Question

Banner Good Samaritan Medical Center is a 662-bed hospital. Like other hospitals, the number of its patients increases in the winter. The full-time equivalent (FTE) nurse requirements for Q1 to Q4 of next year are forecasted to be Q1: 1,300 FTE; Q2: 1,000 FTE; Q3: 800 FTE; and Q4: 1,000 FTE. Banner Good Samaritan employs 1,000 FTE permanent nurses throughout the year. During peak season, it can employ up to 500 additional FTE temporary nurses from local temp agencies. Also, it can use up to 500 FTE of overtime (hours worked beyond an eight-hour shift in a day). Each FTE permanent nurse receives an average of $8,000 a quarter. Each FTE of overtime work receives $12,000 a quarter. Each FTE temp receives $8,000 a quarter, but needs an average of $1,000 for training (charged to the first quarter of employment).

a. Set up this problem as a planning problem and determine the minimum cost plan. Briefly state the trade-off analysis you used. Calculate the total cost. (Note: If demand is less than the number of permanent nurses in a quarter, the nurses will still be paid but the idle time will be used as paid holidays and/or for further training.)

b. What factors, other than cost, should be considered? Explain.

Answer 1

a.

We can set this up as a linear programming model in order to determine the minimum cost schedule to fulfill our requirement.

Let the regular time nurses for each quarter be denoted by X1, X2, X3, and X4.

Let the overtime nurse for each quarter be denoted by Y1, Y2, Y3, and Y4

Let the temp nurse for each quarter be denoted by Z1, Z2, Z3, and Z4

Our planning problem model will be

Minimize Z where

Z = 8000(X1 + X2 + X3 + X4) + 12000(Y1 + Y2 + Y3 + Y4) + 8000(Z1 + Z2 + Z3 + Z4)

Subject to

X1, X2, X3, X4 = 1000

Y1, Y2, Y3, Y4 <= 500

Z1, Z2, Z3, Z4 <= 500

X1 + Y1 + Z1 >= 1300

X2 + Y2 + Z2 >= 1000

X3 + Y3 + Z3 >= 800

X4 + Y4 + Z4 >= 1000

X1, X2, X3, X4, Y1, Y2, Y3, Y4, Z1, Z2, Z3, Z4 >= 0

This completes the problem formulation.

b.

One more factor that must be considered in this scenario is the shift timing and the availability of the nurses during each shift. While costing is an issue, we must also schedule nurses optimally so that the patient care or coverage can be maximized.