Richland Health has three hospitals in the greater Tampa, Florida area. Demand for patient services varies considerably during the fall and winter months due to the temporary influx of the aged population. From October through March, providing adequate nursing staff is extremely difficult for Richland Health. Last year, to address this problem, Richland Health contracted with Cross Country TravCorp to hire traveling nurses during these 6 months. TravCorp offered to provide nurses under the following four contract options:
|
Option
|
Length of Employment
|
Cost
|
|
1
|
One Month
|
$5,000
|
|
2
|
Two Months
|
$11,600
|
|
3
|
Three Months
|
$17,000
|
|
4
|
Four Months
|
$24,000
|
Longer contract periods are more expensive because fewer nurses are willing to commit to longer work assignments. During the next six months, Richland has projected the following needs for additional nurses.
|
Month
|
Oct.
|
Nov.
|
Dec.
|
Jan.
|
Feb.
|
March.
|
|
15
|
28
|
24
|
20
|
35
|
36
|
|
Each month, Richland can hire as many nurses as needed under each of the four options. For instance, if Richland hires five nurses in October under Option 2, Cross Country TravCorp will supply Richland with five traveling nurses who will work two months: October and November. For this, Davis must pay 5($11,600) = $58,000. Richland Health does not want to commit to any contractual obligations for traveling nurses beyond March. No traveling nurses should be employed past March.
Each nurse hired in the traveling-nurse program must receive training at the time of hire, at a cost to Richland Health of $1750 per hire, regardless of the option under which the nurse is hired. The training program is required even if the person has worked for Richland Health in the past.
Richland Health needs to know how many traveling nurses to hire in each of the 6 months under each of the 4 contract options so that it can at least meet its projected demand in each month
Part 1
Assume your manager has given you this task and you need to come up with a solution. Use the first worksheet, denoted Part 1, to determine a feasible solution that meets monthly staffing needs.
Part 2
1. Use the second worksheet to develop a linear programming model to determine the number of nurses Richland Health should hire each month under each contract option in order to meet the projected needs at a minimum total cost. Solve your LP using Microsoft Solver.
2. The current demand for traveling nurses in March is 36. If demand decreases to 31 in March, what would be the new cost? Use the Sensitivity Report to determine your answer;
What's the percentage cost savings between the plan you developed in Part 1 and the optimal plan in Part 2-a?