorable locations to develop in terms of highway accessibility. Total distance rank is the ranking of these 59 locations based on their total distances to the numbered highways and transit network. According to this field, Blocks 33, 56, 55, 5, and 22 have the minimum distance to the both of transit system and highway system so they are the best locations to develop in terms of total accessibility. This field also reveals that Blocks 13, 15, 29, 35, and 34 have the highest distance to highway and transit systems and therefore they are the least suitable locations to develop in terms of total accessibility.



287

Figure 5. Transit distance map.

Commercial rank, residential rank, and mixed rank is another way to breakdown the total accessibility based on proposed land uses. For example, the top five locations for commercial development are Blocks 56, 55, 2, 9, and 3 while the bottom five are 31, 24, 1, 50, and 30. The top five locations for residential development are Blocks 33, 22, 53, 46, and 38 and the bottom five locations are 16, 49, 14, 13, and 15. Finally, the top five locations for mixed development are Blocks 5, 23, 58, 27, and 44 and the bottom five locations are 43, 11, 29, 35, and 34. If the model is valid, it should select the top five locations first. Obviously the bottom five locations should be picked last.

4. Description of real world study area To demonstrate the effectiveness of the model in optimization of a large area, the northern part of New Castle County, Delaware is considered. This area is well developed in terms of highway and transportation networks as well as job and housing markets. The southern part of New Castle County is more rural.


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Figure 6. Highway distance map.

To conduct the application of the model developed in this paper, the land use land cover data in GIS format for the latest available year (2007) is obtained from the Delaware Data Mapping and Integration Laboratory. Using ArcGIS software, all of the areas that are considered vacant and potentially ready for development are identified using a query function. The areas that share borders with forests or wetland are excluded from this list using adjacency tools and queries in ArcGIS. The final candidates are 517 areas ready for development. Figure 8 illustrates the study area and the vacant land that meets all of the above mentioned criteria. Based on the land adjacent to the 517 chosen locations, the suitability of each location (LUI) can be determined. Figure 9 illustrates the proposed land use for each location based on the neighborhood land use. As can be seen from this map, the locations are again categorized into ‘Commercial’, ‘Residential’, and ‘Mixed’ land uses. Figure 10 illustrates the map of distances between each of the 517 locations to the closest transit bus line. In this figure, the closest locations to the transit system are shown together with the farthest locations. So in terms of transit accessibility it is possible to see which locations are better.



289

Figure 7. Total distance map.

Figure 11 illustrates the map of distances between each of the 517 locations to the closest numbered highway. In this figure, the closest locations to the highway system are shown together with the farthest locations. So in terms of highway accessibility it is possible to see which locations are better. Figure 12 illustrates the map of total distances between each of the 517 locations to both transit and highway networks. In this figure, the closest locations to highway and transit networks are shown together with the farthest locations. So in terms of total accessibility it is possible to see which locations are better. The projected household and job increases in the New Castle County area are extracted from the Delaware Population Consortium’s 2010 Annual Population Projections (Anonymous 2010). The first two rows of Table 2 are the exact numbers taken from this report. The second two rows are the net growth in number of households and jobs from 2010 for the future years. Since the study area is a portion of the New Castle County, the future projection numbers are adjusted to represent the study area’s future population and job growth. After using expert opinion, it was decided to use 50% of the

290

Block 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Original land use Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Cropland Herbaceous rangeland Herbaceous rangeland

Land use index

Proposed land use

1 1 1 1.7 1.3 1.7 1.3 1.5 1 2 1.7 2 2 2 2 2 2 2 2 2 2

Commercial Commercial Commercial Mix Mix Mix Mix Mix Commercial Residential Mix Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential

2

Residential

Transit distance

Transit distance rank

Highway distance

Highway distance rank

Total distance

Total distance rank

1314 10 51 1130 3 0 1209 24 36 2211 2185 2140 2142 2143 2224 1942 1944 1458 1333 1114 835

40 10 17 37 7 1 38 14 15 53 52 49 50 51 54 47 48 42 41 35 32

309 8 49 4 13 326 9 662 21 11 10 519 2130 2127 2055 1873 1756 1445 1199 1101 230

33 7 23 1 19 34 11 41 21 16 12 39 57 56 55 54 52 48 45 44 31

1623 18 100 1134 16 326 1218 686 56 2222 2195 2659 4272 4270 4279 3815 3700 2903 2533 2215 1065

39 6 15 33 4 23 34 26 13 43 41 45 55 54 56 51 50 47 44 42 31

8

8

9

9

17

5

Commercial rank

Residential rank

Mix rank

12 3 5 12 1 10 13 11 4 16 15 18 26 25 27 23 22 19 17 15 10 2

R. Taromi et al.


Table 1. Rank table.

Table 1 (Continued)

23 24 25 26 27 28 29 30 31 32 33 34 35

36

Herbaceous rangeland Herbaceous rangeland Herbaceous rangeland Herbaceous rangeland Herbaceous rangeland Herbaceous rangeland Cropland Idle fields Idle fields Idle fields Idle fields Herbaceous Rangeland Farm related buildings Farm related buildings

Land use index

Proposed land use

1.5

Mix

1

Transit distance


Highway distance


Total distance

Total distance rank

8

9

10

13

18

7

Commercial

752

31

706

42

1458

37

2

Residential

266

26

867

43

1133

32

1

Commercial

130

21

145

26

276

20

1.7

Mix

18

12

9

10

28

9

2

Residential

211

24

203

29

414

24

1.8 1 1 2 2 1.8

Mix Commercial Commercial Residential Residential Mix

2684 2418 441 137 0 2569

59 56 27 23 2 58

1670 1505 466 161 11 2484

50 49 38 27 15 59

4354 3922 907 298 11 5053

57 52 28 22 1 59

1.7

Mix

2460

57

2352

58

4812

58

2

Residential

1924

46

1679

51

3603

49

Commercial rank

Residential rank

Mix rank 2

11 11 7 4 7 16 14 10 6 1 18



Block

Original land use

17

21

291

292

Table 1 (Continued)

37

38

39 40 41 42 43 44 45 46 47 48

Farm related buildings Farm related buildings Shrub/brush rangeland Shrub/brush rangeland Shrub/brush rangeland Shrub/brush rangeland Shrub/brush rangeland Shrub/brush rangeland Shrub/brush rangeland Shrub/brush rangeland Shrub/brush rangeland Clear-cut

Land use index

Proposed land use

Transit distance


886

33


Total distance

Total distance rank

Commercial rank

6

2

892

27

9

Highway distance

Residential rank

Mix rank

1

Commercial

2

Residential

0

3

276

32

276

21

5

2

Residential

1785

45

341

35

2127

40

14

2

Residential

1658

44

1323

47

2980

48

20

1

Commercial

109

20

14

20

123

16

2

Residential

1118

36

206

30

1323

35

1.5

Mix

1273

39

178

28

1451

36

14

1.5

Mix

18

11

11

14

29

10

5

2

Residential

469

29

455

36

924

29

8

2

Residential

134

22

125

25

259

19

4

2

Residential

466

28

466

37

932

30

9

1.6

Mix

22

13

8

6

30

11

R. Taromi et al.


Block

Original land use

6 12

6

Block

Original land use

49 50 51 52 53 54 55 56 57 58 59

Transitional Transitional Transitional Transitional Transitional Transitional Transitional Transitional Transitional Transitional Transitional

Land use index 2 1 1 1.5 2 1.3 1 1 1.9 1.5 2

Proposed land use Residential Commercial Commercial Mix Residential Mix Commercial Commercial Mix Mix Residential

Transit distance


Highway distance


Total distance

Total distance rank

2321 1523 528 85 41 227 0 0 56 0 895

55 43 30 19 16 25 4 5 18 6 34

1851 1306 8 80 6 6 13 12 9 27 644

53 46 5 24 4 3 18 17 8 22 40

4172 2829 536 165 47 233 13 12 64 27 1538

53 46 25 17 12 18 3 2 14 8 38

Commercial rank

Residential rank

Mix rank

24 13 8 8 3 9 2 1 7 3 13



Table 1 (Continued)

293


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Figure 8. Study area and vacant land.

future population growth and 75% of future job growth as the anticipated demand for the study area. Expert opinion also revealed that the average house size in the area is about 2000 square feet and the average estimated area needed for each job is about 600 square feet. Therefore, the third two rows of Table 2 are the calculated future demand in square feet for both residential and commercial land uses in the study area. Finally, using expert opinion about the density of the development for both residential and commercial land came to the consensus that the density of 50% should be used for future commercial land use development and a density of 25% should be used for future residential development. These densities ensure there will be sufficient space for parking and other facilities in the developed sites. Initial runs of the model using these demands and densities revealed that total demand (of 52,515,300 square feet) is more than the total capacity of the land and therefore the model becomes infeasible. In fact, considering the densities, the 517 locations result in approximately 18,000,000 square feet of available land for development. In other words, the total demand cannot exceed this number and needs to be adjusted.



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Figure 9. Proposed land use for the vacant land.

To adjust the densities, different portions of the demand are used as new demand. Demand is decreased to the maximum possible numbers that can result in feasible solutions. In fact the apportioning of demand can be determined quite straightforwardly: 18,000,000 as a percentage of 52,515,300 is 34%. However, to make the calculations easier and allow the model the freedom not to choose all land, 25% of the demands are considered instead of 34%. Thus the new reduced demand, which is 25% of the demand in row 3, is recomputed in row 4 of Table 2. Finally, the rounded numbers of the demand shown in row 5 is considered as demand for residential and commercial developments during the years 2015 to 2040. 5. Model application and results The residential and commercial demand discussed in the previous section for the years 2015, 2020, 2025, 2030, 2035, and 2040 – along with 25% residential and 50% commercial densities – are then input into the model.


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Figure 10. Transit network accessibility and distance.

Figure 13 illustrates the locations picked for both commercial and residential developments by the model in the mixed land use scenario for 2040. According to this figure, while neighborhood suitability is disregarded (mixed land use), seven locations are picked for commercial development. For informational purpose and comparison only, three of the seven locations belong to the set of mixed land uses (locations 41, 464, and, 497). Three locations (locations 48, 65, and 506) are originally suitable for commercial land use and one location is originally suitable for residential land use (location 470). The model also picks 229 locations for residential development. Ninety-six of these locations belong to the set that was suitable for mixed land use, 45 belong to the set of commercial land use, and 88 belong to the set of land suitable for residential development. It has to be noted that there is no suitable land use in this run and this classification is informational only and does not have a meaning. Figure 14 illustrates the locations picked for both commercial and residential developments by the model in the neighbor scenario for 2040. According to this figure, while neighborhood suitability is important, five locations are picked for commercial



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Figure 11. Highway network accessibility and distance.

development. All these five belong to the set of commercial land use (locations 3, 48, 65, 481, and 506). The model also picks 235 locations for residential development of which 115 locations belong to the set of residential suitable land and 120 locations belong to the set of mixed land use. Table 3 provides a summary of all model runs. Each row represents the total number of picked locations picked based on the proposed land use (column header). For example, in 2015 if neighbor suitability is considered, a total of four locations (two are suitable for commercial use and two for mixed land use) are picked for commercial development. For the same year, if the suitability of land is not an issue, a total of four locations are picked. These locations are not necessarily the same as the four locations in the neighbor scenario. For residential demand if the suitability of land is considered, 13 locations are picked of which 11 are suitable for mixed development and two for residential development only. If the constraint of suitability of land is omitted, 14 locations are picked.


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Figure 12. Total accessibility and distance.

Finally, in the neighbor scenario for 2015, 73 commercial, 196 mixed and 248 residential locations remain unused (a total of 500) while in the mixed scenario there are 499 unused locations.

6. Conclusions This paper has introduced a location-allocation model to find optimum locations that cause minimum transportation impacts due to future growth in the number of jobs and households. The problem was addressed using a multiobjective approach. Recent literature was reviewed and critiqued, and revealed that most previous studies do not consider transportation effects as their main objective. In addition, the majority of previously researched models consider only one land use at a time. In this paper, the characteristics of a location-allocation model have been defined to determine the optimum locations of vacant land and the development suitable for them.

1 2 3

2010

2015

2020

2025

2030

2035

2040

198,173 275,821 – – – –

207,723 300,059 9,550 24,238 9,550,000 10,907,100 20,457,100

215,962 302,165 17,789 26,344 17,789,000 11,854,800 29,643,800

223,423 299,877 25,250 24,056 25,250,000 10,825,200 36,075,200

230,447 298,784 32,274 22,963 32,274,000 10,333,350 42,607,350

236,157 298,635 37,984 22,814 37,984,000 10,266,300 48,250,300

240,107 299,335 41,934 23,514 41,934,000 10,581,300 52,515,300

Calculated Northern Canal residential demand (SF) Calculated Northern Canal commercial demand (SF)

– –

2,387,500 2,726,775 5,114,275

4,447,250 2,963,700 7,410,950

6,312,500 2,706,300 9,018,800

8,068,500 2,583,338 10,651,838

9,496,000 2,566,575 12,062,575

10,483,500 2,645,325 13,128,825

Used Northern Canal residential demand (SF) Used Northern Canal commercial demand (SF)

– –

2,400,000 2,700,000 5,100,000

4,400,000 3,000,000 7,400,000

6,300,000 2,700,000 9,000,000

8,100,000 2,600,000 10,700,000

9,500,000 2,600,000 12,100,000

10,500,000 2,600,000 13,100,000

Estimated household (#) Estimated jobs by place of work (#) Household growth from 2010 (#) Jobs by place of work growth from 2010 (#) New Castle County residential growth (SF) New Caslte County commercial growth (SF)

Total 4 Total 5 Total



Table 2. Calculated future demand.

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Figure 13. 2040 proposed land use map for mixed land use scenario.

The model also provided a general framework to achieve optimum policies for future development. Based on the literature review, four objectives were chosen as suitable for model formulation: (1) to minimize open space development that encourages efficient urban land utilization; (2) to minimize the incompatibility of adjacent land uses that might prevent environmental deterioration; (3) to minimize distance to other areas, which acts as a coarse-equivalent to accessibility; and (4) to minimize the length of transportation network access within the study area. Due to the inclusion of multiple objectives, its nonlinear structure, and the use of integer decision variables, the model was solved using mixed integer nonlinear programming using LINGO, a well-known optimization software. Finally, to demonstrate the effectiveness of the model in optimization of a large area, the northern part of New Castle County, Delaware was considered as a case study application. Different demands for years 2015–2040 were projected and applied to the model. For each year the model provided a set of potential sites for development along



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Figure 14. 2040 proposed land use map for neighbor land use scenario.

with the proposed land use. Final results were calculated in both neighbor and mixed scenarios and the results compared for each location. One important merit of the model is that it does not require any transportation software or package to consider the key transportation effects of land use locationallocation. This advantage comes from considering the distance between locations instead of shortest time in the model. The other key merit of the model is its ease of operation. Despite how the model might look, it is easy to apply in a real world situation with a few data inputs. Accurate results complement the model. In other words, the model is both easy to apply and accurate in terms of results. Since the model is GIS-based, it can be combined with almost every GIS-based application. It makes the model easy to understand. With ever-increasing online GISbased tools such as Google Earth or Google Maps, there are many possibilities to show the results of the model in ways that are commonly understood by the general public. Finally, the model can be updated and rerun in cases of a major change in the highway network, transit network, or policy change. The model is flexible in terms of

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Table 3. Number of locations picked based on proposed land use and projection year. Proposed land use Neighbor Year

Picked for

C

M

2015

Commercial Residential Unused Total Commercial Residential Unused Total Commercial Residential Unused Total Commercial Residential Unused Total Commercial Residential Unused Total Commercial Residential Unused Total

2

2 11 183 196 3 28 165 196


2020

2025

2030

2035

2040

71 73 9 64 73 7 66 73 5 68 73 5 68 73 5 68 73

R 2 246 248 14 234 248

63 133 196

36 212 248

79 117 196

58 190 248

100 96 196

88 160 248

120 76 196

115 133 248

Total

Mix

4 13 500 517 12 42 463 517 7 99 411 517 5 137 375 517 5 188 324 517 5 235 277 517

4 14 499 517 8 46 463 517 4 93 420 517 11 141 365 517 12 192 313 517 7 229 281 517

updating. Once the input files are updated in GIS, the model can be run to obtain new results. These can be compared to the old results to show the effects of the change on the optimum result. In addition, three main criteria have been considered in the model: distance to the transit network, distance to the highway network, and compactness of the development. An extension of this model would be considering other criteria such as additional land use types, time of land availability, distance to hazardous plants or locations, step by step demand assignment, and probability of land use pick for mixed land use scenario based on LUI, which makes the models more practical but more complicated to solve. Another avenue for future expansion of the model is applying heuristic or metaheuristic algorithms to find optimal or near optimal solutions, especially for more complex multiobjective models for larger areas as case studies. It has to be noted that the current model gives an optimum and best answer. If a heuristic method is going to develop in the future, it has to be tested against an exact solution model such as the one applied in this paper for model evaluation.



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The model can be extended into specific applications, especially integration with some well-known transportation land use planning software such as Cube Land. This integration may need an extensive coding and data collection and may be a useful input for State departments of transportation. While the current model limits residential and commercial density (min and max), it might be useful to limit land density instead of group limitations. This would allow researchers to give more densities in downtown areas to include high-rise buildings and less density to rural areas in order to limit construction. Economic growth is another way of model expansion. If there is a policy to develop certain areas in the future faster than other areas, an economic growth index could be added to the model to ensure that the important areas will be given priority. Real estate price and cost of project is another important factor that could be included in future. Land price and construction price can dramatically change the optimum answers. If the model considers the development cost, the results will be closer to reality than if no cost considerations were included. Minimum property sizes can limit the results too. Currently the model does not consider any limit for construction. This could be easily allowed for by adding another constraint to the model. Finally, the type of land use considered in the model could be increased to consider more land use types other than residential and commercial. However, this may be difficult to model and analyze since more than two land use types changes the model from its current binary condition. Acknowledgments The authors wish to express their gratitude for the technical support provided by the Delaware Center for Transportation and the University of Delaware, and for data and technical expertise provided by the Delaware Department of Transportation.

Disclosure statement No potential conflict of interest was reported by the authors.

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