Transportation Networks, Geospatial Data and Cost Models

Introduction

Route planning is fundamentally a network decision problem. A vehicle does not travel through an abstract space; it moves between locations connected by roads, rail lines, waterways, terminals, depots, and access links. Effective planning therefore requires three integrated representations: a graph describing connectivity, geospatial data describing where infrastructure is located and how it behaves, and a cost model translating movement into time, money, risk, and service consequences.

This chapter develops those representations for graduate-level supply chain analysis. It distinguishes physical distance from travel distance, nominal travel time from time-dependent travel time, and direct transportation cost from generalized cost. It also examines data quality, geographic constraints, GIS workflows, and the managerial implications of network-model design.

Learning Objectives

By the end of this chapter, the reader should be able to:

1. Represent a transportation system using nodes, arcs, paths, and directed graphs.
2. Construct and interpret travel-time, distance, capacity, and cost matrices.
3. Explain how GIS, map data, and location intelligence support route planning.
4. Formulate generalized transportation costs subject to operational constraints.
5. Identify data-quality, governance, ethical, and implementation risks.
6. Apply network concepts to a realistic distribution-planning problem.

1. Transportation Networks as Graphs

A transportation network can be represented by a graph G = (V,A), where V is a set of nodes and A is a set of arcs. A node represents a location at which movement begins, ends, transfers, or is controlled. Examples include suppliers, factories, cross-docks, distribution centres, customers, ports, intersections, charging stations, and border crossings.

An arc represents a feasible movement connection between two nodes. In a road network, an arc may be a directed road segment between intersections. Direction matters: a one-way street is represented by an arc in only one direction, while a two-way road is represented by two directed arcs unless the modelling convention permits an undirected edge.

A useful arc record may contain:

A path is an ordered sequence of arcs connecting an origin to a destination. If path p contains arcs a₁, a₂, ..., a_k, its distance is additive:

where d_a is the length of arc a, measured in consistent distance units. The formula assumes that arc lengths are measured along the network and that no additional distance is incurred at stops or transfers.

Similarly, under additive travel time:

This is appropriate when arc travel times are known and independent. In congested networks, however, t_a may depend on traffic flow, departure time, weather, incidents, and vehicle type. A more realistic notation is t_a(x_a,τ), where x_a is flow on arc a and τ is departure time.

Directed, weighted, and multimodal networks

A weighted graph assigns attributes such as distance, time, or cost to nodes or arcs. A multimodal network includes different movement modes and transfer connections. For example, a shipment may travel by truck from a factory to a rail terminal, by rail to a port, and by truck to a customer. Transfer arcs must represent loading time, handling cost, and possible loss or damage risk.

A time-dependent network changes its arc attributes over time. A road segment may require 20 minutes at 02:00 and 50 minutes at 08:00. A time-dependent shortest path is not necessarily found by adding static distances, because arriving at a downstream arc at a different time may change its travel time.

2. Network Structure and Route Feasibility

The shortest geometric route is not always the shortest feasible route. A route must satisfy physical, legal, operational, and service constraints. Important constraints include:

• vehicle height, width, length, axle-weight, or total-weight limits;
• hazardous-material restrictions;
• low-emission or congestion-charge zones;
• bridge, tunnel, ferry, or border operating hours;
• customer delivery windows;
• driver hours-of-service rules;
• road closures and seasonal restrictions;
• vehicle access requirements at loading locations; and
• required return-to-depot or depot-ending conditions.

Let x_a be a binary variable equal to 1 if arc a is selected and 0 otherwise. A capacity constraint may be written as:

where q_r is the flow of route or commodity r using arc a, x_ar indicates its use, and u_a is arc capacity. This formulation is illustrative; a complete vehicle-routing model requires flow conservation, vehicle assignment, demand fulfilment, and subtour-elimination constraints.

Flow conservation requires that, for an intermediate node, incoming flow equals outgoing flow. For a commodity k at node i:

Here f_ijk is flow of commodity k from node i to node j, and b_ik is net supply: positive at an origin, negative at a destination, and zero at a transshipment node. The equation assumes divisible flow and does not by itself enforce vehicle routes.

3. Geospatial Data and GIS Representation

Geographic information systems combine spatial geometry with attribute data. A road is represented geometrically by a line, but its operational meaning comes from associated attributes: speed limits, turn restrictions, surface type, lane count, toll status, and access permissions.

Coordinate reference systems

Locations are commonly stored as latitude and longitude in a geographic coordinate reference system. These coordinates describe angular position, not planar distance. Directly calculating Euclidean distance from latitude and longitude can produce errors, especially over large areas or at high latitudes. For local distance and area calculations, data should generally be transformed into an appropriate projected coordinate reference system whose units are metres or feet.

For two nearby points represented in a projected system, straight-line distance is:

where x and y are coordinates in the same linear unit. This is a crow-fly distance, not a road distance. It is useful for screening, facility-location approximations, and lower bounds, but it should not replace network distance for delivery planning.

For points on a sphere, the haversine formula estimates great-circle distance:

Here φ denotes latitude in radians, λ longitude in radians, R Earth’s assumed radius, and ∆φ and ∆λ coordinate differences. The formula assumes a spherical Earth and is an approximation; an ellipsoidal geodesic method is preferable when high positional accuracy is required.

From map data to a routable network

A practical GIS workflow includes:

1. Geocoding: converting addresses into coordinates.
2. Validation: checking address confidence, duplicates, missing units, and improbable locations.
3. Map matching: associating points with the correct road segment or access point.
4. Network construction: creating nodes, directed arcs, and connectivity.
5. Attribute enrichment: adding speed, restrictions, tolls, elevation, traffic, and operating rules.
6. Routing: calculating shortest or least-cost paths.
7. Aggregation: producing distance matrices, service territories, and performance reports.

Geocoding error is particularly important in last-mile operations. A point located at a parcel centroid may be on the wrong side of a divided highway, behind a restricted gate, or several hundred metres from the correct loading entrance. Consequently, customer coordinates should be associated with a practical service point rather than merely a postal centroid.

4. Distance, Travel-Time, and Cost Matrices

A matrix stores pairwise attributes between origins and destinations. Let D = [d_ij] be a distance matrix, where d_ij is the shortest network distance from node i to node j. Likewise, T = [t_ij] is a travel-time matrix and C = [c_ij] is a cost matrix.

Matrices may be:

• symmetric, when movement from i to j equals movement in the reverse direction;
• asymmetric, when one-way streets, terrain, tolls, congestion, or turn restrictions create different values; or
• time-dependent, when each cell depends on departure or arrival time.

Road matrices in real operations are often asymmetric. A truck may travel 12 km outbound and 15 km on return because of one-way systems or prohibited turns. Treating such a matrix as symmetric can create infeasible schedules and underestimated cost.

A matrix can be generated using a shortest-path algorithm. Dijkstra’s algorithm is appropriate when all arc weights are non-negative. A* can accelerate a single-origin/destination query by using a lower-bound heuristic, often straight-line distance. Floyd–Warshall computes all-pairs shortest paths but has high computational complexity and is generally more suitable for smaller dense networks. Large logistics systems commonly use contraction hierarchies, graph partitioning, or specialized routing engines.

5. Transportation Cost Models

A cost model should reflect the decision being made. A carrier may care about operating cost, while a shipper may also value inventory, reliability, emissions, customer service, and risk.

A basic route cost can be written as:

where:

• C_p = total cost of path p;
• F_p = fixed trip cost, currency/trip;
• c_d = distance cost, currency/km;
• d_p = path distance, km;
• c_t = time cost, currency/hour;
• t_p = path travel time, hours;
• T_p = tolls and access charges, currency; and
• H_p = handling or stop-related cost, currency.

The model assumes linear distance and time costs. In practice, fuel cost may depend on vehicle weight, grade, speed, and stop-start conditions; labour may include overtime thresholds; and tolls may be nonlinear. Such effects can be represented with additional arc attributes or piecewise-linear functions.

A generalized cost incorporates nonfinancial consequences:

Here S_p is service-delay exposure, R_p reliability or disruption risk, E_p emissions, and Q_p a quality or customer-impact measure. The coefficients v_s, v_r, v_e, and v_q convert those measures into monetary-equivalent values. These coefficients are not universal constants; they should be estimated from managerial preferences, observed penalties, customer research, carbon prices, or regulatory values.

The use of generalized cost requires caution. Adding unlike outcomes is defensible only when units and valuation principles are explicit. Otherwise, the model can conceal subjective preferences behind apparently precise numbers.

Emissions as a cost component

A simple emissions estimate is:

where e_v is an emissions factor in kilograms of CO₂-equivalent per kilometre for the vehicle and operating condition. If load, fuel, and grade matter, a more detailed model uses segment-specific factors e_a and load l_a:

The result depends on the emissions boundary, fuel type, vehicle technology, and data source. It should not be interpreted as an exact physical measurement unless those assumptions are documented.

6. Travel-Time Uncertainty and Reliability

Expected travel time alone can produce poor plans. Two routes may both have an expected duration of 60 minutes, while one has a narrow distribution and the other is highly variable. A planner may therefore use a reliability buffer:

where E[T_ij] is expected travel time, σ_ij is its standard deviation, and z_α is a selected quantile multiplier. This equation assumes a distribution for travel time, often approximately normal for planning purposes. Travel-time distributions are frequently skewed, so empirical percentiles may be preferable. For a 95th-percentile planning time, the relevant value should ideally be estimated directly from historical observations rather than imposed through normality.

Reliability can also be represented probabilistically. If a delivery must arrive within time L, the service constraint is:

where α is the required on-time probability. This formulation is useful for medical deliveries, production-critical components, and customer appointments.

7. Worked Example: Comparing Two Paths

A distributor is evaluating two paths from a depot to a customer. The following assumptions apply:

Using C_p = F_p + c_d d_p + c_t t_p + T_p:

Path A:

C_A = 18 + (0.90 × 42) + (24 × 0.80) + 0 = 75.00

Path B:

C_B = 18 + (0.90 × 35) + (24 × 1.05) + 4 = 79.55

Path A is cheaper by 4.55 currency units despite being 7 km longer. If the value of reliability or congestion exposure on Path B is lower, however, the decision may change. The example demonstrates why distance minimization is not equivalent to cost minimization.

8. Illustrative Case: Urban Grocery Distribution

Background

An illustrative regional grocery distributor serves 180 stores from one distribution centre. Its planning system uses customer postcodes, straight-line distances, and average speeds. The business experiences late deliveries in a dense urban area, even though planned kilometres appear low.

Problem

An audit identifies three issues. First, several store coordinates are postal centroids rather than loading entrances. Second, the model assumes symmetric travel times despite one-way streets and restricted turns. Third, all routes use average daytime speeds and ignore delivery windows, curb access, and congestion near schools.

Analysis

The distributor builds a directed road network and adds speed profiles by 15-minute interval. It geocodes each store to a verified loading point, records vehicle restrictions, and separates travel time from unloading time. Historical GPS traces are used to estimate the 90th-percentile travel time for important road segments. The company also identifies low-emission zones and streets unsuitable for its largest vehicles.

The new generalized cost model includes distance, driver time, tolls, expected late-delivery penalties, and a carbon shadow price. Routes are tested under peak and off-peak departure times. A sensitivity analysis varies the lateness penalty and reliability target.

Approach and outcome

The revised model increases predicted kilometres by 3.8% but reduces late arrivals by 21% in the pilot area. Some apparently short routes are rejected because they require illegal turns or fail the delivery-window constraint. The model also shifts several deliveries to earlier departure times, reducing exposure to school-zone congestion. The financial result is positive because fewer missed windows reduce redelivery and store labour costs.

Learning points

The case illustrates four principles. Geographic accuracy is operational accuracy; network distance is more useful than straight-line distance; feasibility rules must be encoded rather than assumed; and a route model should be evaluated using service outcomes, not only kilometres or solver objective value.

9. Implementation, Governance, and Limitations

Data quality and validation

Common data problems include outdated road networks, duplicate facilities, incorrect coordinates, missing access roads, inconsistent units, and stale restriction data. Validation should include map inspection, coordinate-range checks, sample route comparison with actual journeys, and systematic review of implausible travel times.

Model calibration

A model should be calibrated using observed GPS traces, fuel records, toll statements, delivery timestamps, and driver knowledge. Calibration must avoid confusing correlation with causation. For example, slow travel may reflect loading delays rather than road congestion. Separate operational events where possible.

Privacy and ethics

Vehicle telematics and driver-location data can reveal employee routines, customer behaviour, and sensitive facility information. Organizations should apply data minimization, access control, retention limits, encryption, and lawful processing. Drivers should be informed about monitoring purposes and evaluation rules. Location intelligence must not be used to discriminate against communities or systematically withdraw service without transparent justification.

Regulatory and safety issues

Routing systems must respect road law, dangerous-goods rules, driver-rest requirements, weight restrictions, and local environmental regulations. A mathematically optimal route is unacceptable if it directs a vehicle through a prohibited street or unsafe location. Human review remains essential for exceptional events, ambiguous map data, and emergency operations.

AI and contemporary developments

Machine learning can forecast travel times, classify road conditions, detect map changes from imagery, and predict delivery duration. However, predictive accuracy does not guarantee operational validity. Models may fail under unusual weather, roadworks, strikes, or network disruptions. Explainability, drift monitoring, uncertainty estimates, and fallback procedures are necessary. Digital twins and real-time control towers increasingly combine live traffic, telematics, weather, inventory, and order data, but these systems remain dependent on accurate network semantics and governance.

10. Best-Practice Design Principles

1. Use directed networks unless symmetry is demonstrably valid.
2. Separate physical distance, travel time, service time, and waiting time.
3. Store units and data provenance with every important attribute.
4. Encode vehicle, legal, environmental, and customer constraints explicitly.
5. Prefer network distance to straight-line distance for operational routing.
6. Model time dependence where congestion or operating windows matter.
7. Validate geocoded points at actual service entrances.
8. Use observed data to calibrate travel times and costs.
9. Test sensitivity to fuel rates, wages, penalties, and reliability targets.
10. Report infeasibility and uncertainty rather than hiding them in a single score.
11. Protect personal and commercially sensitive location data.
12. Evaluate models using business outcomes: cost, service, safety, emissions, and resilience.

Chapter Summary

Transportation planning begins with a graph of nodes and arcs, but a useful operational model must also include geographic position, direction, time dependence, capacity, vehicle restrictions, and service rules. Paths aggregate arc-level distances, times, emissions, and costs, while distance and travel-time matrices support large-scale routing and scheduling.

GIS transforms map geometry into a routable network through geocoding, validation, map matching, attribute enrichment, and shortest-path analysis. Straight-line distance is useful for approximation but cannot replace network distance where roads, turns, and access constraints matter. Generalized cost extends financial cost by valuing time, reliability, emissions, and service outcomes; because these valuations are partly managerial, their assumptions must be explicit.

Graduate-level practice requires critical attention to uncertainty, data quality, privacy, regulation, model calibration, and technology limitations. The strongest route-planning systems combine mathematical optimization with reliable geospatial data, operational knowledge, and responsible governance.

Key Terms

Graph: A mathematical representation consisting of nodes and connecting arcs.

Node: A location at which movement begins, ends, transfers, or is controlled.

Arc: A directed movement connection between two nodes.

Path: An ordered sequence of arcs connecting an origin and destination.

Directed network: A network in which movement direction is explicitly represented.

Weighted graph: A graph whose nodes or arcs carry attributes such as time or cost.

Multimodal network: A network containing multiple transportation modes and transfer links.

Flow conservation: The requirement that intermediate-node inflow equals outflow.

Capacity: The maximum flow or usage an arc, facility, or vehicle can accommodate.

GIS: A system for storing, analysing, and displaying geographic and attribute data.

Geocoding: Converting a textual address into geographic coordinates.

Map matching: Associating a location or GPS trace with a road or network segment.

Coordinate reference system: A defined method for representing geographic positions.

Distance matrix: A table of pairwise network distances between locations.

Travel-time matrix: A table of pairwise travel times between locations.

Generalized cost: Financial cost plus monetized time, risk, service, or environmental effects.

Time-dependent network: A network whose arc attributes vary with departure or arrival time.

Reliability: The consistency or probability of achieving a planned travel or service outcome.

Location intelligence: The use of geographic information to support organizational decisions.

Shadow price: An assigned monetary value for a nonmarket effect or constrained resource.

Review Questions

Short Answer Questions

1. What are the principal differences between a node, an arc, and a path?
2. Why can a transportation distance matrix be asymmetric?
3. What is the purpose of map matching in route planning?
4. Distinguish direct transportation cost from generalized cost.
5. Why should travel-time variability be considered in delivery scheduling?

Long Answer Questions

1. Explain how a GIS road dataset is transformed into a routable directed network. Discuss the importance of geocoding, coordinate systems, restrictions, and validation.
2. Compare static, time-dependent, and stochastic transportation networks. Identify contexts in which each representation is appropriate.
3. Develop and explain a generalized cost model for a fleet serving urban customers. Define its variables and discuss the assumptions behind each term.
4. Evaluate the managerial and ethical risks of using vehicle telematics and machine-learning travel-time predictions in route planning.
5. Explain why minimizing kilometres may conflict with minimizing total logistics cost and maximizing service reliability.

Analytical / Application Questions

1. A route is 48 km long and requires 1.2 hours. Its fixed cost is 20 currency units, distance cost is 0.75 per km, time cost is 22 per hour, and tolls are 3. Calculate total route cost using the chapter’s linear cost model.
2. Two routes have equal expected travel time, but Route X has substantially higher variance. Design a decision rule using either a reliability constraint or a percentile planning time, and explain the managerial trade-off.
3. Propose a data and governance plan for correcting inaccurate customer coordinates in a last-mile delivery network. Include validation, privacy, operational ownership, and performance measures.

Multiple Choice Questions with Answers

Question 1

Which element of a transportation graph represents a one-way road segment?

A. A directed arc

B. A demand node

C. A symmetric matrix

D. A coordinate reference system

Correct Answer: A. A directed arc

Question 2

A route is 40 km long, takes 1.5 hours, has a fixed cost of 10, a distance rate of 1 per km, and a time rate of 20 per hour. Ignoring tolls, what is its cost?

A. 50

B. 70

C. 80

D. 100

Correct Answer: C. 80

Question 3

Which statement about straight-line distance is correct?

A. It always equals road distance

B. It accounts automatically for one-way streets

C. It can provide a lower-bound approximation but is not a substitute for network distance

D. It includes loading and unloading time

Correct Answer: C. It can provide a lower-bound approximation but is not a substitute for network distance

Question 4

What does flow conservation require at an intermediate node?

A. All outgoing arcs must have equal physical length

B. Incoming flow must equal outgoing flow

C. Every arc must be used once

D. Travel time must equal distance

Correct Answer: B. Incoming flow must equal outgoing flow

Question 5

Which attribute most directly supports vehicle-feasibility screening?

A. Road colour on a map

B. Postal code format

C. Bridge height restriction

D. Map display scale

Correct Answer: C. Bridge height restriction

Question 6

In the generalized cost model, a shadow value for emissions is used to:

A. Convert an environmental measure into a monetary-equivalent value

B. Eliminate all emissions from the network

C. Calculate geographic coordinates

D. Guarantee a shortest-distance route

Correct Answer: A. Convert an environmental measure into a monetary-equivalent value

Question 7

Why may a road travel-time matrix be asymmetric?

A. All roads have identical speeds in both directions

B. One-way streets, turns, congestion, or restrictions can differ by direction

C. Distance matrices cannot contain numbers

D. GIS systems require symmetry

Correct Answer: B. One-way streets, turns, congestion, or restrictions can differ by direction

Question 8

Which algorithm is appropriate for shortest paths when all arc weights are non-negative?

A. Dijkstra’s algorithm

B. Random sampling only

C. Linear regression without a network

D. A coordinate conversion

Correct Answer: A. Dijkstra’s algorithm

Question 9

A planning time expressed as a high percentile is primarily intended to address:

A. Coordinate units

B. Travel-time reliability

C. Vehicle ownership

D. Map colour selection

Correct Answer: B. Travel-time reliability

Question 10

Which is a key governance practice when using driver-location data?

A. Collect unlimited data indefinitely

B. Publish individual traces openly

C. Apply access controls, purpose limitation, and retention rules

D. Ignore employee notification

Correct Answer: C. Apply access controls, purpose limitation, and retention rules