A
Analysis of inferiority
municipal engineer, 75
Pareto optimality criteria, 73
C
California bearing ratio (CBR), 21
Civil infrastructure management
costs minimization, 210
deterioration curves, 205
dynamic effect, decisions on time, 189–191
environmental impact minimization, 210–211
incorporation, elements, 202
infrastructure management, 195–198
intervention’s criteria, basic/improved, 204
intervention effectiveness, 207–208
operational windows and cost, 208
optimization type
heuristic method, 199
linear programming (dynamic binary) approach, 199
objective and constraints, 200–201
Solver Risk Platform, 202
performance modelling, 191–195
travel time reduction strategy, 202–203
Conditional probabilities, 95–97
Conflicting objectives
maintenance and rehabilitation, 69–70
maximizing lifetime income, 69
Constraint
definition, 3
Construction material company
constraints determination, 65
departure tableau, 66
objective determination, 64–65
problem formulation, 65
D
Decision model
construction, mathematical formulation, 5–8
nature of problem identification, 5
Decision variable/control variable, 3
E
Equation-based approach, 53–55
Estimation
definition, 107
explanatory power standardized beta coefficients, 116–117
mathematical representation, 107–108
pavement deterioration
Excel’s add-in solver set-up, 112
Excel set-up, 111
factors and response identification, 109
sample data deterioration, 110–111
structural number, 109
Thornthwaite Moisture Index, 109
road safety
STATA® linear regression, 113, 115
G
Gradient search
definition, 32
explicit forms, 35
graphical representation, 34
Lagrangian, 33
optimal step size, 32
Pythagoras, 32
Graphical approach
advancement of objective function, 49, 52
identifying objective and constraints, 48
Gravitational approach
multinomial logit, 140
travel demand estimation
attraction constrained, 133–134
production constrained gravitation, 132–133
H
Heine–Borel definition, 24
Heuristic method
evolutionary algorithm, 200
genetic algorithm, 200
I
Infeasible problem, municipal engineer case
departure tableau modified, 61
identities
for basic variables, 62
linear programming problem
pivot operation, non-basic, 62–63
problem formulation modification, 61
Inferiority analysis
municipal engineer, 75
Pareto optimality criteria, 73
Infrastructure management
joining deterioration and improvement
decision-making system, 196
network-wide, 196
objective (constraint), 197–198
total enumeration, 197
optimization algorithm, 197–199
International roughness index (IRI), 108–111, 120, 123
IRI, see International roughness index
K
Kurtosis measure, 86
L
Lagrange method, metal sheet cutting
initial set for metal sheet, 29
solving system of equations, 31–32
square metal abstraction, 29–30
Land use transport models
gravitational approach, 131–136
multinomial logit, 144
policies/planning decisions, 130
population and build space development, 129
problem-solving skill development, 146
random utility approach, 136–140
trip distribution and modal split, 136–140
Lexicographic sorting and analysis, 77, 80
Linear programming (dynamic binary) approach, 199
Linear regression
definition, 98
sample data deterioration, 98–99
Location modelling
basic employment, 141
M
Mathematical analysis
first-order conditions, 28
gradient search
definition, 32
explicit forms, 35
graphical representation, 34
Lagrangian, 33
optimal step size, 32
Pythagoras, 32
Lagrange method, metal sheet cutting
abstraction of square metal, 29–30
initial set for metal sheet, 29
solving system of equations, 31–32
objective function, warranting optimality, 27–28
topology
compactness, 24
complements, 20
empty sets, 20
intersection, 20
open balls, open sets, closed sets, 22–24
sets and spaces, 21
unions, 20
Mathematical formulation construction
pipe capacity, least-square difference, 7
tank capacity, maximum deficit, 7–8
Maximization, 3
Minimization, 3
O
Objective
definition, 3
Optimization and decision making
analysis of inferiority
municipal engineer, 75
Pareto optimality criteria, 73
global objective, weights alternation
floor production example, 71
graphical approach
identifying objective and constraints, 48
objective function advancement, 49, 52
multiple objectives and trade-off analysis, 68–70
ranges, satisfaction and lexicographic analysis
simplex method
equation-based approach, 53–55
unbounded and infeasible, 59
Origin–destination (OD) pairs, travel time, 153
P
Pareto optimality criteria, 73
Pavement deterioration estimation
Excel’s add-in solver set-up, 112
Excel set-up, 111
identification of factors and response, 109
international roughness index (IRI), 108–110
sample data deterioration, 110–111
structural number, 109
Thornthwaite Moisture Index, 109
Pedestrians’ tunnel network
at underground tunnels., 182–183
Performance modelling
deterioration modelling
linear regression, 192
transition probability matrix, 192
deterministic method, 191
improvement modelling
deterioration curve, 194
generic treatments, 195
intervention effectiveness, 193–194
inverted Markov chain, 194
probabilistic method, 191
Positive self-selection process, 9
Predictions
Bridge Condition Index (BCI), 119
incremental, 120
making predictions, 118
Probability
conditional probabilities, 95–97
definition, 95
R
Random utility approach
location decisions, 136
multinomial logit, 139–140, 147
Road safety estimation, 112–115
S
Sample monitor tool, 234
Satisfaction rule, 80
Shortest path problem
applications, 159
distribution/allocation
limiting values, constraints, 163–164
objective set-up, variable, 163–164
optimal values, decision variables, 165–166
solver, 165
expanded flight network, 157–158
mathematical algorithm, 155
one-scale flight network, 156–157
optimization algorithms, 154
Simplex method
auxiliary variable
definition, 66
largest conflicting constraint, 67
normalization of pivot row, 67
pivot operation, 68
system of equations, 67
construction materials company, 64–66
equation-based approach
all-slack basis, 54
basis, 53
basis and ratios, 54
improving the objective, 54–55
initial point, 53
variable replacement, 54
municipal engineer in trouble (infeasible), 60–63
setting up the problem, 51, 53
tableau approach
end of simplex pivot, 57
identities for basic variables, 56–57
normalization, 56
preparing for the tableau, 55–56
simplex pivot, 57
unbounded and infeasible, 59
Skewness, 86
Solver
contractor allocation, 175
definition, left-hand side, 165
set-up, 112
for underground tunnels, 183–184
STATA® linear regression, 113, 115
Statistics
average for sample, 85
average variation, 85
kurtosis, 86
sample histogram, 86
sanitary pipes
skewness, 86
vehicle
collisions
sample data deterioration, 87
variance and standard deviation, 87–88
Surface transportation demand
explanation of trips’ purpose/nature, 10, 12
freight trips
other regions, intermediate producers, 9, 12
land use location set-up, 9–10
objective, 11
T
Thornthwaite Moisture Index, 109
Transport and municipal engineering
coordination, public works
civil infrastructure maintenance and rehabilitation, 176
maintenance and rehabilitation interventions, 178–179
space/time coordination, 177
time and space openings, 178
handmade node structure, 152
network flows
Pedestrians’ tunnel network, 182–184
OD pairs, travel time, 153–154
public works allocation
infrastructure construction, 168
shortest path problem, 154–159
trans-shipment problem, 166–168
Trans-shipment algorithm
Canadian network
generic constraint, 166
U
Unbounded and infeasible problem, 59
Uncertainty
arbitrage, 221
in coefficients
convergence removal, 234
density function, 230
estimation of coefficients, 237
probability distribution, 229
sample data deterioration, 229–230
variability and uncertainty, 234
conditional probabilities, 226
experiment decision tree, 227
final decision tree, 228
marginal probabilities, 228
probability theory, 221
in response
comparison tool, 237
IRI expression, 241
predicted IRI vs. ESALs, 238, 241
sample data deterioration, 238–239
sample data road safety, 242–243
V
Value approach, desirability
cost, mitigation strategies, 223
expected profit and value
historical profit and probability, 222