Chapter 3. Decision Making in Healthcare Facilities

What should I do?

Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 1

Outline

       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 Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 2

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 Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 3

What Causes Poor Decisions?

 Mistakes in the Decision Process   Bounded Rationality: data.

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

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 Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 4

Decision 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.

Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 5

The 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

Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 6

Certainty



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

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Decision 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 Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 8

Decision Tools Table 3.1 Payoff Table …….

Alternative\State of Nature S 1 A 1 O 11 S 2 O 12 A 2 … O 21 … O 22 … A m O m1 O m2 …….

…….

…….

…….

S n O 1n O 2n …..

O mn

Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 9

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.

500 Cases 750 Cases 1000 Cases Alternatives Buy One MRI Unit Buy Two MRI Units Outsource

-15* -150 15 200 100 22.5

300 725 40 * in $ 000s Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 10

Maximin Solution

Alternatives 500 Cases 750 Cases 1000 Cases

Worst

Buy One MRI Unit Buy Two MRI Units

Outsource

-15* -150 15 200 100 22.5

300 725 40 -15 -150

15

* in $ 000s Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 11

Maximax Solution

Alternatives 500 Cases 750 Cases 1000 Cases

Best

Buy One MRI Unit

Buy Two MRI Units

Outsource -15* -150 15 200 100 22.5

300 725 40 300

725

40 * in $ 000s Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 12

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

Chapter 3: Quantitatve Methods in Health Care Management 1.0

.5

.4

.3

.24

.2

.1

0 725,000*

287,500

200,000 112.500

60,600 48,000 17,500 15,000 Buy Two MRI Units

Buy Two MRI Units

Buy Two MRI Units Buy Two MRI Units Buy One MRI Unit Buy One MRI Unit Outsource Outsource Yasar A. Ozcan 13

Opportunity Losses (Regrets)

Alternatives 500 Cases 750 Cases 1000 Cases

Worst

Buy One MRI Unit 30* 0 425 425

Buy Two MRI Units

Outsource 165 0 100 177.5

0 685

165

685 * in $ 000s Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 14

Laplace Strategy

Probability Alternatives 1/3 1/3 1/3 500 Cases 750 Cases 1000 Cases Expected Value Buy One MRI Units

Buy Two MRI Units

Outsource * in $ 000s Chapter 3: Quantitatve Methods in Health Care Management -15* -150 15 200 100 22.5

300 725 40 161.67

225

25.89

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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(A i ) = Σ j p j O ij Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 16

Payoff Table for EMV

Probability Alternatives .2

.6

.2 500 Cases 750 Cases 1000 Cases Expected Value

Buy One MRI Unit

Buy Two MRI Units Outsource -15* -150 15 200 100 22.5

300 725 40

177

175 24.5

* in $ 000s Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 17

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(A i ) = Σ j p j R ij Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 18

Expected Opportunity Loss

Probability .2

.6

Alternative 500 Cases 750 Cases .2

1000 Cases Expected Opportunity Loss

Buy One MRI Unit

Buy Two MRI Units 30* 165 0 100 425 0

91

93 243.5

Outsource * in $ 000s Chapter 3: Quantitatve Methods in Health Care Management 0 177.5

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Expected Value of Perfect Information (EVPI)

EVPI = EVUC-EMV EVUC = Σ j p j (Best O ij given S j ) Probability .2

.6

.2 Alternatives Buy One MRI Unit Buy Two MRI Units Outsource 500 Cases -15* -150

15

750 Cases

200

100 22.5

1000 Cases 300

725

40 * in $ 000s Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 20

Expected Value of Perfect Information (EVPI)

EVPI = EVUC-EMV EVUC = Σ j p j (Best O ij given S j ) EVUC = (.2*15000) + (.6*200000) + (.2*725000) = 268000.

EMV = $177,000

EVPI

= $268,000 – $177,000 =

$91,000

Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 21

What if Payoffs are Costs?

Alternatives 500 Cases 750 Cases 1000 Cases Buy One MRI Unit Buy Two MRI Units Outsource 2,050* 4,050 5 2,075 4,075 10 2,100 4,100 15 * in $ 000s Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 22

Regret Table Using Costs

Alternatives 500 Cases 750 Cases 1000 Cases 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

5-5=

0

10-10=

0

15-15=

0

Outsource * in $ 000s Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 23

Decision Tools-- The Decision Tree

Events 1 Outcomes Outcome 1 Actions Event Node 2 Outcome 4 Action A 3 Outcome 7 1 Decision Node Action B Event Node 2 Outcome 2 Outcome 5 3 Outcome 8 Action C 1 Outcome 3 Event Node 2 Outcome 6 Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 3 Outcome 9 24

Figure 3.1 Decision Tree

Buy Two MRI Units * in $000 Chapter 3: Quantitatve Methods in Health Care Management -$15* 750 Cases, p=.6

$200 $300 -$150 750 Cases, p=.6

$100 $725 $15 750 Cases, p=.6

$22.5

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Analysis of the Decision Tree: Rollback Procedure

-$15* 177 750 Cases, p=.6

$200 $300 -$150 750 Cases, p=.6

$100 177 Buy Two MRI Units ║ 175 * in $000 Chapter 3: Quantitatve Methods in Health Care Management 24.5

$725 $15 750 Cases, p=.6

$22.5

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Multi-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 importance

Combination:

combines two or more of the above procedures.

Chapter 3: Quantitatve Methods in Health Care Management Yasar A. Ozcan 27

Decision Analysis with Non-Monetary Values and Multiple Attributes

Attributes* \ Alternative Cardinal McKesson Owens & Minor Importance Ranking Minimum Acceptable Level

Availability Reliability of IT Technology Quality of Products Cost in $000 per year On Time Delivery 7 7 8 23,749 97% 7 5 9 24,195 95% 7 7 8 23,688 97% 1 2 3 5 4 >= 7 >= 6 >= 7 <=25,000 >=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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The End

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