# New Quantitative Management

Note 1: Show all work
1. Identify and describe a process problem that you have experienced in a health care setting.Develop a cause-and-effect (fishbone) diagram to diagnose the potential causes of the problem. Make sure your diagram includes at least four bones and ten ribs.
2. Consider a small operating room that is used for three types of surgeries; minor surgeries, major surgeries, and elective surgeries. Assume that each major surgery brings a profit of \$2,000, each minor surgery brings a profit of \$800, and each elective surgery brings a profit of \$1,500 to the facility. Also assume that each major surgery takes 4 hours and consumes 15 total hours of labor, each minor surgery takes 0.5 hours and consumes 10 total hours of labor, and each elective surgery takes 2 hours and consumes 12 total hours of labor. In addition, no more than 4 elective surgeries can be assigned to the operating room in a week. Assume that this small operating room is available 40 hours per week, and the facility has a total of 410 labor hours a week that can be devoted to surgeries in this operating room.
a) Formulate the problem to determine the optimal number of surgeries scheduled in a week for each type of surgery that maximizes the profits from surgeries. Clearly identify the decision variables, objective function, and constraints.
b) Solve the problem you formulated in part a) for the optimal number of major, minor, and elective surgeries, and find the profit using the Excel add-in Solver.
3. XYZ Medical Imaging is planning to invest in one of the three magnetic resource imaging (MRI) machines offered in the market. The table below displays the three decision alternatives, the states of nature, the associated payoffs, and the probability of each state of nature occurring. The payoffs are estimated percentage returns on the initial investment.

Equipment Type High Demand Low Demand
General Electric MRI machine 6% 4%
Fonar Upright MRI machine 20% -8%
Phillips Open MRI machine 12% 2%
Probability of states of nature 40% 60%
a) Draw the decision tree for the problem.
b) Calculate the expected percentage return for each alternative to determine the best option.
c) Conduct a sensitivity analysis on the probability of high demand (from 0% to 100%) for the decision making process (i.e. which option should be selected based on the probability of high demand).
4. Sarah works at a university that has two pharmacies, one on campus and one off campus. Sarah heard from the students that the off campus pharmacy charges higher prices than the on campus pharmacy even though the two locations by policy should not be differing on price. The table below shows the dollar amount for 32 receipts for the on campus pharmacy and 35 receipts for the off campus pharmacy.
On Campus Pharmacy Off Campus Pharmacy
\$57.92 \$50.35 \$41.64 \$77.89 \$70.61 \$104.97
\$63.79 \$76.22 \$72.23 \$83.99 \$77.34 \$89.18
\$69.20 \$38.57 \$35.48 \$52.61 \$57.99 \$35.04
\$39.32 \$45.90 \$65.80 \$30.82 \$87.03 \$86.96
\$59.73 \$60.17 \$29.27 \$103.28 \$49.54 \$85.66
\$71.83 \$30.29 \$59.86 \$39.92 \$72.29 \$57.58
\$53.30 \$52.36 \$58.23 \$70.16 \$49.97 \$31.38
\$53.11 \$33.19 \$46.20 \$29.42 \$50.83 \$44.62
\$80.31 \$75.84 \$73.32 \$65.79 \$49.35 \$51.13
\$26.08 \$37.59 \$58.50 \$60.76 \$33.23 \$96.12
\$52.52 \$53.98 \$87.84 \$77.47 \$55.80
\$79.80 \$49.44

Assume that the underlying sampling distributions are normal distributions with equal variances. Using the data, set up and perform a t-test at a 95% confidence level to determine if there is a difference in the average prescription bills between the two populations of receipts.
5. The following table provides sample data for different types of insurance coverage in Minnesota and Texas.
Types of Insurance
Employer Individual Medicaid Medicare Other Public Uninsured Total
Minnesota 1059 116 149 165 17 149 1655
Texas 3600 300 900 675 75 1875 7425

a) Produce histogram to compare the insurance coverage in two states and discuss if they appear to have similar coverage types.
b) Produce a Pareto chart for each state and discuss what they indicate.
c) Calculate the probability that a resident of Minnesota or Texas will be insured by Medicare or Medicaid.
d) Determine the 95% and 99% confidence intervals for the proportion of uninsured in each state.
e) Determine the 99% confidence interval for the difference in the proportions of uninsured in Minnesota and Texas.
f) Set up and perform a hypothesis test to determine if the proportion of uninsured differs at a 95% confidence level between the two states.
6. Solve for exercise 1 of Chapter 9 presented on pages 250&251.
7. Solve for exercise 2 of Chapter 9 presented on page 251&252.
8. Draw a detailed value stream map for a process you are familiar with. What are the cycle and throughput times for the process? What is the percent value added in this process? Identify at least three kaizen opportunities on your map.