Slides Of Break Even Analysis
Management Science in Healthcare
Introduction
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 | $307,116.00 | 9 | 4 |
Y = β0 + β1X1 + β2X2
H₀: β = 0
Ha: β ≠ 0
α = .05
Regression Test
Low MAD suggests better forecasting
Positive correlation of medium strength
35% of sample results can be explained by the model
Regression Test
Y = 2.69 + (0.0000103*X1) – (0.127*X2)
Very low level of significance F means the independent variables highly influenced the Y variable
All p-values < .05 level of significance and follow expectations
The Hospital Researcher rejects H₀ and determines that the income and distance from the hospital heavily influence the number of ER visits an individual household makes in a year
Regression Recommendations
The Boiling Springs Zamora Hospital needs to be aware of the significant impact income and distance from the hospital have on the number of times a household visits the ER.
As income increases, individuals are less likely to be concerned about the costs of visiting the ER and are more willing to visit for minor needs.
As distance from the hospital increases, an individual may decide to visit a closer hospital or local doctor instead.
The hospital should advertise their health care provisions more to bring in a larger market of lower income people and improve their ambulance services to reassure farther households their services are capable of reaching farther distances.
THE END
Cost TypeOption 1Option 2Option 3
Cost 1Fixed250,000$ 150,000$ 220,000$
Cost 2Variable3,000$ 5,000$ 3,200$
BREAKEVEN POINTSUnitsDollars
Option 1 vs Option 250$ 400,000$
Option 1 vs Option 3150$ 700,000$
Option 2 vs Option 339$ 344,444$
Value
0
0.8
1.1
1.06
0.35
0.61
0.37
Correlation coefficient
Coefficient of determination (r^2)
MAPE (Mean Absolute Percent Error)
Regression line
# visits = 2.69
+ 0 * income
-0.13 * distance (miles)
Statistics
Measure
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
Observations100
ANOVA
dfSSMSFSignificance F
Regression264.3648026332.1824013128.424195931.92495E-10
Residual97109.82519741.13221853
Total99174.19
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%
Intercept2.6935389680.2799096489.6228872038.74664E-162.13799583.2490821362.13799583.249082136
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
