lOMoARcPSD|53162341
OPTIMIIZATION
Cons: no software to build b/c req. human
insight expertise, takes lots of prac. to learn
Opt. 4 presscriptive analy.(airplane mechanic
scheduling, GPS routing for cars, army recruit
asset usage, diet prob.)
OPT. Elements: dec.var.: dec. the opt. solver
will pick the best values for |constraints:
restrictions on those dec. we made(need 2 has a
relation be refl. by constraint) | obj. func.: meas.
quality of sol., a set of values for dec. var. which
we trying to max. or min. (can have alpha, beta, Lin.prog, convex prog, network-> guranteed
Expo. smoothing: OF(min.err.)
factor d)| feasible sol: set of values 4 dec.var. opt. sol. while integer & non-convex end up w/
that satify all constrain in opt. prob.| opt. sol: infeasible sol.(no sol. satisfy constraint)/ local
feas. sol. that has best obj.func.values) optimum(sol. Is != best)
How 2 create dec.var.: things we can make network prog.: a type of lin. prog(solve quicker
about/change, cant create dec.var.on a fact) than lin. prog., usage: GPS routing shortest
How 2 create constraints: 1.create const. to limit path, assign. prob.(worker vs job), max.
poss. sol. | 2. the opt. prob., using ineq. |3. flow( the amt of how much oil can get via
equality to des. Interactions bet. Dec.var. |4.cant pipe.)
create fact const.| 5. x_I>-0(non-negativity) OPT. For STAT. MODELS: notion def. for stat.
Diet Prob: Models(x_ij: var. that changes, a_1:constant
coeff. vice versa)
Lin. Reg. : Obj.Funt:(min. sum of n data pts i ARIMA & GARCH OF(min.pred.err.)
Lasso. Reg. : stand.reg w/ 1 constraint add to
restrict sum of var.
STOCHASTIC OPT.:
We implicitly assume we knew all input of
ridge Reg. : restriction on sum of sq. var. data, if there is uncertainty & random we use 1.
model conservatively method
Elastic : combine 2 terms into 1 const.
Call Center Prob:
Log. Reg. : var. r reg. coeff, OF(min. pred.err)
2. Scenario modeling:create diff.
CLASS. OPT. MODELS: scenarios&optimize all of them(use
Lin. Prog.:(uses in delivery serv, fin. Inst. heuristic)
Def robust sol: worse-case outcome over all
Stock Market Prob: poss. Scenarios is least bad
Hard class. : const(each data pt need to
correct class, OF;(min. margin bet. SV)
Convex Prog.:(uses: SVM, lin.reg., engin. prob) Dynamic program: diff.struc/use
states(specify what’s going on in the sys.,
e.g. status of a bug detect & fixed), then @
each state, dec.-maker makes a decision,
then sys. move to that state / can use
bellman’s eq. to deter. opt.dec. to make @
every state, gives no uncertainty
soft class. : OF(min.margin & class. Err.) Stochastic Dynamic program:can change
dyn.prog. model by incorporate w/ prob. If
Convex opt., integer, & gen. non-convex prog.
Downloaded by Jesus Rincon ()
lOMoARcPSD|53162341
we know the prob. of going from 1 state to Geo. Dist.:1. #s of failures be4 u get a succ. in bet. each call = exponetial with parameter mu |
another a series of bern. trials&has 2 poss. outc., trials for 1 employee, can calc. 1. expected frac. of
Markove dec. Process: if we have independent & prob. of succ. is same for each time our employee is busy |2. expect wait time
discret(fixed or countable) set of states & trial | 2. how many interv. U need to go via for a person before speaking to our employee |
dec, prob. only depend on curr. state & before getting 1st job offer | 3. it has a 3. real-life e.g. :expect #s of calls in a queue
decision memoryless property, if u intend to repeat Memoryless property: if we find that the
experiment until 1st succ., given 1st succ. has ! arrivals of calls to the queue fit a Poisson
HOW OPT. ALGO. WORKS
= occured, the latter trials doesnt depend on distribution, then it is memoryless, if
Two main steps(1. initialization:start w/ a sol. prev. failures something != memoryless, then != exponential
that can be simple, bad, feasi.) / 2. or poisson
repeat(start w/ curr. sol. ->find improving Balking: cust. deciding not to join queue it it is
direction(t) --> add step size to theta --> new To use together: product reliability & too long
sol.=old sol. + improving direction(t)*step situations that req. of calc. the waiting times SIMU. TYPES:
size(theta, which will be change) -> keep e.g. how much time will go before a major Deterministic simu.: never vary,gave same
repeat ->sol. doesnt change/run out of time hurricane hits the Atlantic Seaboard? OR how inputs & outputs, no randomness
Newton’s eq.:( above steps similar to this eq. long will the trans. in my car last before it Stochastic simu.: has diff. output each time
on finding root of f(x), @ step n, a curr. sol., breaks? (evt must happen more than once, running the model b/c sysm include
find improving direction & our new sol. : time elaspe bet. 2 evts is expo.n & evt randomness | 2. stock market and exchange
independent) rate fluctuations
xn+1=xn-1*t(might gurantee to find opt.sol)
total number of trials through the first success WEIBULL: Continous-time simu.: model changes that are
= pr(k) = (1-p)^(n-1) * p | to find the #s of trials 1. amt of time it takes something to fail esp. if happening continously(chem proces) &
before the 1st failure = Pr(k) = p^k * (1-p) time bet. failure(w/ expo. Dist., e.g. food w/ modeled w/ differential eq.
Poisson Dist.: 1.useful to pred. prob. of certain const. shelf life | 2. k=1(when failure rate Discrete-event simu.: sym. only changes @
evt happening when u know how often the evt =constant w/ time, reduce to expo. dist, subs. discrete time pts when something
has occ. & gives u the prob. of a given #s of 1/lambda.), k<1(failure dec, e.g. parts w/ happens( call center, changes happen when
evt happening in a fixed interval of time| 2. defects), k>1(tires) someone calls or worker finish talking to
airport situation: P(x; μ ), the μ is avg. #s of some1 & start to talk to some1 else) & avg.
arrivals in a time pd(#s of evt occurence) & x = values not good enough | 2. e.g. wafer process
x pple that arrive given the avg arrival rate Arena simu: 1.can be used to build small &
lambda(#s of pple or #s of storms we think will complex simulations with lots of diff. process |
Global max.:OB(max) vs global min.(OB->min) happen given the avg. #s of evt occurence(e.g. 2. airport baggage simu. to decide #s of bag
PROB-BASED MODELS & pred. the prob. of more books sell next sat. tugs that will be needed & where they should
Prob. Dist.: desc. all poss. values&likelihood based on avg. #s of txtbooks sold) | 3. if given be located to ensure the arriving bags moved
of a ran.var. can take within a given range(1. avg. prob. & u want to find prob. of a certain #s quickly both from planes to the baggage claim
Data fitting software: can fit to prob. dist.& tell
of evt--> use poisson & if ur q’s has exact & cancer treatment clinic simu. & airline's
f(x) must be non-neg. 4 each value of ran.var. u best fit para., most approriate value of
prob. & u want to find prob. of evt happening global flight network simu.:
& 2. prob. of particular range must be bet.0 to lambda
in a certain #s of times out of--> use bin. dist.| Elements of simu. model: 1.entities(can pass
1) QQ PLOT:
4. poisson dist. is != memoryless, it is the dist. via a network of queue) | 2. modules(represent
Bernoulli: 1. use to model a single event or 1. whether two dist. data are about same &
of waiting times in the poisson process that is parts of a process) | 3. action to take &
bin. Dist. W/ single trial & can only has 2 help to see when there’s extreme pt @ high &
memoryless(expo.dist.) resources(e.g. workers) & dec. pts & ways to
poss. Outc.(success/failure)&evt indepent | low tails&if normal, should fit nicely as
45degree to the straight line(if both sets of track stat. about simu. in its entities
2.e.g. single coin toss Simu. Cons: replication, cant run a stoc. simu.
quantiles came from same dist.) , if a S -shape
QQ plot, data don’t fit well, u will see it has 1 time b/c of 1 random outc. , may or may not
higher values for lower quantiles vs lower be representative, need to validate as much as
values for higher quantiles | 2. plot horizontal poss. against real data(e.g. simu. shows 250
axis(data plot) vs vertical axis(theoretical vs real prod. Of 100)
Binomial dist.: consist of single evt repeated PRESCRIPTIVE SIMU.
mult. times, 2 poss. outcomes, #s of trials fixed, values of percentiles)
Uses: what-if type of q’s about sys(e.g. how r
evt indepdent, prob. of success is same in each the overall process throughput change if
trial / diff. from bernoulis: if each bernoulli trial is Expo.Dist.1. prob. dist. that desc. time bet. evt company invest in 100k on a faster machine
independent, #s of succ. in bern. has a bin., if in a poisson process(if arrival = poisson, avg for 1 step process) & can simu. with diff. opt. &
bern. dist. Is bin. dist. w/ n=1 |2. #s of succ. sales #s of arrival rate(lambda) bet. time = inter- compare results to see best action
calls) -->due to central limit theorem, when n arrival time & arrival will follow the expo. dist. Comparison: run 1st simu. model with 1 setup
inc., n trials & prob. P succ. will get closer to with 1 over lambda as the avg. inter-arrival of baggage tugs for each gate vs run the 2nd
norm.dist., e.g. think of as survey the whole pop. time & on the other hand, if times bet. arrivals simu. model with one tug for every 2 gates -->
-->convert into norm. are expo. distr. with an avg. inter-arrival time 1 then compare the simulated sys. performance
over lambda, then the arrival follows the bet. the two | 2. do a basic test to see the
poisson dist. with an avg lambda arrival/unit of means of the 2 simu. models, for each
time) scenario, we can then see which met. is better
& see how often 1 is better than the other, this
method is a non-parametric test that can give
u valuable info.
This study source was downloaded by 100000899606070 from CourseHero.com on 02-22-2026 22:22:26 GMT -06:00 Simu. Drawbacks: if there's missing info. or
QUEUE incorrect assumptions, simu. might give
constructed so the queue lengths & waiting
wrong answers ( in the call center simu. we
time can be predicted / suppose call arrival =
might assume every worker ans. calls equally
Poisson with lambda parameter, the call length
quicker but in reality, there's many variability
https://www.coursehero.com/file/250927868/Midterm-2-cheatsheet-from-the-lecturespdf/
Downloaded by Jesus Rincon ()
OPTIMIIZATION
Cons: no software to build b/c req. human
insight expertise, takes lots of prac. to learn
Opt. 4 presscriptive analy.(airplane mechanic
scheduling, GPS routing for cars, army recruit
asset usage, diet prob.)
OPT. Elements: dec.var.: dec. the opt. solver
will pick the best values for |constraints:
restrictions on those dec. we made(need 2 has a
relation be refl. by constraint) | obj. func.: meas.
quality of sol., a set of values for dec. var. which
we trying to max. or min. (can have alpha, beta, Lin.prog, convex prog, network-> guranteed
Expo. smoothing: OF(min.err.)
factor d)| feasible sol: set of values 4 dec.var. opt. sol. while integer & non-convex end up w/
that satify all constrain in opt. prob.| opt. sol: infeasible sol.(no sol. satisfy constraint)/ local
feas. sol. that has best obj.func.values) optimum(sol. Is != best)
How 2 create dec.var.: things we can make network prog.: a type of lin. prog(solve quicker
about/change, cant create dec.var.on a fact) than lin. prog., usage: GPS routing shortest
How 2 create constraints: 1.create const. to limit path, assign. prob.(worker vs job), max.
poss. sol. | 2. the opt. prob., using ineq. |3. flow( the amt of how much oil can get via
equality to des. Interactions bet. Dec.var. |4.cant pipe.)
create fact const.| 5. x_I>-0(non-negativity) OPT. For STAT. MODELS: notion def. for stat.
Diet Prob: Models(x_ij: var. that changes, a_1:constant
coeff. vice versa)
Lin. Reg. : Obj.Funt:(min. sum of n data pts i ARIMA & GARCH OF(min.pred.err.)
Lasso. Reg. : stand.reg w/ 1 constraint add to
restrict sum of var.
STOCHASTIC OPT.:
We implicitly assume we knew all input of
ridge Reg. : restriction on sum of sq. var. data, if there is uncertainty & random we use 1.
model conservatively method
Elastic : combine 2 terms into 1 const.
Call Center Prob:
Log. Reg. : var. r reg. coeff, OF(min. pred.err)
2. Scenario modeling:create diff.
CLASS. OPT. MODELS: scenarios&optimize all of them(use
Lin. Prog.:(uses in delivery serv, fin. Inst. heuristic)
Def robust sol: worse-case outcome over all
Stock Market Prob: poss. Scenarios is least bad
Hard class. : const(each data pt need to
correct class, OF;(min. margin bet. SV)
Convex Prog.:(uses: SVM, lin.reg., engin. prob) Dynamic program: diff.struc/use
states(specify what’s going on in the sys.,
e.g. status of a bug detect & fixed), then @
each state, dec.-maker makes a decision,
then sys. move to that state / can use
bellman’s eq. to deter. opt.dec. to make @
every state, gives no uncertainty
soft class. : OF(min.margin & class. Err.) Stochastic Dynamic program:can change
dyn.prog. model by incorporate w/ prob. If
Convex opt., integer, & gen. non-convex prog.
Downloaded by Jesus Rincon ()
lOMoARcPSD|53162341
we know the prob. of going from 1 state to Geo. Dist.:1. #s of failures be4 u get a succ. in bet. each call = exponetial with parameter mu |
another a series of bern. trials&has 2 poss. outc., trials for 1 employee, can calc. 1. expected frac. of
Markove dec. Process: if we have independent & prob. of succ. is same for each time our employee is busy |2. expect wait time
discret(fixed or countable) set of states & trial | 2. how many interv. U need to go via for a person before speaking to our employee |
dec, prob. only depend on curr. state & before getting 1st job offer | 3. it has a 3. real-life e.g. :expect #s of calls in a queue
decision memoryless property, if u intend to repeat Memoryless property: if we find that the
experiment until 1st succ., given 1st succ. has ! arrivals of calls to the queue fit a Poisson
HOW OPT. ALGO. WORKS
= occured, the latter trials doesnt depend on distribution, then it is memoryless, if
Two main steps(1. initialization:start w/ a sol. prev. failures something != memoryless, then != exponential
that can be simple, bad, feasi.) / 2. or poisson
repeat(start w/ curr. sol. ->find improving Balking: cust. deciding not to join queue it it is
direction(t) --> add step size to theta --> new To use together: product reliability & too long
sol.=old sol. + improving direction(t)*step situations that req. of calc. the waiting times SIMU. TYPES:
size(theta, which will be change) -> keep e.g. how much time will go before a major Deterministic simu.: never vary,gave same
repeat ->sol. doesnt change/run out of time hurricane hits the Atlantic Seaboard? OR how inputs & outputs, no randomness
Newton’s eq.:( above steps similar to this eq. long will the trans. in my car last before it Stochastic simu.: has diff. output each time
on finding root of f(x), @ step n, a curr. sol., breaks? (evt must happen more than once, running the model b/c sysm include
find improving direction & our new sol. : time elaspe bet. 2 evts is expo.n & evt randomness | 2. stock market and exchange
independent) rate fluctuations
xn+1=xn-1*t(might gurantee to find opt.sol)
total number of trials through the first success WEIBULL: Continous-time simu.: model changes that are
= pr(k) = (1-p)^(n-1) * p | to find the #s of trials 1. amt of time it takes something to fail esp. if happening continously(chem proces) &
before the 1st failure = Pr(k) = p^k * (1-p) time bet. failure(w/ expo. Dist., e.g. food w/ modeled w/ differential eq.
Poisson Dist.: 1.useful to pred. prob. of certain const. shelf life | 2. k=1(when failure rate Discrete-event simu.: sym. only changes @
evt happening when u know how often the evt =constant w/ time, reduce to expo. dist, subs. discrete time pts when something
has occ. & gives u the prob. of a given #s of 1/lambda.), k<1(failure dec, e.g. parts w/ happens( call center, changes happen when
evt happening in a fixed interval of time| 2. defects), k>1(tires) someone calls or worker finish talking to
airport situation: P(x; μ ), the μ is avg. #s of some1 & start to talk to some1 else) & avg.
arrivals in a time pd(#s of evt occurence) & x = values not good enough | 2. e.g. wafer process
x pple that arrive given the avg arrival rate Arena simu: 1.can be used to build small &
lambda(#s of pple or #s of storms we think will complex simulations with lots of diff. process |
Global max.:OB(max) vs global min.(OB->min) happen given the avg. #s of evt occurence(e.g. 2. airport baggage simu. to decide #s of bag
PROB-BASED MODELS & pred. the prob. of more books sell next sat. tugs that will be needed & where they should
Prob. Dist.: desc. all poss. values&likelihood based on avg. #s of txtbooks sold) | 3. if given be located to ensure the arriving bags moved
of a ran.var. can take within a given range(1. avg. prob. & u want to find prob. of a certain #s quickly both from planes to the baggage claim
Data fitting software: can fit to prob. dist.& tell
of evt--> use poisson & if ur q’s has exact & cancer treatment clinic simu. & airline's
f(x) must be non-neg. 4 each value of ran.var. u best fit para., most approriate value of
prob. & u want to find prob. of evt happening global flight network simu.:
& 2. prob. of particular range must be bet.0 to lambda
in a certain #s of times out of--> use bin. dist.| Elements of simu. model: 1.entities(can pass
1) QQ PLOT:
4. poisson dist. is != memoryless, it is the dist. via a network of queue) | 2. modules(represent
Bernoulli: 1. use to model a single event or 1. whether two dist. data are about same &
of waiting times in the poisson process that is parts of a process) | 3. action to take &
bin. Dist. W/ single trial & can only has 2 help to see when there’s extreme pt @ high &
memoryless(expo.dist.) resources(e.g. workers) & dec. pts & ways to
poss. Outc.(success/failure)&evt indepent | low tails&if normal, should fit nicely as
45degree to the straight line(if both sets of track stat. about simu. in its entities
2.e.g. single coin toss Simu. Cons: replication, cant run a stoc. simu.
quantiles came from same dist.) , if a S -shape
QQ plot, data don’t fit well, u will see it has 1 time b/c of 1 random outc. , may or may not
higher values for lower quantiles vs lower be representative, need to validate as much as
values for higher quantiles | 2. plot horizontal poss. against real data(e.g. simu. shows 250
axis(data plot) vs vertical axis(theoretical vs real prod. Of 100)
Binomial dist.: consist of single evt repeated PRESCRIPTIVE SIMU.
mult. times, 2 poss. outcomes, #s of trials fixed, values of percentiles)
Uses: what-if type of q’s about sys(e.g. how r
evt indepdent, prob. of success is same in each the overall process throughput change if
trial / diff. from bernoulis: if each bernoulli trial is Expo.Dist.1. prob. dist. that desc. time bet. evt company invest in 100k on a faster machine
independent, #s of succ. in bern. has a bin., if in a poisson process(if arrival = poisson, avg for 1 step process) & can simu. with diff. opt. &
bern. dist. Is bin. dist. w/ n=1 |2. #s of succ. sales #s of arrival rate(lambda) bet. time = inter- compare results to see best action
calls) -->due to central limit theorem, when n arrival time & arrival will follow the expo. dist. Comparison: run 1st simu. model with 1 setup
inc., n trials & prob. P succ. will get closer to with 1 over lambda as the avg. inter-arrival of baggage tugs for each gate vs run the 2nd
norm.dist., e.g. think of as survey the whole pop. time & on the other hand, if times bet. arrivals simu. model with one tug for every 2 gates -->
-->convert into norm. are expo. distr. with an avg. inter-arrival time 1 then compare the simulated sys. performance
over lambda, then the arrival follows the bet. the two | 2. do a basic test to see the
poisson dist. with an avg lambda arrival/unit of means of the 2 simu. models, for each
time) scenario, we can then see which met. is better
& see how often 1 is better than the other, this
method is a non-parametric test that can give
u valuable info.
This study source was downloaded by 100000899606070 from CourseHero.com on 02-22-2026 22:22:26 GMT -06:00 Simu. Drawbacks: if there's missing info. or
QUEUE incorrect assumptions, simu. might give
constructed so the queue lengths & waiting
wrong answers ( in the call center simu. we
time can be predicted / suppose call arrival =
might assume every worker ans. calls equally
Poisson with lambda parameter, the call length
quicker but in reality, there's many variability
https://www.coursehero.com/file/250927868/Midterm-2-cheatsheet-from-the-lecturespdf/
Downloaded by Jesus Rincon ()
