Chapter 3. Decision Making in Healthcare Facilities

Chapter 3: Quantitatve MChapter 3: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement

Yasar A. OzcanYasar A. Ozcan 11

Chapter 3. Chapter 3. Decision Making in Healthcare FacilitiesDecision Making in Healthcare Facilities

What should I do?



OutlineOutline Decision Process What Causes Poor Decisions? The Decision Level & Decision Milieu Decision Making under Uncertainty

– Payoff Table– Methods

Decision Making under Risk– EVM, EOL, EVPI– Decision Tree Approach– Rollback Procedure

What if Payoff Values are Cost? Decision Analysis with Non-Monetary Values & Multiple-

Attributes– Dominance– Minimum Attribute Satisfaction– Most Important Attribute



The Decision Process Identification of the problem and its nature Specification of objectives and decision criteria Development of alternatives Analysis and comparison of alternatives Selection of the best alternative Implementation of the choice Controlling and monitoring the results



What Causes Poor Decisions?What Causes Poor Decisions? Mistakes in the Decision Process

Bounded Rationality: is the limits imposed on decision making by costs, human abilities and errors, time, technology, and the tractability of data.

Suboptimization: is characterized by Decisions are often departmentalized as separate organizational units compete for scarce resources. Individual departments often seek solutions that benefit their own department, but not necessarily the healthcare organization as a whole.



Decision TheoryDecision Theory

represents a general approach to decision making which is suitable for a wide range of operations management decisions, including: capacity, service design, location planning, equipment selection, etc.



The Decision Level & Decision MilieuThe Decision Level & Decision Milieu

Certainty-- Known values for parameters of interest

Uncertainty-- Impossible to assess the likelihood of various possible future events

Risk-- Certain parameters have probabilistic outcomes

Certainty-- Known values for parameters of interest

Uncertainty-- Impossible to assess the likelihood of various possible future events

Risk-- Certain parameters have probabilistic outcomes



CertaintyCertainty

Certainty rarely exists, especially in health care decisions. But if it does, simply choose the best available option (highest profit/least cost).



Decision Making under UncertaintyDecision Making under Uncertainty

Maximin-- best of the worst (pessimist)

Maximax-- best of the best (optimist)

Hurwitz-- allows you to adjust the probabilities/weighing between maximin and maximax or pessimist vs. optimist

Laplace-- best average payoff

Minimax Regret-- best of the worst regrets



Table 3.1 Payoff Table

Alternative\State of Nature

S1 S2 ……. Sn

A1 O11 O12 ……. O1n

A2 O21 O22 ……. O2n

… … … ……. …..

Am Om1 Om2 ……. Omn

Decision Tools



Example 3.1: A major imaging center is not able to meet the increased demand from patients for MRIs. The administration is willing to explore the possibilities by evaluating such alternatives as adding one or two additional units or out sourcing to other image centers and earning a commission of $30.00 per MRI.

A feasibility analysis showed that three major demand chunks could occur in the future, summarized as 500, 750 and 1000 additional MRI requests. The financial analysis of the potential business summarizes profits/losses under additional MRI demand chunks in a payoff table shown in Table below.

Alternatives500 Cases 750 Cases 1000 Cases

Buy One MRI Unit -15* 200 300

Buy Two MRI Units -150 100 725

Outsource 15 22.5 40

* in $ 000s



Maximin Solution

* in $ 000s

Alternatives 500 Cases 750 Cases 1000 Cases Worst

Buy One MRI Unit -15* 200 300 -15

Buy Two MRI Units -150 100 725 -150

Outsource 15 22.5 40 15



Maximax Solution

* in $ 000s

Alternatives 500 Cases 750 Cases 1000 Cases Best

Buy One MRI Unit -15* 200 300 300

Buy Two MRI Units -150 100 725 725

Outsource 15 22.5 40 40



Hurwitz Solution

For optimism with α = 0.5.

Then the HV value for the three alternatives would be:

HV (Buy one MRI unit) = .5(300,000)+(.5)(-15,000) = 142,500.HV (Buy two MRI units)= .5(725,000)+(.5)(-150,000)= 287,500.HV (Outsource) = .5(40,000)+(.5)(15,000) = 27,500.

α HV Decision Alternative

1.0 725,000* Buy Two MRI Units

.5 287,500 Buy Two MRI Units

.4 200,000 Buy Two MRI Units

.3 112.500 Buy Two MRI Units

.24 60,600 Buy One MRI Unit

.2 48,000 Buy One MRI Unit

.1 17,500 Outsource

0 15,000 Outsource



Opportunity Losses (Regrets)

* in $ 000s

Alternatives 500 Cases 750 Cases 1000 Cases Worst

Buy One MRI Unit 30* 0 425 425

Buy Two MRI Units 165 100 0 165

Outsource 0 177.5 685 685



Laplace Strategy

* in $ 000s

Probability 1/3 1/3 1/3 ExpectedValue

Alternatives 500 Cases 750 Cases 1000 Cases

Buy One MRI Units -15* 200 300 161.67


Outsource 15 22.5 40 25.89



Expected Value Model

Once the healthcare manager has assessed the probability distribution, computation of the expected values for each alternative is straightforward, as follows:

EMV(Ai) = Σj pj Oij



Payoff Table for EMV

* in $ 000s

Probability .2 .6 .2 Expected Value


Buy One MRI Unit -15* 200 300 177


Outsource 15 22.5 40 24.5



Expected Opportunity Loss

The probabilities can also be incorporated into the regrets (or opportunity losses) calculated earlier. In this way the healthcare manager can assess the expected losses and try to minimize them with proper decision. Calculations of expected opportunity loss follow the formula:

EOL(Ai) = Σj pj Rij



Expected Opportunity Loss

* in $ 000s

Probability .2 .6 .2 Expected Opportunity LossAlternative 500

Cases750

Cases1000

Cases

Buy One MRI Unit 30* 0 425 91

Buy Two MRI Units 165 100 0 93

Outsource 0 177.5 685 243.5



Expected Value of Perfect Information (EVPI)

EVUC = Σj pj (Best Oij given Sj)

EVPI = EVUC-EMV

Probability .2 .6 .2


Buy One MRI Unit -15* 200 300

Buy Two MRI Units -150 100 725

Outsource 15 22.5 40

* in $ 000s



Expected Value of Perfect Information (EVPI)

EVUC = Σj pj (Best Oij given Sj)

EVUC = (.2*15000) + (.6*200000) + (.2*725000) = 268000.

EVPI = EVUC-EMV

EMV = $177,000

EVPI = $268,000 – $177,000 = $91,000



What if Payoffs are Costs?


Buy One MRI Unit 2,050* 2,075 2,100

Buy Two MRI Units 4,050 4,075 4,100

Outsource 5 10 15

* in $ 000s



Regret Table Using Costs


Buy One MRI Unit 2,050-5=2,045* 2,075-10=2,065 2,100-15=2,085

Buy Two MRI Units 4,050-5=4,045 4,075-10=4,065 4,100-15=4,085

Outsource 5-5=0 10-10=0 15-15=0

* in $ 000s



Decision Tools-- The Decision TreeDecision Tools-- The Decision Tree

DecisionNode

EventNode

EventNode

EventNode

Actions

Action A

Action B

Action C

OutcomesEvents 1

2

3

1

2

3

1

2

3

Outcome 1

Outcome 4

Outcome 7

Outcome 2

Outcome 5

Outcome 8

Outcome 3

Outcome 6

Outcome 9



Buy O

ne M

RI Unit

Buy Two MRI Units

Outsource

500 Cases, p=.2

750 Cases, p=.6

1000 Cases, p=.2

500 Cases, p=.2

750 Cases, p=.6

1000 Cases, p=.2

500 Cases, p=.2

750 Cases, p=.6

1000 Cases, p=.2

-$15*

$300

$200

-$150

$100

$725

$15

$22.5

$40

Figure 3.1 Decision Tree

* in $000



177

177

175

24.5

Buy O

ne M

RI Unit

Buy Two MRI Units

Outsource

500 Cases, p=.2

750 Cases, p=.6

1000 Cases, p=.2

500 Cases, p=.2

750 Cases, p=.6

1000 Cases, p=.2

500 Cases, p=.2

750 Cases, p=.6

1000 Cases, p=.2

-$15*

$300

$200

-$150

$100

$725

$15

$22.5

$40

║

║

* in $000

Analysis of the Decision Tree: Rollback Procedure



Multi-attribute DecisionsMulti-attribute Decisions

Dominance Procedure: compares a pair of alternatives attribute by attribute.

Minimum Attribute Satisfaction Procedure: satisfactory levels are set for each alternative

Most Important Attribute Procedure: attributes are ranked in order of importanceattributes are ranked in order of importance

Combination: combines two or more of the combines two or more of the above procedures.above procedures.



Decision Analysis with Non-Monetary Decision Analysis with Non-Monetary Values and Multiple AttributesValues and Multiple Attributes

Attributes* \ Alternative

Cardinal McKesson Owens & Minor

Importance Ranking

MinimumAcceptable

Level

Availability 7 7 7 1 >= 7

Reliability of IT Technology

7 5 7 2 >= 6

Quality of Products

8 9 8 3 >= 7

Cost in $000 per year

23,749 24,195 23,688 5 <=25,000

On Time Delivery 97% 95% 97% 4 >=95%

*Attributes are scored on a 1-10 scale (with the exception of those associated with costs

and on-time-delivery percentage), score of 10 being most favorable.



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Chapter 3. Decision Making in Healthcare Facilities

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