GATECH Midterm 2 Analytics///
ISYE 6501 Midterm 2 - Intro
Analytics Modeling - ISYE-6501-
OAN-O01-QCH-A
A company has created a stochastic discrete-event simulation model of its customer
service call center, including call arrivals, resource usage (workers who specialize in
answering each type of calls, supervisors, etc.), and call duration. The call center is not
first-come-first-served; a call from a major client will be answered first, ahead of even
long-waiting callers with smaller accounts. When a new call comes in, the call center will
run the simulation to quickly give the caller an estimate of the expected wait time before
being helped. How many times does the company need to run the simulation for each
new caller (i.e., how many replications are needed)? - Answer-Many times, because of
the variability and randomness
The figure above shows the average of the first x simulated wait times, as new
replications ("runs") are run and added into the overall average. It is not showing the
wait time just for each replication. For example, after x=101 replications, the wait time of
the 101st replication is not necessarily 72, but the average of those 101 replications is
about 72. - Answer-Look next questions
-The simulation COULD have been stopped after 400 runs (replications).
-The simulation COULD even have been stopped after 300 runs (replications). -
Answer-- Could
-Could
The simulated wait time WAS NOT 50 or less just once out of all the runs (replications).
- Answer-- was not
The expected wait time of simulated runs (replications) IS LIKELY to be between 65 and
75. - Answer-IS LIKELY
There IS NOT very little variability in the simulated wait time of the runs (replications). -
Answer-IS NOT
Suppose it is discovered that simulated wait times are 50% higher than actual wait
times, on average. What would you recommend that they do? - Answer-Investigate to
see what's wrong with the simulation, because it's a poor match to reality.
, For each of the seven optimization problems below, select its most precise
classification. In each model, are the variables, all other letters ( , , ) refer to known
data, and the values of are all positive. Each classification might be used, zero, one, or
more than one time in the seven questions. - Answer-Look next questions
Minimze ∑i cixi
subject to ∑i aijxi ≥ bj for all j
all xi ≥ 0 - Answer-Linear program
Minimze ∑i cixiˆ2
subject to∑i aijxi ≥ bj for all j
all xi ≥ 0 - Answer-Convex quadratic program
Minimze for all all ∑i ci |xi − 6|
subject to ∑i aijxi ≥ bj for all j
all xi ≥ 0 - Answer-Convex program
Minimize ∑i cixi
subject to ∑i aijxi ≥ bj for all j
all xi ∈ {0, 1} - Answer-Integer program
Minimize ∑i ci sin xi
subject to ∑i aijxi ≥ bj for all j
all xi ≥ 0 - Answer-General non-convex program
Minimize ∑i cixi
subject to ∑i ∑k aikjxixk ≤ bj for all j
all xi ≥ 0 - Answer-General non-convex program
Minimize ∑i (log ci ) xi
subject to ∑i aijxi ≥ bj for all j
all xi ≥ 0 - Answer-linear program
A supermarket is analyzing its checkout lines, to determine how many checkout lines to
have open at each time. At busy times (about 10% of the times), the arrival rate is 5
shoppers/minute. At other times, the arrival rate is 2 shoppers/minute. Once a shopper
starts checking out (at any time), it takes an average of 3 minutes to complete the
checkout. [NOTE: This is a simplified version of the checkout system. If you have
deeper knowledge of how supermarket checkout systems work, please do not use it for
this question; you would end up making the question more complex than it is designed
to be.]
a. The first model the supermarket tries is a queuing model with 4 lines open at all
times. We would expect the queuing model to show that wait times are [ Select ] .
ISYE 6501 Midterm 2 - Intro
Analytics Modeling - ISYE-6501-
OAN-O01-QCH-A
A company has created a stochastic discrete-event simulation model of its customer
service call center, including call arrivals, resource usage (workers who specialize in
answering each type of calls, supervisors, etc.), and call duration. The call center is not
first-come-first-served; a call from a major client will be answered first, ahead of even
long-waiting callers with smaller accounts. When a new call comes in, the call center will
run the simulation to quickly give the caller an estimate of the expected wait time before
being helped. How many times does the company need to run the simulation for each
new caller (i.e., how many replications are needed)? - Answer-Many times, because of
the variability and randomness
The figure above shows the average of the first x simulated wait times, as new
replications ("runs") are run and added into the overall average. It is not showing the
wait time just for each replication. For example, after x=101 replications, the wait time of
the 101st replication is not necessarily 72, but the average of those 101 replications is
about 72. - Answer-Look next questions
-The simulation COULD have been stopped after 400 runs (replications).
-The simulation COULD even have been stopped after 300 runs (replications). -
Answer-- Could
-Could
The simulated wait time WAS NOT 50 or less just once out of all the runs (replications).
- Answer-- was not
The expected wait time of simulated runs (replications) IS LIKELY to be between 65 and
75. - Answer-IS LIKELY
There IS NOT very little variability in the simulated wait time of the runs (replications). -
Answer-IS NOT
Suppose it is discovered that simulated wait times are 50% higher than actual wait
times, on average. What would you recommend that they do? - Answer-Investigate to
see what's wrong with the simulation, because it's a poor match to reality.
, For each of the seven optimization problems below, select its most precise
classification. In each model, are the variables, all other letters ( , , ) refer to known
data, and the values of are all positive. Each classification might be used, zero, one, or
more than one time in the seven questions. - Answer-Look next questions
Minimze ∑i cixi
subject to ∑i aijxi ≥ bj for all j
all xi ≥ 0 - Answer-Linear program
Minimze ∑i cixiˆ2
subject to∑i aijxi ≥ bj for all j
all xi ≥ 0 - Answer-Convex quadratic program
Minimze for all all ∑i ci |xi − 6|
subject to ∑i aijxi ≥ bj for all j
all xi ≥ 0 - Answer-Convex program
Minimize ∑i cixi
subject to ∑i aijxi ≥ bj for all j
all xi ∈ {0, 1} - Answer-Integer program
Minimize ∑i ci sin xi
subject to ∑i aijxi ≥ bj for all j
all xi ≥ 0 - Answer-General non-convex program
Minimize ∑i cixi
subject to ∑i ∑k aikjxixk ≤ bj for all j
all xi ≥ 0 - Answer-General non-convex program
Minimize ∑i (log ci ) xi
subject to ∑i aijxi ≥ bj for all j
all xi ≥ 0 - Answer-linear program
A supermarket is analyzing its checkout lines, to determine how many checkout lines to
have open at each time. At busy times (about 10% of the times), the arrival rate is 5
shoppers/minute. At other times, the arrival rate is 2 shoppers/minute. Once a shopper
starts checking out (at any time), it takes an average of 3 minutes to complete the
checkout. [NOTE: This is a simplified version of the checkout system. If you have
deeper knowledge of how supermarket checkout systems work, please do not use it for
this question; you would end up making the question more complex than it is designed
to be.]
a. The first model the supermarket tries is a queuing model with 4 lines open at all
times. We would expect the queuing model to show that wait times are [ Select ] .
