Richland Health Has Three Hospitals In Greater Tampa Area

Richland Health Has Three Hospitals In The Greater Tampa Florida Area

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 four contract options with different lengths and costs: one month ($5,000), two months ($11,600), three months ($17,000), and 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 in each month: October, November, December, January, February, and March. Each month, Richland can hire as many nurses as needed under each of the four options. For example, hiring five nurses in October under the two-month option will provide nurses for October and November, costing $58,000 for those five nurses. Additionally, each nurse hired must undergo training costing $1,750, regardless of prior experience. No contracts beyond March are allowed, and no nurses should be employed past March.

The task is to determine, for each month, how many nurses to hire under each contract option to meet the projected demand while minimizing total costs.

Paper For Above instruction

The management of Richland Health faces a complex staffing problem necessitating the strategic hiring of traveling nurses to ensure adequate patient care during peak months. The fluctuating demand in the fall and winter months, especially from October through March, requires an optimized approach to staffing that balances cost, contractual commitments, and operational needs.

This problem can be effectively modeled through both heuristic and linear programming methods. A heuristic approach (Part 1) involves trial-and-error planning to arrive at a feasible staffing solution that can meet each month's nurse demand at a minimal, though not necessarily optimal, cost. Such an approach provides immediate insight but may not guarantee the most cost-effective staffing plan.

In comparison, developing a linear programming (LP) model (Part 2) allows for a systematic optimization of staffing decisions. This LP model considers the costs associated with various contract options, the fixed staffing needs per month, and the constraints on employment duration and total hiring costs. By inputting this model into Excel's Solver, an optimal solution can be obtained, minimizing the total expenditure on traveling nurses.

The problem also involves analyzing the impact of monthly demand fluctuations, exemplified by the February demand change from 35 to 31 nurses. By examining the sensitivity report generated by Solver, we can assess how such variations influence overall staffing costs and whether the initially optimized plan remains cost-effective under different demand scenarios.

The costs associated with each hiring option and training are central to the decision-making process. The four options range from one to four months, with costs escalating with longer commitments. Training costs are constant regardless of contract length, creating a fixed overhead per hire that influences overall cost calculations. Managing these aspects within the LP model allows for efficient resource allocation and cost savings.

Implementing the LP model involves defining decision variables for the number of nurses hired in each month under each contract option, establishing constraints for meeting monthly demands, and setting bounds to prevent employment beyond March. Solver's optimal solution is validated through the solution report and the sensitivity analysis, which provides insights into how changes in demand or costs affect the employment plan.

In conclusion, employing linear programming approaches to staffing problems like that of Richland Health ensures cost minimization while meeting operational needs. The inclusion of sensitivity analysis further enhances decision-making by illustrating the robustness of staffing plans against demand variability. Such models are invaluable tools for healthcare administrators managing complex, fluctuating staffing requirements efficiently.

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