Desicion tree need it for today

DECISION TREE

St. Vol Hospital needs reliable cardiology coverage on Saturdays to maintain their reputation as a first rate healthcare facility. The coverage is now considered required for emergent care, primarily responding to Code STEMI’s. The local cardiologist group has offered several “fee for coverage” options that need to be evaluated. Note that these fees are for the “coverage” only, i.e. the cardiologist would still separately bill the patient for any procedures performed. As CMO for the hospital, you need to recommend a strategy that minimizes the expected cost to the hospital.

The cardiology group has offered the following three options. One option is for the hospital to simply pay a fixed fee of $1200 each week for emergent cardiology coverage on Saturdays irrespective of whether or not there are any Code STEMI’s that occur. A second option is that the hospital pays a base fee ($700) for coverage, but then also pays a per-call-in fee of $400 for each Code STEMI. A third option is that there is no base fee, but there is a higher per-call-in fee of $1300 for each Code STEMI.

Data was pulled for the prior 12 months (52 weeks) and the number of Code STEMI’s for the 52 Saturdays in the data set was observed to be as follows:

013131

Number of Code STEMI’s		Number of Saturdays
	Total

Part A) Construct and evaluate a decision tree for this decision situation (use the values in the table to compute probabilities). Clearly identify and explain the most cost-effective option and its cost implications.

Part B) After further discussions, a variation of the first option was put forth by the cardiology group. On Saturday mornings, the hospital often finds itself with several patients who were admitted the day before and only need stress testing. Under the current system, these patients will stay in the hospital until Monday, at which time they will undergo their stress tests and be discharged. If some or all of these patients could have their stress tests performed on Saturday, the hospital costs would be reduced by having lower weekend census. In fact, the hospital estimates a cost savings of $800 for each patient that needs stress testing and gets it done on Saturday rather than waiting till Monday. The cardiology group (which has traditionally resisted doing any stress testing on Saturdays) has now offered a fourth option as follows. The group will provide emergent cardiology coverage on Saturdays for a fee of $2000, but will also do stress testing if there are patients who need it and if the hospital is willing to call in and pay for the necessary support staff. If needed, the support staff can be called in on Saturday morning at a total cost of $900 for a 4-hour period (note, a call-in is guaranteed 4 hours). The prior 52 weeks were analyzed and the number of waiting stress-test patients on Saturday mornings was given as follows:

Number of Saturdays

110217313

49Total52

Number of patients awaiting stress testing

Each stress test takes less than one hour so it would never be necessary for the support staff to work more than 4 hours.

Clearly, on any given Saturday, it wouldn’t make sense to call in support staff and do testing if there were no admitted patients waiting for stress testing. On the other hand, if there were 4 patients waiting, it is easy to show that it makes sense to bring in the support staff and do the testing. Somewhere in-between, is there an optimal policy for whether or not to call in support staff and doing stress testing on waiting patients that minimizes overall costs?

The above question can be answered by constructing and evaluating a decision tree for this fourth option. What is the most cost effective strategy and what are the expected financial implications? Compared with the first three options, what would you recommend?

TREE SAMPLE ATTACHED POWER POINT

Situation

David Chang is the owner of a small electronics company. In six months, a proposal is due for an electronic timing system for the 20

6 Olympic Games. For several years, Chang’s company has been developing a new microprocessor referred to as the X-32. The X-32 is a breakthrough component that would allow Chang to develop a timing system that would be superior to any product currently on the market. However, progress in R&D has been slow, and Chang is unsure about whether his staff can complete the X-32 microprocessor in time.

If they continue the R&D and succeed in developing the X-32, there is an excellent chance that Chang’s company will win the $1 million Olympic contract. If they continue the R&D but do not successfully complete the X-32, there is a small chance they will still be able to win the same contract with an alternative, inferior timing system that is a modification of one already developed. If they do not continue R&D, there is no chance to win the contract.

If he continues the project, Chang must invest $200K in R&D expenses. In addition, making a proposal requires developing a prototype timing system at an additional cost of $50K. Finally, if Chang wins the contract, the finished product will cost an additional $150K to produce.

Decision Tree: a tool for representing, evaluating, and communicating a decision process. A decision tree is constructed using branches and nodes.
Symbols:
Square represents a decision node.
Circle represents an uncertain event node
Triangle represents a terminal node.
Structuring the Decision Situation

2
© 2013, Charles E. Noon, Ph.D.

Structuring the Decision Situation

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win

3
© 2013, Charles E. Noon, Ph.D.

Structuring the Decision Situation

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win
-200K
-50K
+850K
-50K
+850K

4
© 2013, Charles E. Noon, Ph.D.

Structuring the Decision Situation

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win
-200K
-50K
+850K
-50K
+850K

.40
.60
.90
.10
.05
.95
5
© 2013, Charles E. Noon, Ph.D.

Structuring the Decision Situation

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win
-200K
-50K
+850K
-50K
+850K

+600K
-200K
0
-250K
+600K
-200K
-250K
.40
.60
.90
.10
.05
.95
6
© 2013, Charles E. Noon, Ph.D.

Structuring the Decision Situation

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win

+600K
-200K
0
-250K
+600K
-200K
-250K
.40
.60
.90
.10
.05
.95
7
© 2013, Charles E. Noon, Ph.D.

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win

+600K
-200K
0
-250K
+600K
-200K
-250K
.40
.60
.90
.10
.05
.95

Strategy 1
“Abandon”
8
© 2013, Charles E. Noon, Ph.D.
“Abandon” Strategy 1

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win

+600K
-200K
0
-250K
+600K
-200K
-250K
.40
.60
.90
.10
.05
.95

Strategy 2
“Continue ; Make ; Make”

9
© 2013, Charles E. Noon, Ph.D.
“Continue; Make: Make” Strategy 2

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win

+600K
-200K
0
-250K
+600K
-200K
-250K
.40
.60
.90
.10
.05
.95

Strategy 3
“Continue ; Make ; Don’t Make”

10
© 2013, Charles E. Noon, Ph.D.
“Continue ; Make ; Don’t Make” Strategy 3

Uncertainty in Net Cash Flow

.50
.50
1.00
$20
$60
$0
or
Expected Monetary Value (EMV) = the sum of the payoffs times their probabilities.
EMV=$20
EMV=$30
11
© 2013, Charles E. Noon, Ph.D.

Uncertainty in Net Cash Flow
EMV = .50(60) – .40(25) +.10(30) = $23K

.40
Loss
of $25K

.50
.10
Gain
of $60K
Gain
of $30K

.40
– $25K

.50
.10
+ $60K
+ $30K
12
© 2013, Charles E. Noon, Ph.D.

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win

+600K
-200K
0
-250K
+600K
-200K
-250K
.40
.60
.90
.10
.05
.95
Evaluating According to EMV
13
© 2013, Charles E. Noon, Ph.D.

ã 1998, Charles Noon / All Rights Reserved
Notes

Evaluating According to EMV

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win

+600K
-200K
0
-250K
+600K
-200K
-250K
.40
.60
.90
.10
.05
.95
515K
-207.5K

14
© 2013, Charles E. Noon, Ph.D.

ã 1998, Charles Noon / All Rights Reserved
Notes

Evaluating According to EMV

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win

+600K
-200K
0
-250K
+600K
-200K
-250K
.40
.60
.90
.10
.05
.95
515K
-207.5K

Evaluating According to EMV

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win

+600K
-200K
0
-250K
+600K
-200K
-250K
.40
.60
.90
.10
.05
.95
515K
-207.5K

-200K
515K
86K

Evaluating According to EMV

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win

+600K
-200K
0
-250K
+600K
-200K
-250K
.40
.60
.90
.10
.05
.95
515K
-207.5K

-200K
515K
86K

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win

+600K
-200K
0
-250K
+600K
-200K
-250K
.40
.60
.90
.10
.05
.95
515K
-207.5K
-200K
515K
86K

Strategy with highest EMV
“Continue ; Make ; Don’t Make”
18
© 2013, Charles E. Noon, Ph.D.
“Continue; Make; Don’t Make Strategy with highest EMV

Abandon
Continue
R&D
Succeeds
R&D
Fails
Make
Proposal
Don’t Make
Proposal
Don’t Make
Proposal
Make
Proposal

Lose
Lose
Win
Win

+600K
-200K
0
-250K
+600K
-200K
-250K
.40
.60
.90
.10
.05
.95
515K
-207.5K
-207.5K
515K
81.5K

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