Quantitative Methods in Health Care Management
Case Analysis – Resource Allocation
Notes: All subparts of each question are worth 0.75 points each. To receive credit you must submit the Excel spreadsheets in which you calculate your answers.
1. The CEO at your hospital group has asked you to determine the most profitable approach to expanding capacity (i.e., number of beds) across your three locations. The estimated increase in profits from expansion is $1000/bed at Wesley Chapel, $1250/bed at Brandon, and $700/bed at Clearwater. You have a total of 500 beds to allocate across the three locations. There are 400 nursing hours that you be allocated across the facilities. The Wesley Chapel location requires 15 nursing hours per bed, the Clearwater location requires 12 hours per bed, while the Brandon location requires 20 hours per bed. Finally, you must account for the administrative support requirements for each facility. Specifically, there are 350 possible hours and the Wesley Chapel location requires 20 hours per bed and the Brandon and Clearwater locations both require 5 hours per bed.
While not realistic, for this problem you can allocate a proportion of beds (in other words, you do not have to force the optimal values to be integers).
Using the above information, answer the following questions.
- Identify the decision variables.
- Specify the objective function using mathematical notation.
- Specify the constraints using mathematical notation.
- How should your group allocate the additional beds?
- What would be the change in profits from your allocation?
- Which constraints are binding at the optimum? Which are not?
- Are there any locations to which you will not allocate beds? If so, what would be the effect on profits of allocating a bed to that location?
- For each of the constraints that are binding, what would be the effect on profits from increasing the constraint amount (i.e., RHS number) by one unit?
2. You have been asked to determine the least costly staffing schedule for your clinic. You need to staff the clinic with eight individuals Monday through Friday and four on Saturday and Sunday. Your clinic guarantees your staff three consecutive days off each week. Any cycle that does not include a Saturday or Sunday costs your clinic $800 per cycle. Cycles that include Saturday or Sunday (but not both) cost $900 per cycle, while cycles that include both Saturday and Sunday cost $1000 per cycle. Cycles must be hired in whole units. With this information, complete the following tasks:
- Identify the decision variables.
- Specify the objective function using mathematical notation.
- Specify the constraints using mathematical notation.
- How many of each cycle should your clinic employ and what is the total cost that that your clinic will incur?
- Identify those constraints that are binding and those that are not.
