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Slides Of Break Even Analysis

Slides Of Break Even Analysis

Slides Of Break Even Analysis

Management Science in Healthcare


Boiling Springs Zamora Hospital

New Implementation of Management Science Tools

More effective and efficient

Break-Even, Linear, Assignment, Decision, and Regression Analysis

Break- Even Analysis

Break-Even Description

Problem … A new branch of the hospital is opening up and new equipment must be purchased.

3 different versions of the equipment where there is a direct correlation between efficiency of the machine and its costs.

Version 1 (fixed cost= 250,000 and variable cost= 3,000)

Version 2 (fixed cost= 150,000 and variable cost= 5,000)

Version 3 (fixed cost= 220,000 and variable cost= 3,200)

Which version of the new equipment will be most suitable for purchase while minimizing costs?


Break-Even Analysis Calculation

Linear Programming

Linear Programming Problem Description

Problem … In-patients are not getting enough nutrients in each meal such as Iron, B12, Calcium and too much Cholesterol

Constraint 1: The amount of nutrients in a meal at the hospital for cancer patients that need: Iron 20mg, B12 200mg, Calcium 300mg, and (less) Cholesterol 400mg

These are the four nutrients that have been identified as needing parameters when planning hospital food meals


Linear Programming Calculation

Minimize Cost Z= .08×1+.03×2+.06×3+.04×4
X1 Milk
X2 Cereal
X3 Eggs
X4 Bacon

Linear Programming Calculation Constraints

Constraint (mg) Nutrition
8×1+4×2+2×4 >= Iron 20
4×1+5×2+14×3+4X4 >= B12 200
10X1+2X2+2X3+6X4 >= Calcium 300
4×1+25×3+20×4 <= Cholesterol 400

Linear Programming Calculation Solution

Variable Type Value (ounces)
Milk Integer 18
Cereal Integer 13
Eggs Integer 0
Bacon Integer 16
Solution Value $2.47

Assignment application

Assignment Description

Boiling Springs Zamora Hospital has recently seen an increase in x-ray completion times. Because they pride themselves on efficiency and low rate times, the Director of the radiation department desires to assign technicians to each machine based on the time (in minutes) that it takes for them to complete a x-ray.

Because the hospital is, also, focused on cost, Boiling Springs Zamora Hospital desires to know what technicians to assign when minimizing costs based on wages per hour.

Based information given, which technician should operate each machine?

Time-Based Assignment Calculation

X-ray 1 X-ray 2 X-ray 3 X-ray 4 X-ray 5
Tech 1 10 15 16 13 11
Tech 2 12 15 17 12 13
Tech 3 13 17 19 14 15
Tech 4 13 18 18 15 12
Tech 5 11 14 16 13 13

*Time is in minutes

Wages-Based Assignment Calculation

Tech 1 is paid $26 per hour

Tech 2 is paid $23 per hour

Tech 3 is paid $20 per hour

Tech 4 is paid $20 per hour

Tech 5 is paid $26 per hour

X-ray 1 X-ray 2 X-ray 3 X-ray 4 X-ray 5
Tech 1 $4.33 $6.50 $6.93 $5.63 $4.77
Tech 2 $4.60 $5.75 $6.52 $4.60 $4.98
Tech 3 $4.33 $5.67 $6.33 $4.67 $5.00
Tech 4 $4.33 $6.00 $6.00 $5.00 $4.00
Tech 5 $6.07 $6.07 $6.93 $5.63 $5.63

Assignment Recommendations

When minimizing time…

Tech 1 should operate X-ray 3

Tech 2 should operate X-ray 4

Tech 3 should operate X-ray 1

Tech 4 should operate X-ray 5

Tech 5 should operate X-ray 2

When minimizing cost…

Tech 1 should operate X-ray 1

Tech 2 should operate X-ray 4

Tech 3 should operate X-ray 3

Tech 4 should operate X-ray 5

Tech 5 should operate X-ray 2

Decision Analysis

Decision Analysis Description

Boiling Springs Zamora Hospital is looking to open a new, smaller branch in a new location. We want to put a new branch in a completely different city in North Carolina based on the interest rate in the specific building found in that region.

The success will depend on the interest rate.

Given the percentage of interest rate decreasing, increasing, and remaining stable, which location will produce the most profit?

Decision Analysis Calculation

Location Decline Stable Increase Expected Value
0.25 0.45 0.30
Wilmington $100,500 $142,660 $145,800 $133,062
Charlotte $140,850 $100,250 $178,900 $133,995
Raleigh $120,680 $135,900 $160,400 $139,445
Asheville $190,420 $150,600 $110,300 $148,465
Gastonia $120,700 $149,700 $120,500 $133,690
Hickory $130,400 $120,790 $110,890 $120,223

Regression analysis

Regression Analysis

The Boiling Springs Zamora Hospital wants to evaluate variables that may effect the number of times an individual household visits the emergency room.


Variables Expectation
Y Number of ER visits
X1 Annual Income ($) Positive Relationship (+)
X2 Distance from hospital (miles) Negative Relationship (-)


Regression Analysis Data

Survey # Income Level Distance from hospital (min) # visits/year
1 $14,855.00 6 1
2 $17,696.00 16 0
3 $11,603.00 17 0
4 $14,711.00 8 1
5 $21,937.00 10 1
6 $10,695.00 9 1
7 $24,184.00 12 0
99 $214,389.00 10 2
100 $307,116.00 9 4

Y = β0 + β1X1 + β2X2


H₀: β = 0


Ha: β ≠ 0


α = .05

Regression Test

Low MAD suggests better forecasting

Positive correlation of medium strength

35% of sample results can be explained by the model

Regression Test

Y = 2.69 + (0.0000103*X1) – (0.127*X2)


Very low level of significance F means the independent variables highly influenced the Y variable

All p-values < .05 level of significance and follow expectations

The Hospital Researcher rejects H₀ and determines that the income and distance from the hospital heavily influence the number of ER visits an individual household makes in a year


Regression Recommendations

The Boiling Springs Zamora Hospital needs to be aware of the significant impact income and distance from the hospital have on the number of times a household visits the ER.

As income increases, individuals are less likely to be concerned about the costs of visiting the ER and are more willing to visit for minor needs.

As distance from the hospital increases, an individual may decide to visit a closer hospital or local doctor instead.

The hospital should advertise their health care provisions more to bring in a larger market of lower income people and improve their ambulance services to reassure farther households their services are capable of reaching farther distances.


Cost TypeOption 1Option 2Option 3

Cost 1Fixed250,000$ 150,000$ 220,000$

Cost 2Variable3,000$ 5,000$ 3,200$


Option 1 vs Option 250$ 400,000$

Option 1 vs Option 3150$ 700,000$

Option 2 vs Option 339$ 344,444$









Correlation coefficient

Coefficient of determination (r^2)

MAPE (Mean Absolute Percent Error)

Regression line

# visits = 2.69

+ 0 * income

-0.13 * distance (miles)



Error Measures

Bias (Mean Error)

MAD (Mean Absolute Deviation)

MSE (Mean Squared Error)

Standard Error (denom=n-2-1=97)

Regression Statistics

Multiple R0.607872661

R Square0.369509172

Adjusted R Square0.356509361

Standard Error1.064057578



dfSSMSFSignificance F




CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%


Income Level1.03012E-051.97139E-065.2253624879.95373E-076.38855E-061.42139E-056.38855E-061.42139E-05

Distance from hospital (min)-0.1266870240.020935714-6.0512397052.70169E-08-0.168238622-0.085135427-0.168238622-0.085135427

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