5. the existing operating room. In
addition, BIR is planning on building another operating room
and has options on which
equipment to install as well as how to perform the scheduling
for the room. BIR would further
appreciate your insight into this problem.
To best aid BIR hospital, they want you to investigate the best
deterministic and stochastic
scheduling system for their current operating room (Part 1 and
Part 2 respectively) as well as
determine the best equipment and scheduling system for the new
operating room (Part 3).
Part 1
For the first analysis, BIR would like to determine the optimal
scheduling system under the
assumption that the number of nurses needed for each surgeon is
known with absolute certainty.
In most cases this is true, but they will change this assumption
for the next part.
For their current system, BIR needs to determine which
surgeons are assigned to which operating
blocks from Monday through Friday. Currently they have the
following three 4 hours blocks
6. each weekday: 8 AM to 12 PM, 12 PM to 4 PM, and 4 PM to 8
PM. Hence, there is a total of 15
surgery blocks per week. They currently employ 3 surgeons: Dr.
Miller who requires 5 total
blocks, Dr. Halpert who requires 4 total blocks, and Dr.
Walterscheid who requires 5 total
blocks. Based on their current estimates (which are revisited in
Part 2), Dr. Miller requires 8
nurses to be staffed whenever he is scheduled in the operating
room, Dr. Halpert requires 5
nurses to be staffed whenever she is scheduled in the operating
room, and Dr. Walterscheid
requires 11 nurses to be staffed whenever he is scheduled in the
operating room. Each of the
surgeons also were allowed to rank each of the available time
blocks on a scale of 0 to 4 based
on which slots they would prefer. They were allowed to assign
up to three total blocks to be any
one rating (i.e. they could assign at most three blocks a value of
0) and a rating of 0 is best (they
really want that time slot) and a rating of 4 is worst (they really
want to avoid that time slot). The
ratings they provided are shown in the tables below:
Dr. Miller time block preference:
7. Monday Tuesday Wednesday Thursday Friday
8 AM to 12 PM 0 0 0 2 2
12 PM to 4 PM 1 1 1 2 3
4 PM to 8 PM 4 4 4 3 3
Dr. Halpert time block preference:
Monday Tuesday Wednesday Thursday Friday
8 AM to 12 PM 0 3 3 1 1
12 PM to 4 PM 3 4 4 1 2
4 PM to 8 PM 4 0 0 2 2
Dr. Walterscheid time block preference:
Monday Tuesday Wednesday Thursday Friday
8 AM to 12 PM 1 0 3 3 4
12 PM to 4 PM 1 0 2 3 4
4 PM to 8 PM 1 0 2 2 4
8. BIR would like the surgeons to be scheduled such that the
cumulative rating sum for whenever
the surgeons are scheduled is less than or equal to 24.
Additionally, BIR needs help scheduling their operating room
nursing staff based on the
schedule of the surgeons (which you decide). Specifically, BIR
typically schedules a nurse based
on one of nine options:
to Thursday 8 AM to 8 PM ($32/hour)
to 4 PM ($28/hour)
to 8 PM ($28/hour)
8 AM to 8 PM, Wednesday/Thursday 8 AM to
4 PM ($28/hour)
to 8 PM ($28/hour)
Hence, whenever a nurse is hired, they are assigned to one of
9. these schedules. Clearly BIR needs
to hire enough nurses to match the schedule of the surgeons.
However, BIR doesn’t want to
schedule nurses so poorly that there more than 30 idle nurse-
blocks per week (i.e. if they need 8
nurses from 8 AM to 12 PM on Monday but have 10 scheduled,
this counts 2 idle nurse-blocks
from the upper limit of 30). Additionally, the total salary
expenses on nurses should not exceed
$17,000 for a week. Given this information, BIR’s primary goal
is to schedule the surgeon
blocks and the nurses such that the minimum number of nurses
are employed given the
aforementioned requirements.
However, BIR recognizes that other solutions may exist.
Specifically, they are interested in the
possible solutions assuming that the surgeons and nurses are
scheduled such that:
ting sum is minimal
-blocks are minimal
10. BIR identified that each of these objective should be focused on
assuming all other constraints
are still valid (i.e. weekly nurse salary does not exceed $17,000,
etc.). Additionally, to avoid
impractical solutions, BIR recommends ensuring that the total
number of nurses hired does not
exceed a given threshold whenever one of the three
aforementioned objectives is optimized.
Since they do not know how many nurses are currently needed,
they recommend you determine
this limit. Additionally, the solutions obtained may be very
sensitive to this limit so it is
recommended multiple limits are tested.
Ultimately, BIR wants one recommended surgery and nursing
scheduling given the criteria.
Multiple plans will likely be developed but one final plan must
be recommended.
Part 2
Given the solution from Part 1, BIR would like you to
reevaluate your decision making assuming
that the estimates on the number of nurses needed were not
accurate. Instead, each surgeon has
provided historical data on the number of nurses required during
their block. Specifically, each
11. surgeon provided 100 samples on the number of nurses they
needed. BIR would like you to
reevaluate your Part 1 decision given these samples.
It is suggested that your recommended solution from Part 1 is
reevaluated given this new data.
BIR recommends fitting statistical distributions to this new data
to determine the distribution of
the number of nurse-blocks which are overstaffed and the
number of nurse-blocks which are
understaffed. Since these values will not be known with
certainty (since the number of needed
nurses is not known with certainty), it is recommended that the
expected, maximum, and
minimum over and understaffed nurse-blocks are reported.
Since the recommendation from Part
1 is not final, it is possible to reevaluate your decision from
Part 1 at this juncture.
Part 3
In addition to the current operating room, BIR hospital is also
planning on building an additional
operating room and would like advice on which equipment to
install and how to plan scheduling
in the room. Specifically, they can design the room to have no
12. special equipment, special
equipment for Ophthalmology operations (eye surgery), special
equipment for robotic surgery, or
special equipment for both types of surgeries. As a baseline,
BIR has determined that the room
will be used for 7 or 8 basic procedures per day (without any
special equipment) with a
probability of 60% and 40% respectively. Additionally, if
robotic surgery equipment is installed,
3 or 4 more procedures can be performed per day with
probabilities 30% and 70% respectively
and if ophthalmology equipment is installed, 2 or 3 more
procedures can be performed per day
with probabilities 35% and 65% respectively. However, at most
14 procedures can be performed
in a day which may limit the amount which can be scheduled in
the case where both sets of
special equipment are installed. For each procedure, BIR
receives $3,000 in profit.
Once the number of procedures/day are known (important, the
number of procedures is already
known!), BIR can determine how they want to schedule their
employees. They can either keep
their current scheduling (which costs nothing since it is built
13. into the procedure profit) or they
can call-in staff members (expedited) in the morning which will
always satisfy all procedure
demands. This second option costs $4000 for the day. If the
second option is selected (expedited
scheduling), they will know the exact profit for the day based
on the profit/procedure and the
extra cost of $4,000.
If they select the first option (standard scheduling), then they
don’t incur extra cost immediately,
but there is a probability that they will have to call in temporary
workers immediately if they did
not schedule correctly. Since these workers are only hired on a
per-procedure basis, they are
extremely expensive. If they have to call in only some workers
(essentially a few extra nurses), it
costs $3,000 and if they have to call in a significant number of
workers (nurses and surgeons) it
costs $12,000. The probability of having to call in these extra
workers is given in the table below
based on the number of procedures that day.
Procedures No Extra Empl. Some Extra Empl. Significant Extra
14. Empl.
7 95% 5% 0%
8 91% 7% 2%
9 82% 12% 6%
10 71% 17% 12%
11 58% 22% 20%
12 31% 31% 38%
13 21% 34% 45%
14 11% 31% 58%
Given this information, BIR would like to know which
equipment they should install and what
scheduling methodology they should employ based on the
number of procedures such that the
expected profits are as large as possible. Additionally, the
profit/procedure ($3,000), the cost of
expedited scheduling ($4,000), and the cost of calling in some
extra employees and a significant
number of extra employees are preliminary and may change.
BIR would like you to investigate
what happens if these initial values change and should they
change their decision making based
15. on these changes.
Beth Israel Regional Hospital Surgical and Nurse
Scheduling Study
Christopher Wishon
Executive Summary:
TO ALL STUDENTS: This section should be a brief summary
of the work and final
recommended solutions. Essentially, this can be read to fully
understand what
techniques/methods you utilized and to understand your final
recommended findings without
having to read the rest of your report. This is conceptually
equivalent to an ‘abstract’ if you are
more comfortable with that term.
16. Project Definition
TO ALL STUDENTS: This section should serve as an
introduction for the report. At a high-
level, this will likely duplicate much of the information
provided in the case study document.
This is completely fine to do since it is important to tell a
sponsor/employer that you considered
all aspects of the problem they gave you. Be careful though to
not duplicate things you mention
in the ‘approach and analysis’ sections.
Part 1 Approach and Analysis
To best address the needs for BIR hospital, an integer
optimization model was developed to
determine the optimal surgical and nursing schedules.
Specifically, an optimization models
requires a set of controllable values (such as the assignment of
surgical blocks to a specific
surgeon) and a goal which must be met (such as hiring the
minimal number of nurses). This goal
and these values are restricted by a set of limits/constraints
which must be met in the final
17. solution. This framework was applied to obtain all solutions in
this section.
For these problems, two sets of controllable values (hereafter
referred to as decision variables)
were developed. The first set of decision variables represent the
assignment of specific time
blocks to specific surgeons. These were restricted such that only
one surgeon could ever be
assigned to one time block and that each surgeon was assigned
the required number of time slots.
The other set of decision variables represented the number of
nurses which needed to be hired for
each of the nine possible staffing schedules. These values were
restricted such that enough
nurses were hired to meet the demand for nurses based on the
surgeon schedule (i.e. the other
decision variables). These variables were further restricted by
the requirements that at most
$17,000 was spent weekly on nursing payroll, surgical
scheduling deviation is at most 24, and
idle nurse-blocks does not exceed 30. The full optimization
model is provided in Appendix A.
Given these variables and these requirements, the first integer
optimization model was solved
18. such that the ideal surgical and staff schedule was identified
assuming that the minimum number
of nurses was hired. This identified that the minimum number of
nurses needed is 13. Hence,
there is no solution for 12 or less nurses which satisfy all of the
other requirements. Given this
value, the goal of the current model was modified such that the
number of idle nurse-blocks was
minimal, the nursing salary was minimal, or the surgery rating
sum was minimal. For each of
these goals, the model was solved assuming at most 13 nurses
could be hired. In addition, the
same goals were used assuming at most 14 and 15 nurses could
be hired in case more efficient
solutions could be identified if slight increases in nursing levels
were permitted.
In total, these tests identified 10 surgical and nursing schedule
solutions. These are the solution
with the minimal number of nurses as well as the solutions for
the other three goals given at most
13, 14, and 15 nurses could be hired. These solutions are
summarized in Table 1. This table
indicates the number of nurses hired in the solution, the
quantity of idle nurse-blocks, the
19. surgeon rating sum, and the nursing salary. Furthermore, the
nursing hiring pattern is shown in
Table 2 for each solution and the surgeon scheduling pattern for
each surgeon is shown in Table
7 through 9 in Appendix A.
Table 1: Part 1 solution summary for key statistics
Scenario Max. Nurse
Limit
Nurses
Hired
Surgeon Rating
Deviation
Unused
Nurse Period
Nursing
Salary ($)
Min Nurses N/A 13 21 14 13752
21. Scenario
Min.
Nurses
Min. Surgeon
Rating
Min. Unused
Nurses
Min. Nurse
Salary
Max. Nurse Limit N/A 13 14 15 13 14 15 13 14 15
M to F 8 AM to 4 PM 7 0 0 0 0 0 0 8 8 8
M to F 12 PM to 8 PM 0 4 4 4 0 0 0 5 5 5
M to W 8 AM to 8 PM 1 1 2 4 2 2 2 0 0 0
T to Th 8 AM to 8 PM 0 0 2 2 0 0 0 0 0 0
W to F 8 AM to 8 PM 0 0 0 0 5 5 5 0 0 0
M/Th 8 - 8, T/W 8 - 4 0 7 3 4 2 1 2 0 0 0
M/Th 8 - 8, T/W 12 - 8 4 0 2 0 4 5 4 0 0 0
T/F 8 - 8, W/Th 8 - 4 0 1 1 0 0 0 0 0 0 0
22. T/F 8 - 8, W/Th 12 - 8 1 0 0 1 0 0 0 0 0 0
Based on the prior two tables (in addition to the three tables in
Appendix A), numerous
observations are possible. First and foremost, the optimal
scheduling pattern when the nurisng
salary is minimized is not sensitive to the limit on nurses as the
solution does not change if the
limit is modified. Furthermore, even though Table 2 shows
differing solutions when using a limit
of 14 nurses compared with a limit of 13/15 nurses when the
goal is to minimize the quantity of
idle nurse-blocks, Table 1 indicates that these solutions are all
equivalent. Hence, the solution is
insensitive to the number of nurses available when minimizing
the quantity of idle nurse-blocks
as well. These observations indicate that at most 13 nurses are
needed if either of the
aforementioned goals are desired.
The only solution is which is sensitive to changes in the limits
in nurses available is if the desired
goal is to minimize the surgeon rating sum. Specifically, as the
limit on nurses increases, Table 1
demonstrates that the number of hired nurses increases which is
23. unique to this objective.
However, for each increase in hired nurses, the surgeon rating
sum only decreases by one unit.
Since the increase in the nurses available also increases the
salary costs and quantity of idle
nurse-blocks, the solutions for minimizing the surgeon rating
sum when 14 and 15 nurses are
available are not recommended as the decrease in the rating sum
is outweighed by the increase in
all of the other measures.
Hence, only 4 unique possible solutions are reasonable for
selection (those solutions which result
in only hiring 13 nurses). Of these possibilities, the
recommended solution is the plan obtained
when the goal is to minimize the nursing salary. This plan was
chosen as it is a good compromise
between all of the developed schedules. Specifically, it clearly
has the lowest nursing salary (by
nearly $1000) and the second best surgeon rating sum as it trails
the best surgeon rating sum by
only a value of 4. The next best surgeon rating sum is 7 above
the minimum thereby
24. demonstrating a large gap between these options. With respect
to the idle nurse-blocks, the
recommended solution has the worst value, but only has 1 more
idle nurse-block than the second
best option which has 14 idle nurse-blocks. Hence, it is still
competitive in this category as well.
Given these advantages, the recommended solution based on the
Part 1 analysis recommends
assigning Dr. Miller the 8 AM to 12 PM time blocks on every
week day, assigning Dr. Halpert
the 4 PM to 8 PM time slot every weekday except for Monday
and assigning Dr. Walterscheid to
the 12 PM to 4 PM time blocks every weekday. To staff the
operating room, it is recommended
to hire 8 nurses on the Monday to Friday from 8 AM to 4 PM
shift and to hire 5 nurses on the
Monday to Friday from 12 PM to 8 PM shift.
Part 2 Approach and Analysis
Given the now unpredictable number of nurses, a simulation
model was developed to further
refine the Part 1 decision. For summary, a simulation model
requires mathematical equations
which calculate some output of interest (such as the quantity of
under and over staffed nurse-
25. blocks) given some inputs which are not predictable with
absolute certainty. For this problem,
the only inputs which match this description are the number of
nurses needed by a surgeon which
had statistical distributions fit to the provided data sample.
Using these distributions and the
mathematical equations, randomly generated values for the
number of nurses needed based on a
given surgeon schedule were generated multiple times and the
quantity of under and over staffed
nurse-blocks were recorded for each set of generated values.
This is equivalent to the real-world
scenario as the quantity of under and over staffed nurse-blocks
will vary by the day and the
simulation model is able to replicate this behavior quickly and
reliably. In total, 10,000 days
were simulated and the statistics of the output values were
calculated. The full details regarding
the distributions and the mathematical equations used in the
simulation model are provided in
Appendix B.
Given this approach, each of the unique solutions generated in
Part 1 were tested on the
26. simulation model. This includes the recommended plan from
Part 1 as well as the surgical and
nursing schedules from the Part 1 model when the objective was
to minimize the total number of
nurses hired, minimize the surgeon rating sum at each of the
total nursing levels, and minimize
the quantity of idle nurse-blocks. While these were not
recommended in Part 1, they were
included in this analysis since the stochastic nature of the
nursing needs may result in one of
these plans being a better choice given the current assumptions.
Once all of the simulations were completed, the average,
maximum, minimum, and standard
deviation on the quantity of under and over staffed nurse-blocks
were recorded for the simulated
10,000 days. These calculations are shown in Table 3. The
principal results from Table 3 are that
the simulation analyses reinforce the observations from Part 1
that the solutions obtained when
14 and 15 nurses are permitted when the objective is to
minimize the surgeon rating sum are not
competitive. Specifically, Part 1 demonstrated that only
minimal benefit was achieved during
27. these scenarios at a very high cost of nursing salary and idle
nurse-blocks. Table 3 also
demonstrates this pattern as the slight decrease in nursing sum
from Part 1 is drastically
outweighed by major increases in all statistical measures for the
overstaffed nurse-blocks. While
these extra nurses due result in small decreases in the statistical
measures for understaffed nurse-
blocks, this benefit does not outweigh the extremely high costs.
Hence, these solution are again
not recommended.
Table 3: Part 2 simulation results
Scenario Min.
Nurses
Min. Surgeon
Rating
Min. Unused
Nurses
Min. Nurse
Salary
28. Max. Nurse Limit N/A 13 14 15 13 13
Overstaffed
Nurse-
Blocks
Average 23.97 24.05 30.43 37.45 19.67 26.46
Minimum 5 7 12 18 5 9
Maximum 45 46 56 59 41 45
St. Deviation 5.28 5.18 5.61 5.84 4.83 4.96
Understaffed
Nurse-
Blocks
Average 5.87 5.95 5.33 4.35 7.57 7.36
Minimum 0 0 0 0 0 0
Maximum 20 18 18 16 25 22
St. Deviation 3.08 3.12 2.85 2.645 3.43 3.53
By eliminating these 2 solutions, 4 possible solutions remain.
The initially recommended
solution from Part 1 (the solution obtained when the goal is to
minimize the nursing salary) is no
29. longer recommended. The principal rationale behind this change
is because this solution has the
highest statistical measures for the overstaffed nurse-blocks and
the second highest statistical
measures for the understaffed nurse-blocks of the 4 remaining
solutions. This solution was a
good compromise in Part 1, but only by a small margin
compared with the other solutions. By
adding the Part 2 results to this observation, this small
advantage no longer remains and one of
the other solutions should be recommended.
Based on Table 3, it is not advisable to schedule according to
the solution obtained when the
objective was to minimize the quantity of idle-nurse blocks.
This solution provides the lowest
statistics with respect to the overstaffed nurse-blocks but
provided the worse statistics with
respect to the understaffed nurse-blocks. Since having
understaffing during critical procedures is
ill-advised, this solution is not recommended.
The best option between the remaining two solutions is from the
model when the objective was
to minimize the number of nurses hired. From Table 3, this
30. solution has slightly lower statistics
for both under and overstaffed nurse-blocks compared with the
solution when the goal was to
minimize the surgeon rating sum with only 13 nurses available.
Furthermore, Table 1 shows that
the recommended solution is better in all categories except for
the surgeon rating sum. While this
might dissatisfy some of the surgeons, the $360/week savings
($18,000 for a year) in nursing
salary more than justifies this increase in surgeon rating.
The final recommended solution from the combined analyses in
Part 1 and Part 2 is to schedule
Dr. Miller on Monday and Friday from 12 PM to 4 PM and
Tuesday, Wednesday, and Friday
from 12 PM to 4 PM, schedule Dr. Miller on Monday, Tuesday,
Wednesday, and Thursday from
4 PM to 8 PM, and to schedule Dr. Waltersheid on Monday and
Thursday from 8 AM to 12 PM
and Tuesday, Wednesday, and Thursday from 12 PM to 4 PM.
To staff the operating room, it is
recommended to hire 7 nurses on the Monday through Friday
from 8 AM to 4 PM shift, 1 nurse
31. on the Monday to Wednesday 8 AM to 8 PM shift, 4 nurses on
the Monday/Thursday from 8
AM to 8 PM and Tuesday/Wednesday from 12 PM to 8 PM
shift, and 1 nurse on the
Tuesday/Friday from 8 AM to 8 PM and Wednesday/Thursday
from 12 PM to 8 PM shift.
Part 3 Approach and Analysis
To best address the problem described by BIR hospital, a
decision tree was constructed. In
essence, a decision tree is a graphical tool which allows all
possible ‘what-if’ scenarios to be
displayed which is appropriate for this decision making process
as the possible scenarios are
finite. The decision tree was created such that decisions were
made in order to maximize the
expected profits from the second operating room. Furthermore,
the unknown cost and revenue
estimates were incorporated into the decision tree such that the
values could be changed and the
effects documented. Results from those tests are shown at the
conclusion of this section.
The decision tree was constructed with four levels of events and
decisions given the possible
scenarios with respect to time. The first modeled decision had
32. four possible options which
represent each of the equipment options (no special equipment,
equipment for Ophthalmology,
equipment for Robotic surgeries, or both). Given these
decisions, the possible number of
operations scheduled were considered and the likelihood of each
scenario was calculated. For
each procedure scenario, the option to select expedited or
standard staffing was modeled. If
standard staffing was chosen, the three possibilities for calling
in extra staff were included with
the probabilities updated to reflect the procedures in that
scenario. This full tree is shown in
Appendix C.
Given this tree, it was determined that the optimal decision is to
install both sets of equipment.
Then, regardless of the number of operations, expedited
scheduling should always be employed.
If these decisions are employed, the average daily profit is
$36,704. This expected profit result,
as well as the results from installing other options for
equipment, are shown in Table 4. These
results demonstrate that installing both sets of equipment result
in over $6,000 in additional
33. profit compared with the next best alternative.
Table 4: Expected Part 3 profits given equipment decisions
Equipment Expected Profit
None $21,930
Robotic $30,177
Ophthalmology $28,686
Both $36,704
Given these results, changes in the estimates profit/procedure
were studied. Initially, an estimate
of $3,000 was provided, but values between $100 and $5,000
were tested and Figure 1 shows the
expected daily profit based on installing different equipment
assuming the correct staffing
decisions are made for each equipment selection. This figure
demonstrates that the optimal
decisions are relatively insensitive to changes in the
profit/procedure. Specifically, the
recommended decisions (installing both pieces of equipment) is
optimal so long as the
34. profit/procedure is above $600. The optimal decision if the
profit/procedure were to be below
$600 is to install neither set of specialty equipment. In such a
situation, the optimal staffing in
this scenario is to use the standard staffing procedures (as
opposed to expedited).
Figure 1: Optimal equipment installation given changes in
profit/procedure
The results from modifying the estimated expedited staffing
costs are shown in Figure 2
according to the different equipment selection decisions
assuming the optimal staffing decisions
are made. As shown in Figure 2, both sets of specialty
equipment should be installed regardless
of the expedited staffing costs. However, the line segments in
the top-most lines show that the
optimal staffing decision changes based on this cost. The
optimal staffing decision for each line
segment and for each procedure quantity scenario is shown in
Table 5.
Figure 2: Optimal equipment installation given changes in
expedited staffing costs
35. Table 5: Optimal staffing decision given changes to the
estimated expedited staffing cost
Expedited Staffing Cost Range 12 Procedures 13 Procedures 14
Procedures
$7,900 and above Standard Standard Standard
$6,450 to $7,900 Standard Standard Expedited
$5,500 to $6,450 Standard Expedited Expedited
$5,500 and below Expedited Expedited Expedited
Finally, Figures 3 and 4 show the changes in expected daily
profit for each of the possible
equipment selection decisions given changes in the cost
estimates for having to call in only a
small number of staff members under standard staffing protocol
and for having to call in an
extensive number of staff members under standard staffing
protocol respectively. These were
initially assumed to be costs of $3,000 and $12,000. Figure 3
shows that the optimal decision
making is not affected by changes to the cost for calling in
some staff under standard staffing.
However, Figure 4 demonstrates that the optimal equipment
selection does not change, but the
36. staffing protocol can change. Table 6 shows the optimal staffing
decision as a function of the
number of daily procedures and the cost for having to call in a
significant number of employees.
Figure 3: Optimal equipment installation given changes in the
cost to call in some staff
members assuming standard staffing protocol
Figure 4: Optimal equipment installation given changes in the
cost to call in a significant
number of staff members assuming standard staffing protocol
Table 6: Optimal staffing decision given changes in the cost to
call in a significant number
of staff members assuming standard staffing protocol
Significant Staff Cost 12 Procedures 13 Procedures 14
Procedures
$8,000 and above Expedited Expedited Expedited
37. $6,600 to $8,000 Standard Expedited Expedited
$5,300 to $6,600 Standard Standard Expedited
$5,300 and below Standard Standard Standard
In summary, the optimal decisions are to install both sets of
specialty equipment and to use
expedited shipping regardless of the number of procedures
assuming the estimated costs and
profits are accurate. These recommendations are sensitive to
changes in the profit/procedure, cost
for expedited staffing, and cost for calling in a significant
number of staff under standard staffing
protocol. However, these changes rarely affect the optimal
decision to install both sets of
specialty equipment so BIR is highly recommended to fully
equip their new operating room, but
to carefully monitor cost estimate changes to modify their
staffing protocol when needed.
Conclusions and Recommended Actions
TO ALL STUDENTS: This section should serve as a conclusion
for the report. It should briefly
summarize the work you performed and remind the reader of the
recommendations you made.
38. Appendix A: Part 1 Extra Tables and Model
Table 7: Scheduling for Dr. Miller given different optimization
objectives
Scenario Min.
Nurses
Min. Surgeon
Rating
Min. Unused
Nurses
Min. Nurse
Salary
Max. Nurse Limit N/A 13 14 15 13 14 15 13 14 15
Mon. 8 AM to 12 PM 0 1 0 1 1 1 1 1 1 1
Mon. 12 PM to 4 PM 1 0 0 1 1 1 1 0 0 0
Mon. 4 PM to 8 PM 0 0 0 0 1 1 1 0 0 0
39. Tue. 8 AM to 12 PM 1 1 1 0 0 0 0 1 1 1
Tue. 12 PM to 4 PM 0 0 0 0 1 1 1 0 0 0
Tue. 4 PM to 8 PM 0 0 0 0 0 0 0 0 0 0
Wed. 8 AM to 12 PM 1 1 1 1 1 1 1 1 1 1
Wed. 12 PM to 4 PM 0 0 1 1 0 0 0 0 0 0
Wed. 4 PM to 8 PM 0 0 0 0 0 0 0 0 0 0
Thu. 8 AM to 12 PM 0 1 1 0 0 0 0 1 1 1
Thu. 12 PM to 4 PM 0 1 1 1 0 0 0 0 0 0
Thu. 4 PM to 8 PM 0 0 0 0 0 0 0 0 0 0
Fri. 8 AM to 12 PM 1 0 0 0 0 0 0 1 1 1
Fri. 12 PM to 4 PM 1 0 0 0 0 0 0 0 0 0
Fri. 4 PM to 8 PM 0 0 0 0 0 0 0 0 0 0
Table 8: Scheduling for Dr. Halpert given different optimization
objectives
Scenario Min.
Nurses
Min. Surgeon
Rating
41. Fri. 12 PM to 4 PM 1 1 1 1 1 1 1 0 0 0
Fri. 4 PM to 8 PM 0 1 1 1 1 1 1 1 1 1
Table 9: Scheduling for Dr. Walterscheid given different
optimization objectives
Scenario Min.
Nurses
Min. Surgeon
Rating
Min. Unused
Nurses
Min. Nurse
Salary
Max. Nurse Limit N/A 13 14 15 13 14 15 13 14 15
Mon. 8 AM to 12 PM 0 0 0 0 0 0 0 0 0 0
Mon. 12 PM to 4 PM 1 1 1 0 0 0 0 1 1 1
Mon. 4 PM to 8 PM 0 1 1 1 0 0 0 0 0 0
42. Tue. 8 AM to 12 PM 1 0 0 1 0 0 0 0 0 0
Tue. 12 PM to 4 PM 0 1 1 1 0 0 0 1 1 1
Tue. 4 PM to 8 PM 0 0 1 1 0 0 0 0 0 0
Wed. 8 AM to 12 PM 1 0 0 0 0 0 0 0 0 0
Wed. 12 PM to 4 PM 0 1 0 0 1 1 1 1 1 1
Wed. 4 PM to 8 PM 0 0 0 0 1 1 1 0 0 0
Thu. 8 AM to 12 PM 0 0 0 0 1 1 1 0 0 0
Thu. 12 PM to 4 PM 0 0 0 0 1 1 1 1 1 1
Thu. 4 PM to 8 PM 0 1 1 1 1 1 1 0 0 0
Fri. 8 AM to 12 PM 1 0 0 0 0 0 0 0 0 0
Fri. 12 PM to 4 PM 1 0 0 0 0 0 0 0 0 0
Fri. 4 PM to 8 PM 0 1 1 0 0 0 0 1 1 1
Optimization Model Decision Variables:
���1 Binary variable reserving Monday 8 AM – 12 PM for Dr.
Miller
���2 Binary variable reserving Monday 12 PM – 4 PM for Dr.
Miller
���3 Binary variable reserving Monday 4 PM – 8 PM for Dr.
Miller
���1 Binary variable reserving Tuesday 8 AM – 12 PM for
Dr. Miller
���2 Binary variable reserving Tuesday 12 PM – 4 PM for Dr.
43. Miller
���3 Binary variable reserving Tuesday 4 PM – 8 PM for Dr.
Miller
���1 Binary variable reserving Wednesday 8 AM – 12 PM for
Dr. Miller
���2 Binary variable reserving Wednesday 12 PM – 4 PM for
Dr. Miller
���3 Binary variable reserving Wednesday 4 PM – 8 PM for
Dr. Miller
���1 Binary variable reserving Thursday 8 AM – 12 PM for
Dr. Miller
���2 Binary variable reserving Thursday 12 PM – 4 PM for
Dr. Miller
���3 Binary variable reserving Thursday 4 PM – 8 PM for Dr.
Miller
���1 Binary variable reserving Friday 8 AM – 12 PM for Dr.
Miller
���2 Binary variable reserving Friday 12 PM – 4 PM for Dr.
Miller
���3 Binary variable reserving Friday 4 PM – 8 PM for Dr.
Miller
���1 Binary variable reserving Monday 8 AM – 12 PM for Dr.
Halpert
���2 Binary variable reserving Monday 12 PM – 4 PM for Dr.
Halpert
���3 Binary variable reserving Monday 4 PM – 8 PM for Dr.
Halpert
���1 Binary variable reserving Tuesday 8 AM – 12 PM for
Dr. Halpert
���2 Binary variable reserving Tuesday 12 PM – 4 PM for Dr.
Halpert
���3 Binary variable reserving Tuesday 4 PM – 8 PM for Dr.
Halpert
���1 Binary variable reserving Wednesday 8 AM – 12 PM for
Dr. Halpert
���2 Binary variable reserving Wednesday 12 PM – 4 PM for
44. Dr. Halpert
���3 Binary variable reserving Wednesday 4 PM – 8 PM for
Dr. Halpert
���1 Binary variable reserving Thursday 8 AM – 12 PM for
Dr. Halpert
���2 Binary variable reserving Thursday 12 PM – 4 PM for
Dr. Halpert
���3 Binary variable reserving Thursday 4 PM – 8 PM for Dr.
Halpert
���1 Binary variable reserving Friday 8 AM – 12 PM for Dr.
Halpert
���2 Binary variable reserving Friday 12 PM – 4 PM for Dr.
Halpert
���3 Binary variable reserving Friday 4 PM – 8 PM for Dr.
Halpert
���1 Binary variable reserving Monday 8 AM – 12 PM for Dr.
Walterscheid
���2 Binary variable reserving Monday 12 PM – 4 PM for Dr.
Walterscheid
���3 Binary variable reserving Monday 4 PM – 8 PM for Dr.
Walterscheid
���1 Binary variable reserving Tuesday 8 AM – 12 PM for
Dr. Walterscheid
���2 Binary variable reserving Tuesday 12 PM – 4 PM for Dr.
Walterscheid
���3 Binary variable reserving Tuesday 4 PM – 8 PM for Dr.
Walterscheid
���1 Binary variable reserving Wednesday 8 AM – 12 PM for
Dr. Walterscheid
���2 Binary variable reserving Wednesday 12 PM – 4 PM for
Dr. Walterscheid
���3 Binary variable reserving Wednesday 4 PM – 8 PM for
Dr. Walterscheid
45. ���1 Binary variable reserving Thursday 8 AM – 12 PM for
Dr. Walterscheid
���2 Binary variable reserving Thursday 12 PM – 4 PM for
Dr. Walterscheid
���3 Binary variable reserving Thursday 4 PM – 8 PM for Dr.
Walterscheid
���1 Binary variable reserving Friday 8 AM – 12 PM for Dr.
Walterscheid
���2 Binary variable reserving Friday 12 PM – 4 PM for Dr.
Walterscheid
���3 Binary variable reserving Friday 4 PM – 8 PM for Dr.
Walterscheid
�1 Integer variable for Shift Pattern 1 (Monday – Friday 8 AM
to 4 PM)
�2 Integer variable for Shift Pattern 2 (Monday – Friday 12 PM
to 8 PM)
�3 Integer variable for Shift Pattern 3 (Monday – Wednesday 8
AM to 8 PM)
�4 Integer variable for Shift Pattern 4 (Tuesday – Thursday 8
AM to 8 PM)
�5 Integer variable for Shift Pattern 5 (Wednesday – Friday 8
AM to 8 PM)
�6 Integer variable for Shift Pattern 6 (Mon. & Thurs. 8 AM to
8 PM, Tues. & Wed.
8 AM to 4 PM)
�7 Integer variable for Shift Pattern 7 (Mon. & Thurs. 8 AM to
8 PM, Tues. & Wed.
12 PM to 8 PM)
�8 Integer variable for Shift Pattern 8 (Tues. & Fri. 8 AM to 8
PM, Wed. & Thurs. 8
AM to 4 PM)
�9 Integer variable for Shift Pattern 9 (Tues. & Fri. 8 AM to 8
46. PM, Wed. & Thurs.
12 PM to 8 PM)
��1 Integer variable for number of non-working nurses for
Monday 8 AM – 12 PM
��2 Integer variable for number of non-working nurses for
Monday 12 PM – 4 PM
��3 Integer variable for number of non-working nurses for
Monday 4 PM – 8 PM
��1 Integer variable for number of non-working nurses for
Tuesday 8 AM – 12 PM
��2 Integer variable for number of non-working nurses for
Tuesday 12 PM – 4 PM
��3 Integer variable for number of non-working nurses for
Tuesday 4 PM – 8 PM
��1 Integer variable for number of non-working nurses for
Wednesday 8 AM – 12 PM
��2 Integer variable for number of non-working nurses for
Wednesday 12 PM – 4 PM
��3 Integer variable for number of non-working nurses for
Wednesday 4 PM – 8 PM
��1 Integer variable for number of non-working nurses for
Thursday 8 AM – 12 PM
��2 Integer variable for number of non-working nurses for
Thursday 12 PM – 4 PM
��3 Integer variable for number of non-working nurses for
Thursday 4 PM – 8 PM
��1 Integer variable for number of non-working nurses for
Friday 8 AM – 12 PM
��2 Integer variable for number of non-working nurses for
Friday 12 PM – 4 PM
��3 Integer variable for number of non-working nurses for
Friday 4 PM – 8 PM
47. Optimization Model Objective Function:
Minimize �1 + �2 + �3 + �4 + �5 + �6 + �7 + �8 + �9
The objective functions for the other optimization models are
the left hand side of the
matching constraints below.
Optimization Model Constraints:
���1 + ���2 + ���3 + ���1 + ���2 + ���3 + ���1
+ ���2 + ���3 + ���1 +
���2 + ���3 + ���1 + ���2 + ���3 = 5 (Dr. Miller
Time Block Assignment
Requirement)
���1 + ���2 + ���3 + ���1 + ���2 + ���3 + ���1
+ ���2 + ���3 + ���1 + ���2 +
���3 + ���1 + ���2 + ���3 = 4 (Dr. Halpert Time Block
Assignment Requirement)
���1 + ���2 + ���3 + ���1 + ���2 + ���3 + ���1
+ ���2 + ���3 + ���1 +
���2 + ���3 + ���1 + ���2 + ���3 = 5 (Dr.
Walterscheid Time Block Assignment
Requirement)
���1 + ���1 + ���1 ≤ 1 (At most one assignment for
Monday 8 AM to 12 PM)
���2 + ���2 + ���2 ≤ 1 (At most one assignment for
Monday 12 PM to 4 PM)
48. ���3 + ���3 + ���3 ≤ 1 (At most one assignment for
Monday 4 PM to 8 PM)
���1 + ���1 + ���1 ≤ 1 (At most one assignment for
Tuesday 8 AM to 12 PM)
���2 + ���2 + ���2 ≤ 1 (At most one assignment for
Tuesday 12 PM to 4 PM)
���3 + ���3 + ���3 ≤ 1 (At most one assignment for
Tuesday 4 PM to 8 PM)
���1 + ���1 + ���1 ≤ 1 (At most one assignment for
Wednesday 8 AM to 12 PM)
���2 + ���2 + ���2 ≤ 1 (At most one assignment for
Wednesday 12 PM to 4 PM)
���3 + ���3 + ���3 ≤ 1 (At most one assignment for
Wednesday 4 PM to 8 PM)
���1 + ���1 + ���1 ≤ 1 (At most one assignment for
Thursday 8 AM to 12 PM)
���2 + ���2 + ���2 ≤ 1 (At most one assignment for
Thursday 12 PM to 4 PM)
���3 + ���3 + ���3 ≤ 1 (At most one assignment for
Thursday 4 PM to 8 PM)
���1 + ���1 + ���1 ≤ 1 (At most one assignment for
Friday 8 AM to 12 PM)
���2 + ���2 + ���2 ≤ 1 (At most one assignment for
Friday 12 PM to 4 PM)
���3 + ���3 + ���3 ≤ 1 (At most one assignment for
Friday 4 PM to 8 PM)
�1 + �3 + �6 + �7 − ��1 = 8���1 + 5���1 + 11���1
(Nursing needs Mon. 8 - 12)
�1 + �2 + �3 + �6 + �7 − ��2 = 8���2 + 5���2 +
11���2 (Nursing needs Mon. 12 -
4)
�2 + �3 + �6 + �7 − ��3 = 8���3 + 5���3 + 11���3
(Nursing needs Mon. 4 - 8)
51. ���1, ���2, ���3, ���1, ���2, ���3, ���1, ���2,
���3, ���1, ���2, ���3, ���1, ���2, ���3,
��1, ��2, ��3, ��1, ��2, ��3, ��1, ��2, ��3, ��1,
��2, ��3, ��1, ��2, ��3 are integer
�1, �2, �3, �4, �5, �6, �7, �8, �9 are binary
Appendix B: Part 2 Model
Table 10: Fitted distribution for random variables in simulation
model
Random Variable Distribution Parameters
Dr. Miller Nurse Req. Binomial Trials: 11, Probability: 0.629,
Shift: 1
Dr. Halpert Nurse Req. Int. Uniform Min: 1, Max: 9
Dr. Walterscheid Nurse Req. Binomial Trials: 14, Probability:
0.804, Shift: -1
Simulation Model Random Variables:
���1 Number of nurses for Monday 8 AM – 12 PM for Dr.
Miller
���2 Number of nurses for Monday 12 PM – 4 PM for Dr.
Miller
���3 Number of nurses for Monday 4 PM – 8 PM for Dr.
Miller
���1 Number of nurses for Tuesday 8 AM – 12 PM for Dr.
52. Miller
���2 Number of nurses for Tuesday 12 PM – 4 PM for Dr.
Miller
���3 Number of nurses for Tuesday 4 PM – 8 PM for Dr.
Miller
���1 Number of nurses for Wednesday 8 AM – 12 PM for Dr.
Miller
���2 Number of nurses for Wednesday 12 PM – 4 PM for Dr.
Miller
���3 Number of nurses for Wednesday 4 PM – 8 PM for Dr.
Miller
���1 Number of nurses for Thursday 8 AM – 12 PM for Dr.
Miller
���2 Number of nurses for Thursday 12 PM – 4 PM for Dr.
Miller
���3 Number of nurses for Thursday 4 PM – 8 PM for Dr.
Miller
���1 Number of nurses for Friday 8 AM – 12 PM for Dr.
Miller
���2 Number of nurses for Friday 12 PM – 4 PM for Dr.
Miller
���3 Number of nurses for Friday 4 PM – 8 PM for Dr. Miller
���1 Number of nurses for Monday 8 AM – 12 PM for Dr.
Halpert
���2 Number of nurses for Monday 12 PM – 4 PM for Dr.
Halpert
���3 Number of nurses for Monday 4 PM – 8 PM for Dr.
Halpert
���1 Number of nurses for Tuesday 8 AM – 12 PM for Dr.
Halpert
���2 Number of nurses for Tuesday 12 PM – 4 PM for Dr.
Halpert
���3 Number of nurses for Tuesday 4 PM – 8 PM for Dr.
Halpert
53. ���1 Number of nurses for Wednesday 8 AM – 12 PM for Dr.
Halpert
���2 Number of nurses for Wednesday 12 PM – 4 PM for Dr.
Halpert
���3 Number of nurses for Wednesday 4 PM – 8 PM for Dr.
Halpert
���1 Number of nurses for Thursday 8 AM – 12 PM for Dr.
Halpert
���2 Number of nurses for Thursday 12 PM – 4 PM for Dr.
Halpert
���3 Number of nurses for Thursday 4 PM – 8 PM for Dr.
Halpert
���1 Number of nurses for Friday 8 AM – 12 PM for Dr.
Halpert
���2 Number of nurses for Friday 12 PM – 4 PM for Dr.
Halpert
���3 Number of nurses for Friday 4 PM – 8 PM for Dr.
Halpert
���1 Number of nurses for Monday 8 AM – 12 PM for Dr.
Walterscheid
���2 Number of nurses for Monday 12 PM – 4 PM for Dr.
Walterscheid
���3 Number of nurses for Monday 4 PM – 8 PM for Dr.
Walterscheid
���1 Number of nurses for Tuesday 8 AM – 12 PM for Dr.
Walterscheid
���2 Number of nurses for Tuesday 12 PM – 4 PM for Dr.
Walterscheid
���3 Number of nurses for Tuesday 4 PM – 8 PM for Dr.
Walterscheid
���1 Number of nurses for Wednesday 8 AM – 12 PM for Dr.
54. Walterscheid
���2 Number of nurses for Wednesday 12 PM – 4 PM for Dr.
Walterscheid
���3 Number of nurses for Wednesday 4 PM – 8 PM for Dr.
Walterscheid
���1 Number of nurses for Thursday 8 AM – 12 PM for Dr.
Walterscheid
���2 Number of nurses for Thursday 12 PM – 4 PM for Dr.
Walterscheid
���3 Number of nurses for Thursday 4 PM – 8 PM for Dr.
Walterscheid
���1 Number of nurses for Friday 8 AM – 12 PM for Dr.
Walterscheid
���2 Number of nurses for Friday 12 PM – 4 PM for Dr.
Walterscheid
���3 Number of nurses for Friday 4 PM – 8 PM for Dr.
Walterscheid
Simulation Model Fixed Variables:
���1 Binary variable reserving Monday 8 AM – 12 PM for Dr.
Miller
���2 Binary variable reserving Monday 12 PM – 4 PM for Dr.
Miller
���3 Binary variable reserving Monday 4 PM – 8 PM for Dr.
Miller
���1 Binary variable reserving Tuesday 8 AM – 12 PM for
Dr. Miller
���2 Binary variable reserving Tuesday 12 PM – 4 PM for Dr.
Miller
���3 Binary variable reserving Tuesday 4 PM – 8 PM for Dr.
Miller
���1 Binary variable reserving Wednesday 8 AM – 12 PM for
Dr. Miller
���2 Binary variable reserving Wednesday 12 PM – 4 PM for
55. Dr. Miller
���3 Binary variable reserving Wednesday 4 PM – 8 PM for
Dr. Miller
���1 Binary variable reserving Thursday 8 AM – 12 PM for
Dr. Miller
���2 Binary variable reserving Thursday 12 PM – 4 PM for
Dr. Miller
���3 Binary variable reserving Thursday 4 PM – 8 PM for Dr.
Miller
���1 Binary variable reserving Friday 8 AM – 12 PM for Dr.
Miller
���2 Binary variable reserving Friday 12 PM – 4 PM for Dr.
Miller
���3 Binary variable reserving Friday 4 PM – 8 PM for Dr.
Miller
���1 Binary variable reserving Monday 8 AM – 12 PM for Dr.
Halpert
���2 Binary variable reserving Monday 12 PM – 4 PM for Dr.
Halpert
���3 Binary variable reserving Monday 4 PM – 8 PM for Dr.
Halpert
���1 Binary variable reserving Tuesday 8 AM – 12 PM for
Dr. Halpert
���2 Binary variable reserving Tuesday 12 PM – 4 PM for Dr.
Halpert
���3 Binary variable reserving Tuesday 4 PM – 8 PM for Dr.
Halpert
���1 Binary variable reserving Wednesday 8 AM – 12 PM for
Dr. Halpert
���2 Binary variable reserving Wednesday 12 PM – 4 PM for
Dr. Halpert
���3 Binary variable reserving Wednesday 4 PM – 8 PM for
Dr. Halpert
���1 Binary variable reserving Thursday 8 AM – 12 PM for
56. Dr. Halpert
���2 Binary variable reserving Thursday 12 PM – 4 PM for
Dr. Halpert
���3 Binary variable reserving Thursday 4 PM – 8 PM for Dr.
Halpert
���1 Binary variable reserving Friday 8 AM – 12 PM for Dr.
Halpert
���2 Binary variable reserving Friday 12 PM – 4 PM for Dr.
Halpert
���3 Binary variable reserving Friday 4 PM – 8 PM for Dr.
Halpert
���1 Binary variable reserving Monday 8 AM – 12 PM for Dr.
Walterscheid
���2 Binary variable reserving Monday 12 PM – 4 PM for Dr.
Walterscheid
���3 Binary variable reserving Monday 4 PM – 8 PM for Dr.
Walterscheid
���1 Binary variable reserving Tuesday 8 AM – 12 PM for
Dr. Walterscheid
���2 Binary variable reserving Tuesday 12 PM – 4 PM for Dr.
Walterscheid
���3 Binary variable reserving Tuesday 4 PM – 8 PM for Dr.
Walterscheid
���1 Binary variable reserving Wednesday 8 AM – 12 PM for
Dr. Walterscheid
���2 Binary variable reserving Wednesday 12 PM – 4 PM for
Dr. Walterscheid
���3 Binary variable reserving Wednesday 4 PM – 8 PM for
Dr. Walterscheid
���1 Binary variable reserving Thursday 8 AM – 12 PM for
Dr. Walterscheid
���2 Binary variable reserving Thursday 12 PM – 4 PM for
57. Dr. Walterscheid
���3 Binary variable reserving Thursday 4 PM – 8 PM for Dr.
Walterscheid
���1 Binary variable reserving Friday 8 AM – 12 PM for Dr.
Walterscheid
���2 Binary variable reserving Friday 12 PM – 4 PM for Dr.
Walterscheid
���3 Binary variable reserving Friday 4 PM – 8 PM for Dr.
Walterscheid
�1 Integer variable for Shift Pattern 1 (Monday – Friday 8 AM
to 4 PM)
�2 Integer variable for Shift Pattern 2 (Monday – Friday 12 PM
to 8 PM)
�3 Integer variable for Shift Pattern 3 (Monday – Wednesday 8
AM to 8 PM)
�4 Integer variable for Shift Pattern 4 (Tuesday – Thursday 8
AM to 8 PM)
�5 Integer variable for Shift Pattern 5 (Wednesday – Friday 8
AM to 8 PM)
�6 Integer variable for Shift Pattern 6 (Mon. & Thurs. 8 AM to
8 PM, Tues. & Wed.
8 AM to 4 PM)
�7 Integer variable for Shift Pattern 7 (Mon. & Thurs. 8 AM to
8 PM, Tues. & Wed.
12 PM to 8 PM)
�8 Integer variable for Shift Pattern 8 (Tues. & Fri. 8 AM to 8
PM, Wed. & Thurs. 8
AM to 4 PM)
�9 Integer variable for Shift Pattern 9 (Tues. & Fri. 8 AM to 8
PM, Wed. & Thurs.
61. Appendix C: Part 3 Decision Tree
Figure 5: Part 3 decision tree modeling the decision to choose to
install neither specialty
equipment
Figure 6: Part 3 decision tree modeling the decision to choose to
install ophthalmology
specialty equipment only and have 9 or 10 procedures per day
Figure 7: Part 3 decision tree modeling the decision to choose to
install ophthalmology
specialty equipment only and have 11 procedures per day and to
choose to install robotic
specialty equipment only have 10 procedures per day
62. Figure 8: Part 3 decision tree modeling the decision to choose to
install robotic specialty
equipment and having 11 or 12 procedures per day
Figure 9: Part 3 decision tree modeling the decision to choose to
install ophthalmology and
robotic specialty equipment and have 12 or 13 procedures per
day
Figure 10: Part 3 decision tree modeling the decision to choose
to install ophthalmology and
robotic specialty equipment and have 14 procedures per day
63. SCM 315: Capstone Project Rubric 1
Background: Your capstone project will require your team to
complete multiple decision analyses to solve a
realistic case study. Your team will need to select one of the
provided case studies, identify the
appropriate decision tools to address the problems, perform any
necessary research as
indicated by the case study, complete thorough analyses to
address all aspects of the study,
and summarize your results and findings to develop meaningful
recommendations.
Case Studies: Two case studies are given as options for the
capstone project. Your group must choose one of
these case studies to complete for the project. All parts of the
selected case study must be
addressed during the project. Make sure to read the case studies
multiple times, even after
completing the project, to ensure you address all key aspects of
the problem as each section of
each case requires multiple steps/components.
Decision
Support Tools:
To address the decisions presented by the case study, your team
will need to use two decision
support tools discussed during the second half of this course.
You need to ensure you select
the correct tools for your project. These possible decision
support tools are:
64. teger/Binary Optimization
Capstone
Project
Submission:
Your team will only submit a report. No Excel files will be
submitted or graded. Therefore, it is
extremely important that your group carefully read the
requirements that are listed in this
rubric.
The project report must be typed and consist of no more than 6
pages, excluding the appendix
and title page. There is no limit to the length of the appendix.
The report is due by 11:59 PM
on 4/28/2017. The report is to consist of the following labeled
sections:
o Title, Team Name, Names of Team Members, Executive
Summary (one paragraph)
o Summary of the problem you are attempting to address with
this project
1 Approach and Analysis:
65. o Explanation and discussion of the Part 1 model(s) you used
for your analysis.
Additionally discuss the results from these models along with
your
recommendations.
o Explanation and discussion of the Part 2 model(s) you used
for your analysis.
Additionally discuss the results from these models along with
your
recommendations.
o The final summary and overview of complete case study
recommendations
o Include any additional supporting material (e.g. full
optimization model details, full
size images of decision trees, etc.). If your figures/tables in the
main body of the
SCM 315: Capstone Project Rubric 2
report make the report exceed the page limit, less important
tables can be moved
to the appendix.
66. The report must be formatted with single-spacing, 12 pt. Times
New Roman text, and standard
1 inch margins.
Depending on the analyses your team completed, you must
include the following in the
appendix when appropriate:
o The full, written optimization model (included in the
appendix) – This should be
written appropriately, uses of Excel equations is not permitted
(e.g.
SUMPRODUCT)
bles
o Justification of any assumptions that were made if appropriate
o If you created multiple models for the project, you only need
to write one of the
models in the report
o An image(s) of the decision tree (included in the appendix)
o Justification of any assumptions that were made
o Distributions used for any random inputs (included in the
appendix)
o Complete simulation model (included in the appendix)
67. ables
o Justification of any assumptions that were made
IMPORTANT: You should write the body of the report as if you
were writing the report for the
project’s sponsor. This means that you should avoid technical
details and speak in general
terms about what you did. For an example, they likely don’t
know what an objective function
means or decision variables, but they do understand that you
selected a set of vehicles (the
decision variables) such that they minimized the cost of the
fleet (the objective function). The
appendix is for the grader and contains all of the technical
information. What is absolutely
required in the appendix is given below.
SCM 315: Capstone Project Rubric 3
General
Frequently
Asked
Questions:
The following questions and answers apply to all of the cases.
68. What analysis technique should I use for Part I/Part II of my
case study?
The case studies were designed to require a specific analysis
method discussed during the
second half of the course (integer optimization, linear
optimization, decision trees,
simulation, stochastic optimization). It is your group's task to
identify the most appropriate
technique for each part. If you are unsure you are using the
correct technique, please talk
with the TA.
Can I have an optimization model with multiple objectives? (i.e.
is it possible to maximize
profit and minimize cost in the same model?)
No, this is not possible. We have only dealt with one objective
function per model
throughout the course. It is possible to have multiple objectives,
but it is extremely
uncommon and is an advanced technique. If you have a section
which appears to call for
different objectives, then you need to create a seperate model
for each objective.
Our case study has us conduct multiple optimization models but
requires us to only
recommend one. How should we decide?
This is the first time you have been asked to do this in the
69. course. If you have multiple
answers, it is recommended you complete a cost-benefit
analysis comparing all of the
details of your answers with the cost or profits (depending on
your case study). For
example, consider Case Study 1. Compare the calcium of all of
your possible food plans to
their costs. Maybe one has much higher calcium but is also
more expansive. Is it worth
paying more for that level of calcium? That is up to your group
to decide. As long as your
justification is reasonable and it is clear you did the analysis,
the grader will agree with you.
You should do this for any details of your food plan (or fleet for
case study 2 or portfolio for
case study 3) that you deem important. If the case study
specifically mentions that detail
(like it mentions calcium, protien, etc. for case study 1), then it
is probably important. By
combining all of this analysis together, you should be able to
recommend one option.
In Part II, it seems that we may be able to conduct multiple
decision trees/simulation
analyses/optimization models based on the different results we
obtained in Part I. Is this
recommended?
All of the case studies require the answer from Part I to be used
as an input into Part II.
Therefore, it is possible to try different answers from Part I
(other options besides the one
you recommended) to see how they perform in Part II. The extra
effort will be rewarded.
70. What do we turn in?
You will only be submitting your report. No Excel workbooks
will be opened and analyzed.
SCM 315: Capstone Project Rubric 4
How should the report be formatted?
The details of what is required in the report are listed in the
rubric. Most importantly, the
body of the report (everything but the appendix) should be
written as if it will be read by
the sponsor of the project (for instance, Lewis Hamilton in case
study 1). This implies that
they don't know what optimization is and they likely do not
care. Hence, you should write
enough detail to tell the sponsor what you did, but do not bore
them with all the details or
technical terms. For example, you may want include sentences
like:
"An optimization model was developed which minimized the
overall cost of the fleet of 40
cars but adhered to all of the requirements such as ..."
71. "The model included the following requirements: ..."
"The fleet which had the maximum mpg highway has 3 Toyota
Camrys, ..."
And probably avoid sentences like:
"The objective function of the model is the sumproduct of the
decision variables by the
vehicle costs ..."
"The model has 20 decision variables and they are ..."
My best advice is to write the report as if you are explaining the
project to your
grandmother/grandfather. They likely don't know/care much
about the details/computer
work required, but they can understand it as long as you speak
in basic/general terms.
The appendix of the report is for the grader and is where you
will indicate the details about
your specific work (the optimization models you conducted, the
simulation analyses, the
decision tree, etc.) What is required in the appendix is stated in
the rubric.
It is the end of the semester and I burnt out. Can I be lazy in my
report?
No. Submitting a report where you do not explain all of your
work and results is not
acceptable and extremely obvious. Please be thorough in your
report (especially the
72. appendix) to avoid any point deductions.
Case Study 3
Frequently
Asked
Questions:
How should I decide the return threshold when I minimize Beta,
etc.?
The best order of operations for Part I is to first determine the
maximum possible return.
Once this is known, you can set a return threshold based on this
maximum by minimizing
Beta such that the portfolio does not go below 90% of the
maximum return possible. This
90% just an example and you are free to use whatever you deem
reasonable (to determine
reasonable, think about however much you would imagine the
sponsor would be
responsible earning below the maximum and set this as the
minimum threshold, then test
threshold values between this minimum and the maximum). As
stated, you should test
multiple thresholds, but 3 or 4 is fine.
SCM 315: Capstone Project Rubric 5
73. How to calculate yearly return?
To determine yearly return for a stock, you take three pieces of
information: Shares
invested, Current share price, one year growth. By multiplying
these three items, you can
estimate the value of your investment in a year.
Case Study 4
Frequently
Asked
Questions:
How should I decide the budget when I minimize greenhouse
gas emissions, etc.?
The best order of operations for Part I is to first determine the
minimum cost location and
production plan. Once this is known, you can set a budget based
on this minimum cost by
minimizing greenhouse gas emissions such that the location and
production plan does not
exceed 125% of the minimum cost identified. This 125% just an
example and you are free
to use whatever you deem reasonable (to determine reasonable,
think about however
much you would imagine the sponsor would be responsible
spending over the minimum
and set this as the maximum budget, then test budget values
between the minimum and
this maximum). As stated, you should test multiple budgets, but
3 or 4 is fine.
74. What does North America include?
It may seem obvious, but North America includes the US,
Canada, and Mexico.
Case Study 3
George Soros is planning on starting a new business venture to
open a chain of specialty Hungarian
eateries in California. At the moment, he does not have the
sufficient capital to open all of his planned
restaurants and is seeking a plan in order to gain the sufficient
starting money. Mr. Soros’ plan is to
invest in a high-return, diverse, and low-risk portfolio of stocks
for exactly a year. After the year expires,
he will sell all of his investments in order to start his business.
To assist with his portfolio, Mr. Soros has
approached your team in order to complete a thorough analysis
on the optimal investment portfolio
which will meet his strict requirements.
To best aid Mr. Soros, your team should address two aspects of
the problem: optimal portfolio design
based on the strict requirements of Mr. Soros and portfolio
performance based on historical records.
The description of these problems is in Part 1 and Part 2,
respectively.
Part 1
Throughout a series of meetings and conversations with Mr.
Soros, he has narrowed down his list of
75. potential stock investments to 20 publicly traded companies.
These companies are listed below and are
divided into five different industries. Included in the company
name is also ticker symbol for the
company.
o Lam Research Corp. (LRCX)
o Micron Technology Inc. (MU)
o Equinix (EQIX)
o Apple Inc. (AAPL)
ealth Care:
o Humana Inc. (HUM)
o Magellan Health Inc. (MGLN)
o UnitedHealth Group Inc. (UNH)
o Cigna Corp (CI)
o Enphase Energy (ENPH)
o Hess Corp. (HES)
o Atwood Oceanics (ATW)
o Schlumberger (SLB)
o Intercontinental Exchange (ICE)
o Signature Bank (SBNY)
o BNY Mellon (BK)
o KKR & Co. LP (KKR)
o Mondelez International (MDLZ)
o PepsiCo (PEP)
o WD-40 Co. (WDFC)
o Clorox Co (CLX)
76. To assist your analysis, Mr. Soros’ financial team has provided
your group with a set of relevant data for
each of the aforementioned stocks. This data includes the Beta,
PEG Ratio, and Profit Margin for each
company. The Beta measure is an indicator of volatility or
system risk compared to the benchmark index
where a lower number indicates a less risky investment. The
PEG ratio is the Price/Earnings to Growth
ratio which is used to indicate if the current stock is under or
overvalued (lower values are desirable).
In addition to this data, some necessary information is missing.
One of the key missing elements is the
yearly return on each stock. Your group needs to find this
information using whichever calculation
method you believe to be most appropriate. Regardless of the
data the return is based upon, the final
value should be expressed as a ratio. For example, if the yearly
return of AAPL is 1.56, then each dollar
invested by Mr. Soros will return $1.56 in a year. The other
missing data is the current price of the stock
as this price will limit how many share Mr. Soros can purchase
in any individual company.
To build Mr. Soros’ stock portfolio, he requires your final
recommendation to meet certain
requirements. Most importantly, Mr. Soros’ has set an
investment budget of $1,000,000 which cannot
be exceeded. Also, he wants as much as possible to be invested
so he receives a large monetary return.
Since it may not be possible to ensure all one million dollars is
77. invested, the total investment amount
must exceed $1,000,000 minus the largest price. Secondly, Mr.
Soros wants a diverse portfolio so at
least $10,000 must be invested in each industry across all of the
companies within that industry.
Additionally, Mr. Soros does not want more than 40% of his
total investment capital to be in any one
industry group. Furthermore, the average weighted profit
margin must exceed 20%, the average
weighted Beta is less than 1.2, and the average weighted PEG
ratio is less than 1.4 (for all weighted
calculations, weight the profit margins using the total dollar
investment in that company and assume
that all $1,000,000 is invested). Finally, Mr. Soros has already
invested in Clorox Co., Equinix, and
Signature Bank so he requires that your team’s recommended
investment in each of these stocks
doesn’t exceed $50,000.
Based on your conversation with Mr. Soros, you realize that
multiple investment portfolios should be
created to give Mr. Soros’ many options about which portfolio
to use. Some of the portfolios Mr. Soros
would be interested in are those which meet the following
goals:
All of these portfolios must be subject to the previously
mentioned requirements. However, Mr. Soros
would also like the portfolios which minimize the Beta or PEG
Ratio to still provide a decent return. Since
Mr. Soros does not provide a requirement for this return, it is
recommended that your group develop
78. your own return threshold. Since the portfolio may be very
sensitive to this return threshold, it is highly
recommended that multiple thresholds be tested to demonstrate
how much the portfolio is affected by
the return requirement.
Ultimately, Mr. Soros wants you to perform a complete and
thorough analysis to recommend one
portfolio of investments based on all of the developed portfolios
your team created. Specifically, Mr.
Soros want your group to complete the following work:
-year return of the
necessary public stocks.
multi-criteria objectives proposed by
Mr. Soros.
Part 2
Given the conversation with Mr. Soros, your team has identified
that completing the analysis in Part 1 is
all that is needed to satisfy the requirements of Mr. Soros.
However, the returns used in the prior
analysis do not account for the unpredictability of stock returns.
Hence, your team proposes to continue
the analysis while accounting for this factor.
To assist in this analysis, historical data has been provided in an
Excel workbook. In the worksheet titled
“Historical Return Data”, up to 52 data samples of historical
one-year returns have been recorded for
each of the 20 stocks. Similarly, the worksheet titled
79. “Bankruptcy Risk” include a random sample of 50
data points from each of the industries indicating whether a
random company within that industry
declared bankruptcy within a one-year time span. A company
who filed bankruptcy is indicated by a 1
while a 0 indicates the company did not. The samples are only
given per industry since it is assumed that
all companies within the same industry have the same risk of
bankruptcy. Also, if a company is to
declare bankruptcy, it can be assumed that all stocks in that
company become valueless.
Using this data, your team can provide Mr. Soros with insight
into the distribution of possible returns for
his investment portfolio. There you should use your portfolio
(or test all of your potential portfolios) and
fit distributions to the given data so you can create a model
which will provide an output distribution of
the expected yearly return. From this distribution you should
report the expected return as well as other
statistics including the minimum and maximum return, etc.
Reminder, since Mr. Soros hasn’t purchased
on stocks by the time you complete this analysis, you are able to
modify your recommended portfolio by
revisiting the analysis your team completed in Part 1.
Case Study 4
An American entrepreneur (Steven Wobs) is seeking to establish
manufacturing plants to produce his
three types of music players: the “Tune”, the “uPlayer”, and the
“Mixer”. Steven has identified five
different countries and locations in which it is possible to
80. establish his manufacturing base but he
doesn’t know which he should select. Further complicating the
decision is the different exchange rates,
labor rates, material costs, shipment costs and distances, and
tariff charges associated with each
country. Mr. Wobs contacted your group seeking your
assistance in determining his optimal production
locations such that his costs are reasonable, but he also doesn’t
pay too much in tariff costs or produce
too much in greenhouse gases with respect to his shipping.
Additionally, he mentions that he has
another expedited manufacturing issues he would like you to
address as well.
To best assist Mr. Wobs, your team must recommend the ideal
manufacturing locations and production
amounts for his three products and address his expedited
shipping issues with the best, low cost
solution. The description of these problems is in Part 1 and Part
2, respectively.
Part 1
To establish his manufacturing operations, Mr. Wobs has
determined that he can set up manufacturing
plants in any of the following countries: US, Mexico, Canada,
China, or Spain. Note that he can select any
combination of these and could select all five if that is what you
recommend. In order to create a
manufacturing plant in any of these countries, Mr. Wobs will
have to pay a one-time cost. These costs
(and all other data) are given in the Excel file that accompanies
this PDF. Note that the costs given are
based on the monetary unit of the appropriate country. Your
group must look up the most recent
exchange rate figures so Mr. Wobs has all of his costs in US
Dollars. Mr. Wobs has also been able to
81. estimate total production capacity at each manufacturing plant.
By total, this means that the sum of
music players produced (all three types) must not exceed this
total production capacity. This capacity is
5708 units in the US, 3076 units in Mexico, 5400 units in
Canada, 4616 units in China, and 4956 units in
Spain.
In addition, Mr. Wobs also wants to identify how much of each
of his products to produce in each plant
for a year. Clearly he can only produce goods in a location if he
decides to actually open a manufacturing
plant in that location. The per unit cost (i.e. the cost associated
with producing one of the music players)
of the material costs, labor costs, and shipping costs are given
in the attached file for each music player
and manufacturing location. Again, these are given in the local
currency which must be converted into
US Dollars.
Given this information, Mr. Wobs informs you that your
recommendation must also satisfy specific
requirements which he has determined. Specifically, he has
contracted 5700 Tune players, 3600
uPlayers, and 3230 Mixer players every year and you must
ensure that the production across all the
operating facilities meets these goals. Additionally, for tax
purposes, Mr. Wobs would like 50% or less of
his total production (again, across all music players) to be
produced in North American countries.
However, he doesn’t want to appear to favor international labor
too much so he requires 25% or more
of his total production to come from North American countries.
Finally, each unit of product manufacturing in a foreign country
will suffer a tariff tax. These taxes vary
82. by product and country and are given in the data file. Since the
costs of these tariffs are simply wasted
(i.e. they are not value added), Mr. Wobs would like to ensure
that that the cumulative tariff tax of your
recommended solution does not exceed $32,000 US Dollars
during a year. Additionally, Mr. Wobs is very
environmentally conscience and would like to ensure that the
greenhouse gases produced by shipping
his final products does not exceed 24,000 kilograms CO2
emitted per year. The CO2 emitted per product
for each country are given in the data file.
With all of this information, Mr. Wobs would like to see one
final location and production plan as
recommended by your team. However, he has many competing
goals:
plant) and yearly production
(materials, labor, shipping) costs
(this does not include tariff costs)
costs)
Since these are clearly competing goals (i.e. you can’t satisfy
all of them at once), you will have to create
multiple recommendations (which you will have to select the
best or combine together) satisfying each
of these objectives. For each of these objectives, your
recommended solution should not violate any of
the requirements Mr. Wobs listed. Additionally, since
minimizing CO2 emissions or minimizing total
83. tariff costs without considering the sum of the upfront and
yearly production costs may result in
extremely unreasonable upfront and yearly production costs, it
is recommended that your team develop
a ‘budget’ for this cumulative cost to ensure it doesn’t become
too high when focusing on the other
objectives. Since the final location and production plan may be
very sensitive to this budget, it is highly
recommended that multiple budgets be tested to demonstrate
how much the budget affects the final
solution. It is up to your team to determine ‘reasonable budgets’
for these tests.
Ultimately, Mr. Wobs needs the following:
for the four foreign currencies.
plan. These analyses should focus
on the three objective provided by Mr. Wobs given the
constraints he provided.
which best meets the goals and
requirements outlined by Mr. Wobs.
Part 2
In addition to this problem, one of Mr. Wobs’s current products,
the ‘Ezoo’ has recently had
manufacturing trouble and Mr. Wobs will not be able to meet
his contracted demand without
outsourcing. Therefore, Mr. Wobs would like your advice on
who he should outsource to, if he should
pay for expedited manufacturing, and if he should pay for
expedited shipping to meet his need for 200
84. Ezoos.
Mr. Wobs has three choices on which company to select for his
outsourcing decision: Telihard, Naval,
and Linx. He does not want to split manufacturing so any
solution must have one of these companies
producing all 200 Ezoos. All three of these manufacturers
provided Mr. Wobs two manufacturing
options: standard and expedited. The advantage of expedited is
that the company will immediately stop
its current product and manufacture all of the Ezoos quickly.
Specifically, if Mr. Wobs were to choose
expedited, all Ezoos would be produced in 2 days by Telihard
for $6.80/unit, 3 days by Naval for
$5.91/unit, and 3 days by Linx for $5.58/unit. If Mr. Wobs were
to choose standard manufacturing, none
of the companies can guarantee the number of days all of the
items, but it is cheaper. Specifically,
choosing standard manufacturing is $5.78/unit for Telihard,
$5.02/unit for Naval, and $4.74/unit for
Linx. Additionally, the companies have given the following
probabilities indicating the amount of time in
days the order could be completed:
Telihard
Naval
85. Linx
Once the order is complete, the companies agreed to contact Mr.
Wobs and confirm shipment details.
(NOTE: this is important, Mr. Wobs can choose his shipment
options after knowing the exact details on
manufacturing – i.e. how many days it took). Similarly to the
manufacturing options, Mr. Wobs can
choose standard or expedited shipping from each company. If he
chooses expedited shipping, Mr. Wobs
will pay more, but he will know exactly when the items arrive.
Specifically, expedited shipping from
Telihard is $10.83/unit and takes 4 days, from Naval is
$10.19/unit and takes 4 days, and from Linx is
$10.54/unit and takes 5 days. If he chooses standard shipping, it
is cheaper, but the companies again
can’t guarantee a set amount of days. Specifically, standard
shipping from Telihard costs $9.21/unit,
from Naval costs $8.66/unit, and from Linx costs $8.96/unit.
The following probabilities were provided
by each company indicating the likelihood of the standard
shipping being completed in the indicated
number of days.
Telihard
Naval
86. Linx
The key issue is that Mr. Wobs needs these items in 10 days. So
if the sum of the manufacturing time
and the shipping time is less than or equal to 10, there is no
penalty. However, if this threshold is
exceeded, Mr. Wobs must pay a $25/unit penalty to his
customers for violating his contract. Mr. Wobs
would like your advice on the best manufacturer, manufacturing
option, and shipping option to
minimize his expected costs (sum of manufacturing, shipping,
and any applicable penalty costs).
In addition, Mr. Wobs may be able negotiate with some of the
manufacturers (after all, they would like
his business). To assist Mr. Wobs with this negotiation, he
would like to know the how much the
manufacturing costs (for both standard expedited) would have to
decrease for each of the non-
recommended manufacturers to make their services
recommended with respect to average expected
costs (same as before).
Single Subject with Nested Social Skills
Kimberly Garee
3/16/2017 2:22:04 PM
87. Lesson Plan
Title: Sequencing Lesson Plan for The Little Red Hen
Objectives:
1. Children will understand, follow, and repeat the sequence of
the story in “The Little Red Hen.”
2. Children will work together to build the story from the
sequencing cards.
3. Children will be able to narrate the portions of the story
correlating with the cards they hold with prompting as needed.
Materials:
1. Story cards for “The Little Red Hen.”
2. Hand puppets to correlate with the story.
3. “The Little Red Hen” in English and Spanish with audio.
Pre-Assessment:
The story cards will be presented, and the story will be read
several times with these, encouraging the children to repeat
phrases such as “Not I” as they become familiar with the story.
Instructional Sequence:
1. The story will be read several times so the children can
become familiar with the story sequence and repeated phrases.
2. Children volunteer to describe what is happening on each
story card with assistance as needed as the teacher presents the
story cards in correct sequence.
3. When the children have a good understanding of the story
with the sequencing cards being used as prompts, the teacher
will distribute one card to each student, and help them work
together to build the correct story sequence with the cards and
describe the events depicted on the card they are holding,
thereby telling the story of “The Little Red Hen.”
Post-Assessment:
1. Teacher observes and reduces assistance until the children
are able to build and tell the story from the sequencing cards
with little to no assistance.
2. Teacher observes children during free play as they build and
retell the story of “The Little Red Hen” using the story cards or
88. the hand puppets that correlate to the story.
Notes:
Johnny and Caleb, who are strong in storytelling and language
skills will be given story cards to narrate that entail lengthier
descriptions. Maya will be given the opportunity to listen to the
audio versions of “The Little Red Hen” in her native language
and English to help with comprehension. Jane, who needs to
develop her language skills, will be encouraged to communicate
more fully with her classmates during the cooperative
sequencing portion of the lesson. Kayla and Caleb will be
encouraged to work together during the cooperative portions of
the lesson as Caleb’s strong social skills will help to bring
Kayla into the play. Jack will be encouraged to listen to his
classmates and show understanding of their ideas during the
cooperative portion of the lesson to increase his ability to
consider the needs and wants of others.
Kim
Respond
Lesson Plan Component
Below Expectations
Meets Expectations
Exceeds Expectations
Objective(s)
Objective(s) are not stated. Learners cannot tell what is
expected of them. Learners cannot determine what they should
know and be able to do as a result of learning and instruction.
There is no connection between the objective and a learning
standard.
Objective(s) are stated. Learners have an understanding of what
is expected of them. Learners can determine what they should
know and be able to do as a result of learning and instruction.
There is a brief connection between the objective and a learning
89. standard.
Objective(s) clearly stated. Learners have a clear understanding
of what is expected of them. Learners can determine what they
should know and be able to do as a result of learning and
instruction. There is a strong connection between the objective
and a learning standard.
Materials
Materials and resources are not listed, or only a partial list is
provided.
A complete list of materials, resources, and detailed
descriptions of any special considerations and/or advanced
preparations are provided.
A complete list of materials, resources, and detailed
descriptions of any special considerations and/or advanced
preparations are provided.
A list of additional/alternative materials and resources is also
provided.
Pre-assessment
The pre-assessment does not address prerequisite knowledge or
skills, or prerequisites are vague, or prerequisites are not
appropriate.
Appropriate prerequisite knowledge and skills needed by
students are provided are provided on the pre-assessment.
Appropriate prerequisite knowledge and skills needed by
students are provided on the pre-assessment. An explanation of
their importance to the
learning is provided.
Instructional Sequence
The instructional sequence is not described.
Instructional sequence contain all steps necessary to complete
the activity, but more details
would be helpful.
90. Instructional sequence is clear and detailed and includes a clear
list of sequenced steps for completing the activity.
Special Needs
Modifications and implementations for Johnny, Maya, Jane,
Caleb, Kayla and Jack are not clearly identified
Modifications and implementations are identified for Johnny,
Maya, Jane, Caleb, Kayla and Jack.
Modifications and implementation procedures are clearly stated
and are appropriate for Johnny, Maya, Jane, Caleb, Kayla and
Jack.
Management and Guidance
No description of the expectations for student behavior is
included.
Student expectations are mentioned however they do not clearly
state what is expected.
A detailed list of the expectations for student behavior is
included.
Post Assessment
Assessment is not provided, is incomplete, and/or vague.
There is not a clear relationship between the assessment and the
skills taught during the lesson.
Assessment(s) to be used to evaluate students’ learning is (are)
provided. There is a clear relationship between the
assessment(s), the content, and the skills taught during the
lesson.
Assessment(s) to be used to evaluate students’ learning is (are)
provided. There is a clear relationship between the
assessment(s), the content, and the skills taught during the
lesson. Assessment(s) incorporate(s) a consideration for diverse
student needs. A rationale for the selection of the assessment
technique(s) based on course readings and best practices is
provided.
