# linear programming Application

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
Download the Assignment 3 Template – Fall 2016.xlsx worksheet for this exercise.

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. You will likely use trial-and-error. USE THIS WORKSHEET – DO NOT CREATE YOUR OWN. Try to come up with the best solution that you can – meaning one with the least cost.

Part 2
Use the second worksheet called ?Part 2 – LP? 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. (The orange cells will be your variables.) Solve your LP using Microsoft Solver. Do not develop your own spreadsheet. If you do, you will receive zero credit. You?ll need to generate both the answer report and sensitivity report. Solver should automatically generate separate worksheets for each of these: one with the solution (Answer report) and another with dual prices/RHS ranges (Sensitivity report).
The current demand for traveling nurses in February is 35. If demand decreases to 31 in February, what would be the new cost? Use the Sensitivity Report to determine your answer; no credit will be granted otherwise. Put your answer on the ?Part 2 – LP? worksheet.
What?s the percentage cost savings between the plan you developed in Part 1 and the optimal plan in Part 2-a? Put your answer on the ?Part 2 – LP? worksheet.
What to Submit?
What to Submit : ONE Excel file with 4 worksheets. Worksheets will be called ?Part 1,? ?Part 2 ? LP,? ?Answer Report,? and ?Sensitivity Report.? Solver will automatically generate the last 2 worksheets.

Using Solver in Excel
Don?t see the Solver analysis tool in your version of Excel?

You may need to add Solver to your copy of Excel. To see if you have Solver, click on ?Data,? then Solver should appear under the heading of ?analysis.? If you do not see Solver there, you must add it. To add Solver, go to ?File,? then ?Options,? then ?Add-ins.? In Excel 2013, you?ll see a box at the bottom saying ?Manage ? Excel Add-ins.? Click the ?go? button beside that. A screen will pop up where you can check ?Solver? ? then click ?OK.? This process may be different if you are using an older version of Excel.