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Transport route location
Transport route location A theoretical
framework
William R. Black .!kpurtment
of Geogrq?hy,
A thcorctical distribution
framework
In&mu
University,
for explaining
the historical
of places based on economic
certain ncccssary assumptions.
Rloomitlgton,
follows
this.
Rccausc
the paper graphically
approach
is rcplaccd
potential
for profitable
of the
combinatorial
by a shortest-path routes.
Three
proposed
within
limits of profitability.
the geographic
Keywords:
Following
illustrates the placcmcnt of the
problem
route
location
a of
of routes for two and
addrcsscd.
which scarchcs a profit
historical
route through the statcmcnt
A discussion of the four-node
In each cast the approach
suggests that it merits further
the
cast
graphical
space based on link
problems
arc analyscd
locates routes that arc clearly
The success of the approach in replicating
the three
testing and rcfincmcnt.
Imcatiun theory. routes, network replication
Very few human activities create patterns on the earth’s surface that are as durable as the construction of cities and transportation lines. Although there is an entire body of central place theory to help us explain geographical questions related to the size, spacing and location of cities, there is a virtual absence of theory for explaining historical decisions relating to the location and placement of transport routes. This paper introduces a theoretical approach to the study of route location that will provide a foundation for better understanding why transportation lines were located where they were in the past. These historic decisions often play a critical role in locating later transport lines and, if geographers want to understand why these routes have their present location, it is important to understand the basis for these historic decisions. Of course it is impossible to develop a complete theory of route location here, but one can at least introduce the framework and illustrate its potential utility. There is no intent to develop methods for locating new transportation routes or networks. This is a planning problem that has little to do with the geographical question examined here. Operations researchers and others are now working with multiobjective programming and similar methodologies in an attempt to incorporate all factors believed to be significant for optitrzufly locating future transportation lines. Assuming such methods were available for 86
algorithm.
of a transport
is proposed.
subsidica.
nature
diffcrcnt
using the framework casts cxamincd
hcrc.
placcmcnt
considerations
three nodes, and for three nodes with construction
IN 3740.5. USA
locating transport routes in the past, then they would be important in understanding the criteria behind such decisions. However, their current role in locating facilities is minor: their historic role was non-existent.
Background Beginning more than 25 years ago there was a burst of geographical research activity directed toward replicating or predicting the structure of transportation networks. Garrison and Marble (1962, 1965) directed a major research project in this area, but it was probably the axiomatic approach of Kansky (1963) that was the best known early effort in this area. Boyce (1963) followed with the use of a methodology based on nearest neighbour methods. Black (1969, 1971) introduced a discriminant analysis approach to the problem that functioned within an iterative process to ‘build a network’. MacKinnon and Hodgson (1969) examined the question through a gravity model and optimization framework. Young (1970) also pursued the discriminant analysis approach in trying to understand both network growth and network contraction. These approaches were not particularly successful at replicating or predicting the structure of the regional transport networks of interest. As suddenly as the research area had developed in the early 196Os, it disappeared in the 1970s. Research
096~6923/93/0200~~)9
@ 1993 Butterworth-Heinemann
Ltd
Route location:
questions about the determinants of network structure, the process of network growth and contraction, and the role of competition in this process remain unanswered. However, the research area and its questions are of such basic geographic importance that thev merit further analysis. A review of the literature concerned with the problem of network generation and replication indicates that most of the approaches were woefully inadequate when it came to a theoretical framework for examining the location problem of interest. The one effort that placed the problem within an economic framework (Black, lY6Y) failed. along with the others. to identify the process of network growth correctly. Initial research in this area followed a network paradigm that assumed it was possible to replicate or generate the structure of the entire network (eg Garrison and Marble, 1965; Kansky, 1963). Operational and logical problems with the paradigm diminished interest in the approach. Aside from this, it is uncommon for an entire network to be planned or constructed in this manner. Historically. this did not occur and there are only a few contemporary exceptions (eg the Interstate Highway System and AMTRAK in the USA), and these always rely heavily on a previously existing system for their location. Although transport development was not the major concern of Merrill (lY65), he did examine the problem of transport route development as part of his larger study of migration and the growth of urban settlements in Sweden. Monte Carlo techniques selected links that became parts of transport routes. Unfortunately, later researchers did not recognize Morrill’s general approach, but instead followed a type of link-diffusion paradigm that viewed the spread of a network as similar to the spread of an innovation. Instead of a network or link-diffusion paradigm the proper approach to the study of historical transport location decisions is in terms of individual routes (sets of links) which combine to form networks. Construction of transport networks also proceeds in this manner. Transport routes were and are constructed for different purposes; three of these are notable. There are routes constructed for the potential profits that they will produce; these are based on the ‘traffic principle’. There are also routes constructed to develop a region or remove its natural resources. This type of line is perhaps best represented by the lines of penetration in the Taaffe et al (1963) ideal typical sequence of transport development; these arc based on the ‘colonization principle’. The third type of line is the one constructed to move traffic between different routes or to serve as what Wallace (1965) called bridge lines; these lines are based on a ‘connectivity principle’. Although the concern here is with lines constructed according to the traffic
W. R. Bluck
principle, the existence of the others is recognized. Funds for the construction of transport links today come from some level of government. Although this is also true of industrial development in many parts of the world today, we do not see location theory developing for the contemporary case. On the contrary, theoreticians of industrial location go back to a time when the private entrepreneur located a firm in such a way as to minimize costs or maximize revenues or profits. In the LISA. as well as some other countries, private entrepreneurs built the early transport lines primarily to produce a profit. This was true of numerous roads and highways constructed in the USA during the 18th and 19th centuries. It was also true for railroads in the USA during the IYth and early 20th centuries. In these cases, an entrepreneur would usually identify an origin and destination for a transport line, request state government permission to construct the line of interest and, after receiving this, usually in the form of a charter. acquire the right of way and begin building the line. It is this private environment that will be used to develop a theoretical framework for the analysis of historic transport route location decisions.
The present approach Since the problem of interest here involves location theory and since the whole of this area uses economic postulates, the approach here will also be economic. More specifically, the present approach will use elements of the theory of industrial location as developed by Weber (lYO9), Losch (1940), and Smith (1966, 1971) to develop a theory of route location. The theoretical structure set up by Weber assumes that a given region has a sufficient level of demand for a firm. His theory does not ask the question of whether a firm should consider a completely different region in which to locate. Even within the structure of the theory as proposed by Losch this presence of a firm is taken as given. It may very well be that the firm will not be able to generate a profit in the region, but the initial assumption is that the firm has decided it will locate in the region. Whether the firm remains in the region is a function of revenues, costs or profits depending on the particular theory. The two-node cuse In the present route location context the question of whether a firm will locate in an area is comparable to whether a general decision to connect terminus A to terminus B by some route has been made. Just as Weber sought to find the least-cost location for his firm, the objective here is to find the least-cost location for the transport route. In addition to assuming that a route is to be built, it is convenient to make certain other assumptions at 87
Route locution: W. R. Black the outset regarding environment. Several relaxed later.
the physical and economic of these assumptions will be
(1) The
(2) (3) (4) (5) (6) (7)
region of interest consists of an isotropic plane, which is devoid of variable topography, streams or other factors, which could increase the cost of or prevent the construction of transportation lines. Construction costs vary directly with distance. There can be only direct connections in the transport system; all links begin and end at nodes of the network. None of the nodes in the system is served by the mode under consideration. The region has only two potential termini for a route. There is a constant level of demand (revenues) for flow between nodes in the system. The entrepreneur will attempt to minimize construction cost.
assumptions 5 to 7 are for this Of the above, particular application. They will be relaxed later. Under these assumptions, the minimal construction cost route from A to B will be a straight line (as depicted in Figure 1). This particular solution. under assumption 6 above, would also yield a maximum profit route. Although this is admittedly a very trivial answer to a trivial question, it forms the foundation for more complex cases. Some researchers have attempted to look at a more complicted question regarding the connection of A to B. Here one must consider the works of von Stackelberg (1938) and Losch (1940) with the law of route refraction, or Werner (1968) with his multivariate extension of that ‘law’. There is no comparable problem in industrial location theory although in practice it might be similar to site planning. In the case of a transport route on a uniform plane there would be no circumstance for the use of the law of refraction, although allowing variable topography could result in its use here. The study of historical route location in geography seems to stop at some point short of examining the exact layout of the route. At that point the scale of route location problem becomes an engineering problem and it is assumed that engineering practices dictate the precise location. In a similar manner, identifying the location for an industrial plant stops short of discussing the attributes of its placement on a site. It is an irrelevant point here due to the uniform plane assumptions. but even if this assumption were relaxed it seems that the prediction of
lB
A. Figure I. The Icast-co$t route hctwccn
uniform plane 88
two
points on a
TC
TC
16
9
Figure 2. Graphic cost (TC)
rcprcscntation
with deviations
of variations
in total
from the Icast-cost route
topographically induced curves of a route may lie at least partly within the realm of the civil engineer. Returning to the simple case of a route between A and B, we may represent this graphically as in Figure 2. Note that the total cost line (TC), which is comparable to the space cost curve of Smith (1971), increases with increasing distance from point 0 on the chart. This represents the cost of deviations from the least-cost route between A and B. We may interpret the increase to the left as deviations to the left of the least-cost route and increases to the right as deviations to the right of the least-cost route. If we relax the construction cost minimization assumption, we may have a series of potential routes in the location space between A and B (as represented by Figure 3) and each of these may occupy some point on the TC line as illustrated in Figure 4. If we assume a set level of total revenue (TR) as given by assumption 6, then some of the routes will not be profitable, but it should bc noted that there are still several possible options available for the entrepreneur to obtain a profit (see Figure 4). The geographic, limits (L, and Lz of Figure 4 and the shalied area of Figure 3) crcatcd by total revenues for the locating of the transport route are analogous to the spatial margins of production identified in the industrial case by Smith (1971). The three-node
cme
Now let us assume that we have the terminus A and the terminus B, but let us also assume that there is some intermediate node C. The route location question is whether to construct the route AR or the route ACB. This is the most elementary case of a problem identified a century ago by Wellington (1887) and discussed by Haggett (1966) and Hay (1973). The geographical situation is illustrated by Figure 5 and the graphical situation by Figure 6. As the graph illustrates, passing through the intcrmediate node C will increase costs from x to x’. It will also result in an increase in revenues from y to y’. Note that the points to the right of node C on the TC curve represent longer routes that pass through the intermediate node. Also note that the additional revenue is constant by the addition of node C‘. but
Route
Figure 3. The zone of profitability
for a route between
location:
W. R. Black
A
and B
that costs continue to increase for the longer routes. In this particular case, profits are greater if the route does not pass through the intermediate node, C, since (y - x) is greater than (y’ - x’).
The three-node
case with subsidies
It may be, as illustrated in the foregoing, that C does not have a sufficient level of revenue to merit being connected to the AB route. In this case the local area may offer a certain cash contribution or subsidy to support construction of the route. This was very common during the rail construction era in the USA when companies would survey ‘two alternative routes - a route through each of two rival towns for the purpose of getting the towns to bid against each other for the railroad’ (Johnson, 1910, p. 320). Assuming this subsidy increased revenue to y” (see Figure 6), then it would be more profitable to include C than simply to construct the AB route since (y” - x’) is greater than (y - x). Although such a contribution (subsidy) would usually cover only the construction costs and not the operating cost, this was probably of little consequence since the entrepreneurs would often sell the road or railroad within a year after it was constructed, or, if they retained it, they would simply pass these operating costs on to the users of the system (in the form of tolls or freight rates). If one wanted to evaluate whether the AB route should pass through an intermediate node, D, instead of C, it would be necessary to repeat the prior analysis of the route ACB with the route ADB as the focus. This illustrates the combinatorial nature of the problem under analysis. That is, for
TC
Figure 5. The least-cost route from A to B (AB) alternative
The four-node
C
TR,
I
I
0
Distance Ll
Distance
-
L2
Figure Figure
4. Graphic
ability surrounding
case
In order to determine whether a fourth node, D, should be added to a chartered route, ACB, one reconstructs the graph using the cost of the route ACB as the least cost route. In this case one proceeds in exactly the same fashion as before, ie, one examines the additional costs and revenues of serving D and considers the profits that having D on the system will contribute. Within a deterministic context, if the total profits of serving an ACDB route are greater than those of an ACB route, then the node, D, is added to the route.
T
I
and an
C (ACB)
any set of n nodes (including endpoints), there are as many as l/2 n(n - 1) possible undirected links that may be combined to identify the set of best segments connecting the route termini.
TC
I
route through
reprcscntation
of the zone of profit-
the Icast-cost route (0)
6. The
impact of connecting
(‘ on profits of the
route from A to B: the influence of a subsidy at C on total profits
89
Route location:
W. R. Black
Wellington recognized a different aspect of the combinatorial nature of this problem. It is that the traffic revenue added to the system by another node was more than one would expect from the simple connecting of one node to another node. Instead. traffic would increase to all nodes due to the combinatorial nature of node pairs. In other words, a route from A to B will involve the traffic flow from A to B and B to A. Addition of the point C involves interaction between the pairs AB. AC, BC, BA. CA and CB. The node D makes the traffic pairs AB, AC, AD, BC, BD, CD, BA, CA, DA, CR, DB and DC. Exactly how this can be handled is not clear in an empirical sense, but it can he handled in ;I theoretical context because the theory is sufficiently abstract that one does not have to identify exactly where the additional revenues are produced. It should bc recognized that adding a node to the network makes all of its traffic and demand available to the system. As a result it is unneccssarv to consider the potential origins of its inbound traffic or the potential destinations of its outbound flows. If the place is already connected to a transport system there is a need to consider the impact this has on potential traffic from the place and this is discussed below.
would make the community less attractive. but it would not necessarily prevent a new rail line from passing through it. The potential traffic share at a node, as viewed from the pcrspcctive ol’ the entrepreneurs locating a route. probably dccrcases as a function of the number of transport lines of that mode already serving the place. At the same time it is recognized that, although the potential trafffic and the share of that traffic are important in laying out a line, they are not the only factors; there is also the desire to minimize the overall length of the lint. As a result, when the transport route is being built, it may pass through points of zero attractiveness simply because they are ‘in the way’ of the least-cost route. Of course it is unreasonable to expect that the decisions of a century ago would necessarily yield optimum (minimum cost or maximum profits) routes. There were just too many unknowns to assume that optimal choices could be made. The theoretical structure set forth earlier does identify such routes, but more importantly it identifies other profitable yet non-optimal routes as well. This is of value since it is reasonable to expect that the route selected would be only near optimal for the conditions in existence at the time.
Other extensions
Empirical testing
of the approach
Smith (1971, pp. 1X1-187) notes that the industrial firm must always make three decisions after it has decided to get involved in production. These are: where to locate, what the technology will bc and what the scale of production will be. In the present case we are examining an entrepreneur who has decided to produce transportation. The location question has been examined above, but what about the technology and scale questions‘? The technology question in this case is analogous to the mode question. In an historical sense the question was whether the route constructed would be a bridle road. a plank road, a railroad and so forth. The scale question went to the width of the road to be constructed or the number of tracks as well as the gauge of that track. Thcsc questions arc very important in the transport case since the decisions made will affect the construction costs. future operating costs and potential revenues for the transportation route of interest. These may be incorporated into the framework proposed here at a later date. Competitive
tffects
This theoretical structure at its current level development assumes away any consideration competitive effects. Whether a community already served by rail would have some impact whether it would be connected 10 what could called a ‘Wellington route’. It is recognized that 90
of of was on be this
In order to evaluate the proposed framework it is necessary to relax several of the earlier assumptions that were necessary for the graphical analysis. This is SO simply because most of these assumptions arc not met in the real world. As in the prior analysis we will assume that the termini of a route are known. Potential traffic will be allowed to vary. Topographical variations will be present. but not extreme variations. The number of intermediate nodes is variable. Several assumptions are retained. It is assumed that the intermediate nodes connected will bc connected only directly; there will be no intermediate junctions except at nodes. Construction costs are assumed to be related to distance and entrepreneurs are assumed to be profit maximizers interested in laying out routes that will maximize future profits. Finally, the assumption regarding the abscncc of the mode at all intermediate places is kept only because this was true of the lines examined. ie, the initial assumption was met. It is assumed that an indicator of future profits is some function of estimated construction and operating costs as well as revenues. It would be possible to go through some effort to obtain such estimates, but it is also possible to use surrogates for these. It was assumed that rcvcnues are related to the number of people served and that costs are related to the length of the route. Marc specifically, it was viewed as reasonable to use an indicator of potential profit for individual link pairs. under the assumption that these were selected in an
Route location:
W. R. Black
attempt to maximize profits. As an indicator of potential profits of given nodal pairs. link potential was used. This may be defined as the population of a node i added to the population of a node j divided by the distance between the two nodes. Although the additive element may be disturbing to those familiar with the gravity model, this is a potential measure. It yields a number that is the equivalent of the sum of the potential attractiveness of i to j and the attractiveness of j to i. It is reasonable to assume such potential attractiveness could be diminished by using power functions on the distance variable to reflect topographical variations (ie. differences in construction costs). Empirical evaluation involves finding the ‘shortest path’ between origin and destination termini, where the ‘distance’ between nodes is defined as negative potential. Such a metric space has unknown properties, but the selection of the shortest negative potential route appears to result in a path between the origin and destination composed of a minimum number of segments involving the largest potential links. The resulting route involves a trade-off between distance (in a topological sense) and revenues as given by the potential measure. Such a procedure appears to integrate the key properties of the previous graphical analysis and should result in a route that is located within the geographic limits of profitability. Assuming that this is a reasonable approach for evaluating some of the notions presented here, it was necessary to find some historic situations where the origin and destination for a proposed transportation line were known, where the terrain was relatively flat and where intervening places existed that could have been added to the transport line. A study of rail land acquisition @lack, 1986) provides several situations that could be used to test the theoretical statements expressed here.
I
Routes selected
and Upper Mississippi Rail(3) The Lawrenceburg road (Figure 9a) was constructed and opened to traffic between Cincinnati, Ohio (Lawrenceburg, Indiana) and Indianapolis in 1851.
The routes selected for these tests were rail lines constructed in the state of Indiana in the US Midwest. Although roads could have been utilized, they were constructed at an earlier time for which the population data are less reliable. In addition many of these were constructed at a time when only a few settlements existed in the USA. As a result such tests would not give the best evaluation of the notions proposed here. The lines selected are as follows: (1) The Indianapolis and Peru Railroad (Figure 7a) was constructed between those towns during the early 1850s. It was opened to traffic in 1854. (2) The Madison and Indianapolis Railroad (Figure 8a) was constructed between Madison and Indianapolis during the 1840s. It was opened to traffic in 1847. Journal of
Transport
Geography
199.3 Volume
I Number
2
a
0 0
0
--
0
0
0
0
0
b
0 0
0 0 0 0
0
0
0
0
0 0
0
0
C Figure 7. (a) The
route of the Indianapolis
Railroad;
(b)
graphic
representation
gcncrated
route of the Indianapolis
of the
and Peru route;
(c)
and Peru Railroad
These three railroads were constructed at about the same time (c.1850). Each has Indianapolis as one of its end termini, but this should not bias the tests in any way. Indianapolis was selected as the capital of Indiana in 1825, nine years after statehood, and it experienced rapid initial growth. Two of the other end termini were early river ports on the Ohio River, Cincinnati and Madison. The Ohio River was the major east-west corridor in the middle 1800s. The last terminus was Peru. This town was located on the Wabash-Maumee Canal, which was opened from Toledo. Ohio (on Lake Erie) to Terre Haute, Indiana in 1849. Each railroad passed through lands that were primarily agricultural. Topographic variation was minor in all cases with one notable exception. This was on the Madison to Indianapolis 91
Route location:
W. R. Rlack
b
c
Figure 8. (a) The route of the Madison and Indianapolis Railroad; (b) graphic representation of the route; (c) gcncratcd route of the Madison and Indianapolis Railroad
rail line. The line constructed from Madison to North Madison on the plain above the Ohio River Valley had a grade of nearly 6”/0, making it the steepest grade for this type of railroad in the IJSA. Such a segment would never have been constructed if there was an alternative corridor that could have been built. Abstract representations of the networks to reflect direct connections between places in existence in 1850 were prepared (see Figures 7b. 8b and 9b). The link potentials were calculated using population figures from the population census of 1850 for Indiana. The use of population assumes equal per capita demand for transportation. Although this may be an extreme assumption in some situations, it is reasonable here. Distances to be covered were relatively short, the resource base, soils, climate and terrain were nearly identical, suggesting that wealth and transport demand would not differ significantly on a per capita basis between any of the termini of interest here. Although the terrain in nearly all cases is level to gently rolling, Indiana is not a uniform plain. Therefore the distance variable in the linkpotential measure was raised to the second power. The problem of finding the shortest paths was solved using an algorithm discussed by Whitaker (1984). 92
c
Figure 9. The route of the Lawrcnccburg and IJppcr Mississippi Railroad; (b) graphic rcprcscntation of the route; (c) gcncratcd route of the Lawrcncchurg and Upper Missisippi Railroad
Results of the approach Let us now examine the accuracy of this framework for the individual railroads. Beginning with the Indianapolis and Peru Railroad the approach is not very good (see Figure 7c compared with Figure 7b). The procedure focused on the major end points, connecting Peru to Indianapolis. and indicated that there were no places in between worth connecting to the line of interest. In reality there was a bend in the line to connect Kokomo (not in Figure 7. but represented by the slight inflection to the west between Tipton and Peru). The same was true for Tipton and Noblesville. These three places were not incorporated as towns until after 1850 and their population data may include inaccuracies. Alternatively, the inclusion of these three places on the route constructed may be due to the fact that the counties through which the line passed gave land for the construction of depots or to have the railroad pass through certain communities. Blanchard (1X8.3. p. 254) notes that Tipton County (where Tipton is
Route location:
located) ‘donated certain lands for depots and freight houses and the citizens gave willingly the right of way’. Future refinements of the framework should try to incorporate this tendency in the measure of ‘potential’ attractiveness. In the case of the Lawrenceburg and Upper Mississippi Railroad the results are much better (see Figure 9c compared with 9b). In this case the generated route begins at Lawrenceburg, and connects Greensburg to St Omer to Shelbyville to Indianapolis. With the exception of St Omer this is a perfect replication of the line’s connections. The deviation in the line necessary to reach St Omer would be within the spatial limits of profitability previously mentioned. In this regard Harding (1915) notes that the original survey of the line placed the route through St Omer, but that Greensburg interests pledged $150 000 to the railroad if it would run directly to Greensburg from Lawrenceburg. The third route under analysis, the one from Indianapolis to Madison, has one major inflection point and this is at Columbus (see Figure 8b). Aside from this the actual route passed through Vernon and Franklin with insignificant deviations in the route alignment. Based on local land records the town of Franklin gave two acres to the railroad for a freight station which accounts for that slight deviation from the route generated. These are very encouraging results. Most of the differences between the actual and generated routes appear to be due to local actions not yet included in the framework. It does not seem necessary to evaluate these results statistically since a correlation coefficient calculated to compare the elements of the connection matrix segments in the actual and generated paths would be overwhelmingly significant.
Summary This paper began with an introduction to the route location problem. It was noted that prior attempts to replicate historical route location decisions have been wanting in terms of their theoretical foundation and the empirical accuracy of the procedures developed. A theoretical approach to this problem based on generally accepted tenets of industrial location theory was identified and demonstrated. It was noted that slight deviations in location might be quite reasonable given the notion of spatial limits and non-optimizing, but profit seeking, behaviour on the part of transport entrepreneurs. Moving from the theoretical side to empirical testing, the concept of profitability was defined as a link-potential measure. A shortest-path algorithm was used to identify the segments of three railroad routes constructed in Indiana during the mid-19th century. The results were very encouraging, and there appears to be some merit in further tests of these constructs in the future. Journal of Transport Geogruphy 199.3 Volume I Number 2
W. R. Black
References Black, W.R. (1969) ‘The generation of transportation networks: their growth and structure’, unpublished PhD dissertation, The University of Iowa, Iowa City Black, W.R. (1971) ‘An iterative model for generating transportation networks’, Geographical Analysis, 3, pp. 283-288 Black, W.R. (1986) Railroad land and property in Zndiana, Bloomington, IN: Transportation Rcscarch Center, Indiana University Blanchard, C. (1883) Counties of Howard and Tipton Indiana, Chicago: F.A. Battey Boyce, D.E. (1963) ‘The generation of synthetic transportation networks’, Mimco, Evanston. IL: The Transportation Center at Northwestern University Garrison. W.L. and Marble. D.F. (1962) ‘The structure of transportation networks’. Mimeo. Evanston, IL: The Transportation Center at Northwestern University W.L. and Marble, D.F. (1965) ‘A proGarrison, legomenon to the forecasting of transportation development, Mimeo, Evanston IL: The Transportation Center at Northwestern University Haggett, P. (1966) Locational analysis in human geography, New York: St Martin’s Press Harding, L.A. (1915) History of Decatur County Indiana, Indianapolis: B.F. Bowen Hay, A. (1973) Transport for the space economy: a geographical study, Seattle: University of Washington Press Johnson, E.R. (1910) American railway transporation. New York: Appleton Kansky, K.J. (1963) Structure of transportation networks: relationships between network geometry and regional characteristics, Research Paper No 84, Chicago: Dcpartment of Geography, The University of Chicago LBsch. A. (1940) Die riiumliche Ordnung der Wirtschaft, trans. Woglom, W.W. (1954) The economics of location, New Haven: Yale University Press MacKinnon. R.D. and Hodgson. M.J. (1969) The highway system of Southern Ontario and Quebec: some simple network generation models. Research Report No 18, Toronto: Ccntrc for Urban and Community Studies, University of Toronto Merrill, R.L. (1965) Migration and the spread and growth of urban settlement, Series B. No 26 Lund, Swcdcn: Lund Studies in Geography, The Royal University of Lund Smith, D.M. (1966) ‘A theoretical framework for gcographical studies of industrial location, Economic Geography, 42, pp. 95-l 13 Smith. D.M. (1971) Industrial location, New York: Wiley von Stackclbcrg, H. (193X) ‘Das Brcchungsgcsctz dcs Verkehrs’. Jahrbiicherftir NationalBkonomie und Statistik. Bd. 148, Jcna, trans. Burdack. J. (1990) The law of refraction of transportation. Occasional Paper Series No I, Bloomington, IN: Transportation Specialty Group of the Association of American Gcographcrs Taaffc. E.J.. Merrill, R.L. and Gould, P.R. (lY63) ‘Transport expansion in underdeveloped countries: a comparative analysis’, Geographical Review. 53. pp. 503-529 Wallace, W.W. (1965) ‘The bridge lint: a distinctive type of Anglo-American railroad’, Economic Geography, 41, pp. 1-38
93
Route
location:
W. R. Black
Wcbcr. A. (1WN) Uher dm Stardori der Industrierz. trans. Fricdrich. C.J. (1929) Alfred W&r‘s theory of the locmrion of irzdlrstries. Chicago: University of Chicago Press Wellington. A.M. (1X87) The economic theory of the location of railways. New York: Wiley Werner, C. (1968) ‘The law of refraction in transportation
94
geography: its multivariate extension’. (‘rrr~rrtlirr~~Gcographrr, 12. pp. 2X-N Whitakcr. D. (19X4) OR 011 fhe micro. New York: Wile! Young. C.W. (Ic)70) ‘Transportation network dcvclopmcnt: the railroad network of southern Michigan’. unpublished PhD dissertation. Michigan state University, East LanGng
framework
William R. Black .!kpurtment
of Geogrq?hy,
A thcorctical distribution
framework
In&mu
University,
for explaining
the historical
of places based on economic
certain ncccssary assumptions.
Rloomitlgton,
follows
this.
Rccausc
the paper graphically
approach
is rcplaccd
potential
for profitable
of the
combinatorial
by a shortest-path routes.
Three
proposed
within
limits of profitability.
the geographic
Keywords:
Following
illustrates the placcmcnt of the
problem
route
location
a of
of routes for two and
addrcsscd.
which scarchcs a profit
historical
route through the statcmcnt
A discussion of the four-node
In each cast the approach
suggests that it merits further
the
cast
graphical
space based on link
problems
arc analyscd
locates routes that arc clearly
The success of the approach in replicating
the three
testing and rcfincmcnt.
Imcatiun theory. routes, network replication
Very few human activities create patterns on the earth’s surface that are as durable as the construction of cities and transportation lines. Although there is an entire body of central place theory to help us explain geographical questions related to the size, spacing and location of cities, there is a virtual absence of theory for explaining historical decisions relating to the location and placement of transport routes. This paper introduces a theoretical approach to the study of route location that will provide a foundation for better understanding why transportation lines were located where they were in the past. These historic decisions often play a critical role in locating later transport lines and, if geographers want to understand why these routes have their present location, it is important to understand the basis for these historic decisions. Of course it is impossible to develop a complete theory of route location here, but one can at least introduce the framework and illustrate its potential utility. There is no intent to develop methods for locating new transportation routes or networks. This is a planning problem that has little to do with the geographical question examined here. Operations researchers and others are now working with multiobjective programming and similar methodologies in an attempt to incorporate all factors believed to be significant for optitrzufly locating future transportation lines. Assuming such methods were available for 86
algorithm.
of a transport
is proposed.
subsidica.
nature
diffcrcnt
using the framework casts cxamincd
hcrc.
placcmcnt
considerations
three nodes, and for three nodes with construction
IN 3740.5. USA
locating transport routes in the past, then they would be important in understanding the criteria behind such decisions. However, their current role in locating facilities is minor: their historic role was non-existent.
Background Beginning more than 25 years ago there was a burst of geographical research activity directed toward replicating or predicting the structure of transportation networks. Garrison and Marble (1962, 1965) directed a major research project in this area, but it was probably the axiomatic approach of Kansky (1963) that was the best known early effort in this area. Boyce (1963) followed with the use of a methodology based on nearest neighbour methods. Black (1969, 1971) introduced a discriminant analysis approach to the problem that functioned within an iterative process to ‘build a network’. MacKinnon and Hodgson (1969) examined the question through a gravity model and optimization framework. Young (1970) also pursued the discriminant analysis approach in trying to understand both network growth and network contraction. These approaches were not particularly successful at replicating or predicting the structure of the regional transport networks of interest. As suddenly as the research area had developed in the early 196Os, it disappeared in the 1970s. Research
096~6923/93/0200~~)9
@ 1993 Butterworth-Heinemann
Ltd
Route location:
questions about the determinants of network structure, the process of network growth and contraction, and the role of competition in this process remain unanswered. However, the research area and its questions are of such basic geographic importance that thev merit further analysis. A review of the literature concerned with the problem of network generation and replication indicates that most of the approaches were woefully inadequate when it came to a theoretical framework for examining the location problem of interest. The one effort that placed the problem within an economic framework (Black, lY6Y) failed. along with the others. to identify the process of network growth correctly. Initial research in this area followed a network paradigm that assumed it was possible to replicate or generate the structure of the entire network (eg Garrison and Marble, 1965; Kansky, 1963). Operational and logical problems with the paradigm diminished interest in the approach. Aside from this, it is uncommon for an entire network to be planned or constructed in this manner. Historically. this did not occur and there are only a few contemporary exceptions (eg the Interstate Highway System and AMTRAK in the USA), and these always rely heavily on a previously existing system for their location. Although transport development was not the major concern of Merrill (lY65), he did examine the problem of transport route development as part of his larger study of migration and the growth of urban settlements in Sweden. Monte Carlo techniques selected links that became parts of transport routes. Unfortunately, later researchers did not recognize Morrill’s general approach, but instead followed a type of link-diffusion paradigm that viewed the spread of a network as similar to the spread of an innovation. Instead of a network or link-diffusion paradigm the proper approach to the study of historical transport location decisions is in terms of individual routes (sets of links) which combine to form networks. Construction of transport networks also proceeds in this manner. Transport routes were and are constructed for different purposes; three of these are notable. There are routes constructed for the potential profits that they will produce; these are based on the ‘traffic principle’. There are also routes constructed to develop a region or remove its natural resources. This type of line is perhaps best represented by the lines of penetration in the Taaffe et al (1963) ideal typical sequence of transport development; these arc based on the ‘colonization principle’. The third type of line is the one constructed to move traffic between different routes or to serve as what Wallace (1965) called bridge lines; these lines are based on a ‘connectivity principle’. Although the concern here is with lines constructed according to the traffic
W. R. Bluck
principle, the existence of the others is recognized. Funds for the construction of transport links today come from some level of government. Although this is also true of industrial development in many parts of the world today, we do not see location theory developing for the contemporary case. On the contrary, theoreticians of industrial location go back to a time when the private entrepreneur located a firm in such a way as to minimize costs or maximize revenues or profits. In the LISA. as well as some other countries, private entrepreneurs built the early transport lines primarily to produce a profit. This was true of numerous roads and highways constructed in the USA during the 18th and 19th centuries. It was also true for railroads in the USA during the IYth and early 20th centuries. In these cases, an entrepreneur would usually identify an origin and destination for a transport line, request state government permission to construct the line of interest and, after receiving this, usually in the form of a charter. acquire the right of way and begin building the line. It is this private environment that will be used to develop a theoretical framework for the analysis of historic transport route location decisions.
The present approach Since the problem of interest here involves location theory and since the whole of this area uses economic postulates, the approach here will also be economic. More specifically, the present approach will use elements of the theory of industrial location as developed by Weber (lYO9), Losch (1940), and Smith (1966, 1971) to develop a theory of route location. The theoretical structure set up by Weber assumes that a given region has a sufficient level of demand for a firm. His theory does not ask the question of whether a firm should consider a completely different region in which to locate. Even within the structure of the theory as proposed by Losch this presence of a firm is taken as given. It may very well be that the firm will not be able to generate a profit in the region, but the initial assumption is that the firm has decided it will locate in the region. Whether the firm remains in the region is a function of revenues, costs or profits depending on the particular theory. The two-node cuse In the present route location context the question of whether a firm will locate in an area is comparable to whether a general decision to connect terminus A to terminus B by some route has been made. Just as Weber sought to find the least-cost location for his firm, the objective here is to find the least-cost location for the transport route. In addition to assuming that a route is to be built, it is convenient to make certain other assumptions at 87
Route locution: W. R. Black the outset regarding environment. Several relaxed later.
the physical and economic of these assumptions will be
(1) The
(2) (3) (4) (5) (6) (7)
region of interest consists of an isotropic plane, which is devoid of variable topography, streams or other factors, which could increase the cost of or prevent the construction of transportation lines. Construction costs vary directly with distance. There can be only direct connections in the transport system; all links begin and end at nodes of the network. None of the nodes in the system is served by the mode under consideration. The region has only two potential termini for a route. There is a constant level of demand (revenues) for flow between nodes in the system. The entrepreneur will attempt to minimize construction cost.
assumptions 5 to 7 are for this Of the above, particular application. They will be relaxed later. Under these assumptions, the minimal construction cost route from A to B will be a straight line (as depicted in Figure 1). This particular solution. under assumption 6 above, would also yield a maximum profit route. Although this is admittedly a very trivial answer to a trivial question, it forms the foundation for more complex cases. Some researchers have attempted to look at a more complicted question regarding the connection of A to B. Here one must consider the works of von Stackelberg (1938) and Losch (1940) with the law of route refraction, or Werner (1968) with his multivariate extension of that ‘law’. There is no comparable problem in industrial location theory although in practice it might be similar to site planning. In the case of a transport route on a uniform plane there would be no circumstance for the use of the law of refraction, although allowing variable topography could result in its use here. The study of historical route location in geography seems to stop at some point short of examining the exact layout of the route. At that point the scale of route location problem becomes an engineering problem and it is assumed that engineering practices dictate the precise location. In a similar manner, identifying the location for an industrial plant stops short of discussing the attributes of its placement on a site. It is an irrelevant point here due to the uniform plane assumptions. but even if this assumption were relaxed it seems that the prediction of
lB
A. Figure I. The Icast-co$t route hctwccn
uniform plane 88
two
points on a
TC
TC
16
9
Figure 2. Graphic cost (TC)
rcprcscntation
with deviations
of variations
in total
from the Icast-cost route
topographically induced curves of a route may lie at least partly within the realm of the civil engineer. Returning to the simple case of a route between A and B, we may represent this graphically as in Figure 2. Note that the total cost line (TC), which is comparable to the space cost curve of Smith (1971), increases with increasing distance from point 0 on the chart. This represents the cost of deviations from the least-cost route between A and B. We may interpret the increase to the left as deviations to the left of the least-cost route and increases to the right as deviations to the right of the least-cost route. If we relax the construction cost minimization assumption, we may have a series of potential routes in the location space between A and B (as represented by Figure 3) and each of these may occupy some point on the TC line as illustrated in Figure 4. If we assume a set level of total revenue (TR) as given by assumption 6, then some of the routes will not be profitable, but it should bc noted that there are still several possible options available for the entrepreneur to obtain a profit (see Figure 4). The geographic, limits (L, and Lz of Figure 4 and the shalied area of Figure 3) crcatcd by total revenues for the locating of the transport route are analogous to the spatial margins of production identified in the industrial case by Smith (1971). The three-node
cme
Now let us assume that we have the terminus A and the terminus B, but let us also assume that there is some intermediate node C. The route location question is whether to construct the route AR or the route ACB. This is the most elementary case of a problem identified a century ago by Wellington (1887) and discussed by Haggett (1966) and Hay (1973). The geographical situation is illustrated by Figure 5 and the graphical situation by Figure 6. As the graph illustrates, passing through the intcrmediate node C will increase costs from x to x’. It will also result in an increase in revenues from y to y’. Note that the points to the right of node C on the TC curve represent longer routes that pass through the intermediate node. Also note that the additional revenue is constant by the addition of node C‘. but
Route
Figure 3. The zone of profitability
for a route between
location:
W. R. Black
A
and B
that costs continue to increase for the longer routes. In this particular case, profits are greater if the route does not pass through the intermediate node, C, since (y - x) is greater than (y’ - x’).
The three-node
case with subsidies
It may be, as illustrated in the foregoing, that C does not have a sufficient level of revenue to merit being connected to the AB route. In this case the local area may offer a certain cash contribution or subsidy to support construction of the route. This was very common during the rail construction era in the USA when companies would survey ‘two alternative routes - a route through each of two rival towns for the purpose of getting the towns to bid against each other for the railroad’ (Johnson, 1910, p. 320). Assuming this subsidy increased revenue to y” (see Figure 6), then it would be more profitable to include C than simply to construct the AB route since (y” - x’) is greater than (y - x). Although such a contribution (subsidy) would usually cover only the construction costs and not the operating cost, this was probably of little consequence since the entrepreneurs would often sell the road or railroad within a year after it was constructed, or, if they retained it, they would simply pass these operating costs on to the users of the system (in the form of tolls or freight rates). If one wanted to evaluate whether the AB route should pass through an intermediate node, D, instead of C, it would be necessary to repeat the prior analysis of the route ACB with the route ADB as the focus. This illustrates the combinatorial nature of the problem under analysis. That is, for
TC
Figure 5. The least-cost route from A to B (AB) alternative
The four-node
C
TR,
I
I
0
Distance Ll
Distance
-
L2
Figure Figure
4. Graphic
ability surrounding
case
In order to determine whether a fourth node, D, should be added to a chartered route, ACB, one reconstructs the graph using the cost of the route ACB as the least cost route. In this case one proceeds in exactly the same fashion as before, ie, one examines the additional costs and revenues of serving D and considers the profits that having D on the system will contribute. Within a deterministic context, if the total profits of serving an ACDB route are greater than those of an ACB route, then the node, D, is added to the route.
T
I
and an
C (ACB)
any set of n nodes (including endpoints), there are as many as l/2 n(n - 1) possible undirected links that may be combined to identify the set of best segments connecting the route termini.
TC
I
route through
reprcscntation
of the zone of profit-
the Icast-cost route (0)
6. The
impact of connecting
(‘ on profits of the
route from A to B: the influence of a subsidy at C on total profits
89
Route location:
W. R. Black
Wellington recognized a different aspect of the combinatorial nature of this problem. It is that the traffic revenue added to the system by another node was more than one would expect from the simple connecting of one node to another node. Instead. traffic would increase to all nodes due to the combinatorial nature of node pairs. In other words, a route from A to B will involve the traffic flow from A to B and B to A. Addition of the point C involves interaction between the pairs AB. AC, BC, BA. CA and CB. The node D makes the traffic pairs AB, AC, AD, BC, BD, CD, BA, CA, DA, CR, DB and DC. Exactly how this can be handled is not clear in an empirical sense, but it can he handled in ;I theoretical context because the theory is sufficiently abstract that one does not have to identify exactly where the additional revenues are produced. It should bc recognized that adding a node to the network makes all of its traffic and demand available to the system. As a result it is unneccssarv to consider the potential origins of its inbound traffic or the potential destinations of its outbound flows. If the place is already connected to a transport system there is a need to consider the impact this has on potential traffic from the place and this is discussed below.
would make the community less attractive. but it would not necessarily prevent a new rail line from passing through it. The potential traffic share at a node, as viewed from the pcrspcctive ol’ the entrepreneurs locating a route. probably dccrcases as a function of the number of transport lines of that mode already serving the place. At the same time it is recognized that, although the potential trafffic and the share of that traffic are important in laying out a line, they are not the only factors; there is also the desire to minimize the overall length of the lint. As a result, when the transport route is being built, it may pass through points of zero attractiveness simply because they are ‘in the way’ of the least-cost route. Of course it is unreasonable to expect that the decisions of a century ago would necessarily yield optimum (minimum cost or maximum profits) routes. There were just too many unknowns to assume that optimal choices could be made. The theoretical structure set forth earlier does identify such routes, but more importantly it identifies other profitable yet non-optimal routes as well. This is of value since it is reasonable to expect that the route selected would be only near optimal for the conditions in existence at the time.
Other extensions
Empirical testing
of the approach
Smith (1971, pp. 1X1-187) notes that the industrial firm must always make three decisions after it has decided to get involved in production. These are: where to locate, what the technology will bc and what the scale of production will be. In the present case we are examining an entrepreneur who has decided to produce transportation. The location question has been examined above, but what about the technology and scale questions‘? The technology question in this case is analogous to the mode question. In an historical sense the question was whether the route constructed would be a bridle road. a plank road, a railroad and so forth. The scale question went to the width of the road to be constructed or the number of tracks as well as the gauge of that track. Thcsc questions arc very important in the transport case since the decisions made will affect the construction costs. future operating costs and potential revenues for the transportation route of interest. These may be incorporated into the framework proposed here at a later date. Competitive
tffects
This theoretical structure at its current level development assumes away any consideration competitive effects. Whether a community already served by rail would have some impact whether it would be connected 10 what could called a ‘Wellington route’. It is recognized that 90
of of was on be this
In order to evaluate the proposed framework it is necessary to relax several of the earlier assumptions that were necessary for the graphical analysis. This is SO simply because most of these assumptions arc not met in the real world. As in the prior analysis we will assume that the termini of a route are known. Potential traffic will be allowed to vary. Topographical variations will be present. but not extreme variations. The number of intermediate nodes is variable. Several assumptions are retained. It is assumed that the intermediate nodes connected will bc connected only directly; there will be no intermediate junctions except at nodes. Construction costs are assumed to be related to distance and entrepreneurs are assumed to be profit maximizers interested in laying out routes that will maximize future profits. Finally, the assumption regarding the abscncc of the mode at all intermediate places is kept only because this was true of the lines examined. ie, the initial assumption was met. It is assumed that an indicator of future profits is some function of estimated construction and operating costs as well as revenues. It would be possible to go through some effort to obtain such estimates, but it is also possible to use surrogates for these. It was assumed that rcvcnues are related to the number of people served and that costs are related to the length of the route. Marc specifically, it was viewed as reasonable to use an indicator of potential profit for individual link pairs. under the assumption that these were selected in an
Route location:
W. R. Black
attempt to maximize profits. As an indicator of potential profits of given nodal pairs. link potential was used. This may be defined as the population of a node i added to the population of a node j divided by the distance between the two nodes. Although the additive element may be disturbing to those familiar with the gravity model, this is a potential measure. It yields a number that is the equivalent of the sum of the potential attractiveness of i to j and the attractiveness of j to i. It is reasonable to assume such potential attractiveness could be diminished by using power functions on the distance variable to reflect topographical variations (ie. differences in construction costs). Empirical evaluation involves finding the ‘shortest path’ between origin and destination termini, where the ‘distance’ between nodes is defined as negative potential. Such a metric space has unknown properties, but the selection of the shortest negative potential route appears to result in a path between the origin and destination composed of a minimum number of segments involving the largest potential links. The resulting route involves a trade-off between distance (in a topological sense) and revenues as given by the potential measure. Such a procedure appears to integrate the key properties of the previous graphical analysis and should result in a route that is located within the geographic limits of profitability. Assuming that this is a reasonable approach for evaluating some of the notions presented here, it was necessary to find some historic situations where the origin and destination for a proposed transportation line were known, where the terrain was relatively flat and where intervening places existed that could have been added to the transport line. A study of rail land acquisition @lack, 1986) provides several situations that could be used to test the theoretical statements expressed here.
I
Routes selected
and Upper Mississippi Rail(3) The Lawrenceburg road (Figure 9a) was constructed and opened to traffic between Cincinnati, Ohio (Lawrenceburg, Indiana) and Indianapolis in 1851.
The routes selected for these tests were rail lines constructed in the state of Indiana in the US Midwest. Although roads could have been utilized, they were constructed at an earlier time for which the population data are less reliable. In addition many of these were constructed at a time when only a few settlements existed in the USA. As a result such tests would not give the best evaluation of the notions proposed here. The lines selected are as follows: (1) The Indianapolis and Peru Railroad (Figure 7a) was constructed between those towns during the early 1850s. It was opened to traffic in 1854. (2) The Madison and Indianapolis Railroad (Figure 8a) was constructed between Madison and Indianapolis during the 1840s. It was opened to traffic in 1847. Journal of
Transport
Geography
199.3 Volume
I Number
2
a
0 0
0
--
0
0
0
0
0
b
0 0
0 0 0 0
0
0
0
0
0 0
0
0
C Figure 7. (a) The
route of the Indianapolis
Railroad;
(b)
graphic
representation
gcncrated
route of the Indianapolis
of the
and Peru route;
(c)
and Peru Railroad
These three railroads were constructed at about the same time (c.1850). Each has Indianapolis as one of its end termini, but this should not bias the tests in any way. Indianapolis was selected as the capital of Indiana in 1825, nine years after statehood, and it experienced rapid initial growth. Two of the other end termini were early river ports on the Ohio River, Cincinnati and Madison. The Ohio River was the major east-west corridor in the middle 1800s. The last terminus was Peru. This town was located on the Wabash-Maumee Canal, which was opened from Toledo. Ohio (on Lake Erie) to Terre Haute, Indiana in 1849. Each railroad passed through lands that were primarily agricultural. Topographic variation was minor in all cases with one notable exception. This was on the Madison to Indianapolis 91
Route location:
W. R. Rlack
b
c
Figure 8. (a) The route of the Madison and Indianapolis Railroad; (b) graphic representation of the route; (c) gcncratcd route of the Madison and Indianapolis Railroad
rail line. The line constructed from Madison to North Madison on the plain above the Ohio River Valley had a grade of nearly 6”/0, making it the steepest grade for this type of railroad in the IJSA. Such a segment would never have been constructed if there was an alternative corridor that could have been built. Abstract representations of the networks to reflect direct connections between places in existence in 1850 were prepared (see Figures 7b. 8b and 9b). The link potentials were calculated using population figures from the population census of 1850 for Indiana. The use of population assumes equal per capita demand for transportation. Although this may be an extreme assumption in some situations, it is reasonable here. Distances to be covered were relatively short, the resource base, soils, climate and terrain were nearly identical, suggesting that wealth and transport demand would not differ significantly on a per capita basis between any of the termini of interest here. Although the terrain in nearly all cases is level to gently rolling, Indiana is not a uniform plain. Therefore the distance variable in the linkpotential measure was raised to the second power. The problem of finding the shortest paths was solved using an algorithm discussed by Whitaker (1984). 92
c
Figure 9. The route of the Lawrcnccburg and IJppcr Mississippi Railroad; (b) graphic rcprcscntation of the route; (c) gcncratcd route of the Lawrcncchurg and Upper Missisippi Railroad
Results of the approach Let us now examine the accuracy of this framework for the individual railroads. Beginning with the Indianapolis and Peru Railroad the approach is not very good (see Figure 7c compared with Figure 7b). The procedure focused on the major end points, connecting Peru to Indianapolis. and indicated that there were no places in between worth connecting to the line of interest. In reality there was a bend in the line to connect Kokomo (not in Figure 7. but represented by the slight inflection to the west between Tipton and Peru). The same was true for Tipton and Noblesville. These three places were not incorporated as towns until after 1850 and their population data may include inaccuracies. Alternatively, the inclusion of these three places on the route constructed may be due to the fact that the counties through which the line passed gave land for the construction of depots or to have the railroad pass through certain communities. Blanchard (1X8.3. p. 254) notes that Tipton County (where Tipton is
Route location:
located) ‘donated certain lands for depots and freight houses and the citizens gave willingly the right of way’. Future refinements of the framework should try to incorporate this tendency in the measure of ‘potential’ attractiveness. In the case of the Lawrenceburg and Upper Mississippi Railroad the results are much better (see Figure 9c compared with 9b). In this case the generated route begins at Lawrenceburg, and connects Greensburg to St Omer to Shelbyville to Indianapolis. With the exception of St Omer this is a perfect replication of the line’s connections. The deviation in the line necessary to reach St Omer would be within the spatial limits of profitability previously mentioned. In this regard Harding (1915) notes that the original survey of the line placed the route through St Omer, but that Greensburg interests pledged $150 000 to the railroad if it would run directly to Greensburg from Lawrenceburg. The third route under analysis, the one from Indianapolis to Madison, has one major inflection point and this is at Columbus (see Figure 8b). Aside from this the actual route passed through Vernon and Franklin with insignificant deviations in the route alignment. Based on local land records the town of Franklin gave two acres to the railroad for a freight station which accounts for that slight deviation from the route generated. These are very encouraging results. Most of the differences between the actual and generated routes appear to be due to local actions not yet included in the framework. It does not seem necessary to evaluate these results statistically since a correlation coefficient calculated to compare the elements of the connection matrix segments in the actual and generated paths would be overwhelmingly significant.
Summary This paper began with an introduction to the route location problem. It was noted that prior attempts to replicate historical route location decisions have been wanting in terms of their theoretical foundation and the empirical accuracy of the procedures developed. A theoretical approach to this problem based on generally accepted tenets of industrial location theory was identified and demonstrated. It was noted that slight deviations in location might be quite reasonable given the notion of spatial limits and non-optimizing, but profit seeking, behaviour on the part of transport entrepreneurs. Moving from the theoretical side to empirical testing, the concept of profitability was defined as a link-potential measure. A shortest-path algorithm was used to identify the segments of three railroad routes constructed in Indiana during the mid-19th century. The results were very encouraging, and there appears to be some merit in further tests of these constructs in the future. Journal of Transport Geogruphy 199.3 Volume I Number 2
W. R. Black
References Black, W.R. (1969) ‘The generation of transportation networks: their growth and structure’, unpublished PhD dissertation, The University of Iowa, Iowa City Black, W.R. (1971) ‘An iterative model for generating transportation networks’, Geographical Analysis, 3, pp. 283-288 Black, W.R. (1986) Railroad land and property in Zndiana, Bloomington, IN: Transportation Rcscarch Center, Indiana University Blanchard, C. (1883) Counties of Howard and Tipton Indiana, Chicago: F.A. Battey Boyce, D.E. (1963) ‘The generation of synthetic transportation networks’, Mimco, Evanston. IL: The Transportation Center at Northwestern University Garrison. W.L. and Marble. D.F. (1962) ‘The structure of transportation networks’. Mimeo. Evanston, IL: The Transportation Center at Northwestern University W.L. and Marble, D.F. (1965) ‘A proGarrison, legomenon to the forecasting of transportation development, Mimeo, Evanston IL: The Transportation Center at Northwestern University Haggett, P. (1966) Locational analysis in human geography, New York: St Martin’s Press Harding, L.A. (1915) History of Decatur County Indiana, Indianapolis: B.F. Bowen Hay, A. (1973) Transport for the space economy: a geographical study, Seattle: University of Washington Press Johnson, E.R. (1910) American railway transporation. New York: Appleton Kansky, K.J. (1963) Structure of transportation networks: relationships between network geometry and regional characteristics, Research Paper No 84, Chicago: Dcpartment of Geography, The University of Chicago LBsch. A. (1940) Die riiumliche Ordnung der Wirtschaft, trans. Woglom, W.W. (1954) The economics of location, New Haven: Yale University Press MacKinnon. R.D. and Hodgson. M.J. (1969) The highway system of Southern Ontario and Quebec: some simple network generation models. Research Report No 18, Toronto: Ccntrc for Urban and Community Studies, University of Toronto Merrill, R.L. (1965) Migration and the spread and growth of urban settlement, Series B. No 26 Lund, Swcdcn: Lund Studies in Geography, The Royal University of Lund Smith, D.M. (1966) ‘A theoretical framework for gcographical studies of industrial location, Economic Geography, 42, pp. 95-l 13 Smith. D.M. (1971) Industrial location, New York: Wiley von Stackclbcrg, H. (193X) ‘Das Brcchungsgcsctz dcs Verkehrs’. Jahrbiicherftir NationalBkonomie und Statistik. Bd. 148, Jcna, trans. Burdack. J. (1990) The law of refraction of transportation. Occasional Paper Series No I, Bloomington, IN: Transportation Specialty Group of the Association of American Gcographcrs Taaffc. E.J.. Merrill, R.L. and Gould, P.R. (lY63) ‘Transport expansion in underdeveloped countries: a comparative analysis’, Geographical Review. 53. pp. 503-529 Wallace, W.W. (1965) ‘The bridge lint: a distinctive type of Anglo-American railroad’, Economic Geography, 41, pp. 1-38
93
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location:
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Wcbcr. A. (1WN) Uher dm Stardori der Industrierz. trans. Fricdrich. C.J. (1929) Alfred W&r‘s theory of the locmrion of irzdlrstries. Chicago: University of Chicago Press Wellington. A.M. (1X87) The economic theory of the location of railways. New York: Wiley Werner, C. (1968) ‘The law of refraction in transportation
94
geography: its multivariate extension’. (‘rrr~rrtlirr~~Gcographrr, 12. pp. 2X-N Whitakcr. D. (19X4) OR 011 fhe micro. New York: Wile! Young. C.W. (Ic)70) ‘Transportation network dcvclopmcnt: the railroad network of southern Michigan’. unpublished PhD dissertation. Michigan state University, East LanGng