CEE 3000 Midterm 2

what is this model known as?

what is this model known as?

epidemiology triad

evidence informs _____ and ______ informs models

theories, theories

define a model (also how it is used)

simplified or abstract representation of reality, it is to a tool for evaluation to provide insight and inform decisions, assists in design or management of engineered systems or related policy

the types of models

• iconic

• mathematical

types of iconic models

• physical

• graphical

types of graphical models

• representing physical reality

• representing concepts

types of mathematical models

• symbolic

• simulations

types of simulations (which is a type of mathematical model)

• computer

• live actor

descriptive vs prescriptive (predictive) model

• descriptive - describes expected output based on set of inputs and initial conditions

  • ex. population growth models (if I follow this course of action, what will happen?)

• prescriptive - predicts a course of action; leads to a desired solution

  • ex. optimization models (what is best course of action to follow?)

deterministic vs stochastic

• deterministic - models where data elements are relatively fixed and predictable quantities

  • ex. speed of a vehicle on a road, volume of water in a container given the initial volume and flow

• stochastic - randomness is present; many outcomes possible

  • ex. speed of vehicles on a road network, reservoir inflow during rainy season

mechanistic vs empirical model

• mechanistic - based on understanding of behavior of system components

  • ex. predicting acceleration using force and mass

• empirical - based on observation of data relationships without describing underlying mechanism

  • ex. collection of water temperatures and depth to build a model

what are the steps of model development?

• specification - selecting function form for the model (independent and dependent variables etc)

• calibration - estimate values of parameters and constants through trial and error

• validation - establishing credibility by demonstrating ability to replicate actual data

explain basic concept of optimization

there are decision variables, constraints, and the best decision is is the best combo of decision variables and corresponding value of object functions

math models can help us in the process of _______

optimization decision analysis

mathematical programming does what?

is an optimization tool that finds an extreme point for a decision variable given objects, parameters, and constraints

list some applications of mathematical programming in civil engineering

• deciding what landfills to operate

• deciding which road segments to repair

• size of a reservoir

• highway design

list parts of mathematical program for optimization

objectives, decision variables, constraints

list the types of mathematical programming

optimization by calculus (use calc for min and max), linear programming (objective function and constraints are linear), and integer programming (decision variables can only be integers)

civil engineering decision making has largely been governed by

economic efficiency considerations: it is difficult to quantify benefits monetarily, a investment impacts have wide reach

how has decision making changed?

• governments, organizations, and corporations are increasingly finding superior solutions by identifying diverse variety of decision making criteria

• decision making considered sustainable development

  • has multiple criteria (political, economic, social, environmental, etc)

  • characterized by numerous stakeholders, orgs, govs

  • not all criteria can be quantified

what are some criteria typically considered during various phases of CES decision making?

• system effectiveness

• system efficiency

• economic efficiency

• environmental impacts

• social/cultural impacts

• impacts on local/regional economy

• compatibility with existing policy

Steps for multi criteria decision making

1) initial steps: establish alternatives and establish decision criteria

2)weighting: establish criteria weights

3)scaling: establish neutral scale for measuring different levels and using scale to quantify the impact of each decision for each alternative

4) amalgamation: establish and apply objective function (to determine combined impact of decisions)

describe the framework for MCDM analysis using multi attribute utility theory

• reduce multi criteria problem to single criteria problem that incorporates all the criteria

• the underlying assumption: the decision makers preference structure can be represented by a real value function

define value function

measures preferences over a set of goods and services; represents satisfaction of a consumer from consuming certain goods/services

define decision criteria

criteria by which each alternative is evaluated

define weighting

the relative weights are assigned to each decision criteria which reflects the relative importance of criteria

define scaling

provides common scale of measurement by converting the unit of decision criteria to a unit less scale (involves developing single criteria value functions)

characterizing the relative level of importance of decision making criteria is also known as this

weighting

establishing a common scale of measurement across decision criteria so they can be expressed in commensurable units is also known as this

scaling

define amalgamation

combines the relative weight and a value function to determine the overall value of the alternative

value functions are developed at what step of the decision making process

scaling

when criteria is optimized the most in a tri-criteria problem, it is called this on the graph

Pareto frontier

why important to deal with uncertainty in systems analysis?

• we don’t have perfect knowledge (epistemic uncertainty)

• systems have random elements and random variables can impact system performance (aleatory uncertainty)

how do we incorporate uncertainty in systems analysis?

• through stochastic models: probability theory, statistical modeling, etc

define probability

the likelihood of an event occurring relative to the set of all possible events

two reasons why we might reason under uncertainty

• laziness (modeling all the details of a complex system is costly)

• ignorance (we don’t completely understand what’s going on in the system)

example of uncertain models: sea level rise

probability of an event E is bounded between what two numbers

0 and 1

assumptions in probability theory

• there are a discrete number of random events

• equally likely outcomes

the set of all possible events

(S) sample space: P(S) = 1

an event not within S (sample space)

impossible event: P(O)=0

when two events fill the sample space, these are called ________ events

complementary: P(E) + P(E’) = 1

mutually exclusive events are events that

cannot happen at the same time (simultaneously)

• E ∩ E’ = O or {} (meaning null set)

• P(E ∩ E’) = O (null)

• P(E U E’) = P(E) + E’

collectively exhaustive events are events that

take up the whole sample space and at least one event must occur

• P(E U E’) = P(S) = 1

• ex. rolling 6 sided die has 6 discrete outcomes

events that can occur at the same time

overlapping events

• E ∩ E’ NOT equal to O

ex. flipping a coin and a die at the same time

why do we use conditional probability?

it allows us to reason with partial information

explain conditional probability

if event E depends on C then the occurrence of E depends on the occurrence of C so the conditional probability is given as:

• P(E|C) = P(C ∩ E)/P(C)

events that occur at the same time but have no relationship

statistically independent, overlapping events: E is independent of C if the occurrence of E is not affected by occurrence of C

• P(E|C) = P(E)

• P(E ∩ C) = P(E) * P(C)

NOTE:

define engineering economy

involves formulating, estimating, and evaluating economic outcomes when there are alternatives to accomplish a defined purpose to add the max value in the future

collection of mathematical techniques that simplify economic comparison

engineering economy

the branch of knowledge concerned with the production, consumption, and transfer of wealth

economy

NOTE

define capital costs

initial project cost (materials, construction, permits,etc)

define operations and maintenance costs

recurring costs over the useful life of the project (labor, routine maintenance, reconstruction/rehiblitation) such as painting pavement, pavement overlays, bridge repairs

these are classified under project costs

capital costs

operations and maintenance

define user benefits

user advantages or profits gained and is usually measured in terms of reduction in user costs

ex. improved traffic flow = reduction in travel time costs

ex. constructed water supply system = potable water = reduction in health costs

define salvage value

value of facility/product/service at the end of its useful life (includes recycling and disposal)

these are classified under project benefits (terms)

• user benefits

• salvage value

time value of money refers to…

change in amount of money over a given time period (refers to the earning power of money), how money grows as a function of time, the idea of interest

amount charged for the use of money OR the amount earned for the loan of money

interest

(in general) interest =

Amt owed now - OG Amt borrowed

interest rate is (equation)

(interest accrued per unit time/og amount) x 100%

how is the interest rate determined?

supply and demand

the convention for the interest period

1 year

this is calculated the same way as the interest rate but is from the lenders perspective

rate of return

lowest rate of return considered acceptable for a lender in the private sector

minimum attractive rate of return (MARR)

the MARR in the private sector is equal to the

market rate

the lowest rate of return considered acceptable for public projects (public sector)

social discount rate (SDR)

the idea that different sums of money at different times have equal economic value

economic equivalence

define inflation

overall general upward movement of the price of goods and services in an economy; translates to a reduction in purchasing power

define opportunity cost

the forgone opportunity to invest money whenever money is committed to some investment proposal (forgone opportunity to use your money for smth else)

define a sunk cost

a past cost that cannot be altered by future action (only present and future costs when comparing projects)

interest paid only on the principle

simple interest

• I = P* i *n

when interest is paid on the principle plus the accrued interest, you get this interest type

compound interest

NOTE: Future value of initial investment

simple

• F = P(1 + in)

compound

• F = P(F/P,i,n) where F/P,i,n is the single payment compound amt factor

Total accrued =

(OG amount) + (OG amount)(interest rate)

how is n calculated? (dealing with future value)

n = ln(F/P) / ln (1 +i)