# Operations Mgmt – Linear Programming (Excel)

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Assignment 3

HUMAN RESOURCE STAFFING

Richland Health has three hospitals in the greater Tampa, Florida area. Demand for patient services vary 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 $2,500

2 Two months $5,800

3 Three months $8,500

4 Four months $12,000

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 Mar

Temp Nurses Needed 15 28 24 31 25 19

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($5,800) = $29,000. 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 $875 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 meet its projected demand in each month.

Part 1.

See the posted Excel file under Assignment 3. Use the first worksheet, called ‘Part 1’ to determine a feasible solution to the problem. DO NOT CONSTRUCT YOUR OWN EXCEL SPREADSHEET – USE THE ONE PROVIDED. NO CREDIT WILL BE GIVEN OTHERWISE. Simply fill in the cells so that Richland Health has at least the needed coverage in each of the 6 months, then calculate the total cost. Note that some cells are blocked out because no traveling nurses are to be employed past March. 9 points

Part 2 – a

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 MS 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). 33 points

Part 2 – b

The current demand for traveling nurses in March is 19. If demand does increase to 22 in March, 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.) 5 points

Part 2 – c

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.) 3 pts

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.

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’. I’m not sure if the process to add Solver is exactly the same for older versions of Excel.

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