LP Hospital Assignment

Problem 3: Hospital Assignment Example.pdf

The director of Burtonville Civil Defense Agency has been ordered to draw up a disaster plan for assigning casualties to hospitals in the event of a serious earthquake. For simplicity, we will assume that causalities will occur at two points in the city and will be transported to three hospitals. It is estimated that there will be 300 casualties at point A and 200 at point B. Travel times to hospitals 1, 2, and 3 are 25, 15, and 10 minutes, respectively; from point B they are 20, 5, and 15 minutes. Hospital capacities for emergency cases are 250, 150, and 150 patients. How should the victims be assigned to hospitals to minimize the total time lost in transporting them?

1. What is our objective here?

A. Maximize number of patients B. Minimize number of transports C. Maximize likelihood of victim survival D. Minimize total time lost to transport.

2. Which of the following are "policy variables" that we have control over (that is, want to make the right decisions about)?

A. Capacity at each hospital B. Number transported from each site to each hospital C. Distance to hospitals from sites D. Total time lost to transportation E. The number of casualties at each site

3. How many variables do we have control over?

A. 1 B. 2 C. 3 D. 6 E. 9

A convenient notation will be to denote the number of victims transported from site X to hospital Y as $X_{XY}$. Thus, the number transported to site A to hospital 2 would be $X_{A2}$.

4. In plain language, what are the constraints?

A. Capacity at each hospital B. Number transported from each site to each hospital C. Distance to hospitals from sites D. Total time lost to transportation E. The number of casualties at each site

5. Given the number of variables and the number of constraints, sketch the empty solver style table for this problem.

6. What are the weights that determine how much each of our variables contributes to the objective function? In other words, what weightings connect the variables to the objective (i.e., what is the objective function?)?

7. Add the constraint values to the table

8. What inequality goes with each constraint?

9. For each constraint, identify the impact each variable has on it.

10. Write the constraint equations.

11. Finally, write the equation for the objective function.

12. STOP and THINK! Do we need to think about negative variable values?

Implementing our results in Excel's Solver

13. Set up the blank solver template (or adapt an existing one)

14. Set up the blank solver template (or adapt an existing one)

15. Insert weights, constraint values, constraint contributions, inequalities….

16. Insert the equations for constraints and for objective function

17. Open solver dialog and select correct cells and parameters

18. Run the solver and examine the results. Interpret them in plain language.

19. Run the Answer and Sensitivity Reports. Exam them and interpret.

20. Examine the "Shadow Price" column in the Constraints section of the Sensitivity report. What does the -15 mean in the Hospital 2 Capacity row?