Exercises 8.1: Two Types Of Visits Are Provided By Durham

Exercises 8 1two Types Of Visits Are Provided By The Durham Health C

Exercises 8-1 to 8-2 involve analyzing the capacity and financial aspects of Durham Health Clinic’s service operations, including determining production frontiers, ideal station expansion, and break-even points based on given processing times, staff hours, and contribution margins. Exercise 8-3 assesses staffing requirements for pre-employment physicals, considering staff time per physical and current workload. Exercise 8-4 explores staffing needs under different visit compositions and contractual commitments, considering changes in visit ratios and physicals performed weekly. Exercise 8-5 evaluates how modifications in processing times impact staffing and capacity planning. Exercises 9-1 and 9-2 require applying queuing theory to model a walk-in clinic and hospital pharmacy, calculating probabilities, average system metrics, and financial implications of adjusting service rates, based on arrival and service rates, costs, and system structure.

Paper For Above instruction

The operations management of healthcare facilities relies heavily on capacity analysis, resource allocation, and financial decision-making. In examining Durham Health Clinic, understanding the service processes through the lens of capacity and queuing theory offers vital insights for optimizing efficiency and profitability.

Capacity Analysis and Production Frontiers

For exercise 8-1, the first step involves calculating the processing time at each work station for both first-time and return visits, then determining the clinic’s production frontiers. The data indicate that the reception/discharge, nursing/testing, and medical exam/treatment stations have specific processing times, which directly influence throughput capacity.

The processing times are as follows: reception/discharge takes 0.12 hours, nursing/testing takes 0.38 hours, and medical exam/treatment takes 0.25 hours for each visit type. Staff hours per week are fixed, and the maximum capacity of each station can be determined by dividing total staff hours by the processing time per visit. For example, if staff work 40 hours per week, then the capacity at each station per week is calculated accordingly.

By plotting these capacities, we derive the production frontiers, which identify bottleneck stations—those with the lowest capacity relative to demand. Expanding the station with the smallest capacity will increase the overall clinic throughput, whereas reducing capacity at a less critical station may not significantly impact capacity. Typically, the station with the highest processing time per visit or the lowest staff hours relative to demand is considered the bottleneck—here likely the nursing and testing station given its higher processing time of 0.38 hours per visit.

Analyzing these frontiers provides a strategic basis for capacity expansion, ensuring resources are allocated to maximize throughput and patient service levels.

Financial Analysis and Break-Even Calculations

Exercise 8-2 focuses on profit analysis, where the contribution margin per visit is $35, and fixed costs vary at $4,000, $6,500, and $8,500 weekly. The break-even point (BEP) is calculated as fixed costs divided by contribution margin:

BEP = Fixed Costs / Contribution Margin

Thus, for each fixed cost level, the BEP in visits is computed, guiding managerial decisions regarding patient volume targets necessary to cover costs and achieve profitability.

In practice, these calculations inform capacity planning—ensuring the clinic recruits or schedules sufficient staff and resources to meet the BEP volume, while also considering fluctuations in patient demand. Moreover, understanding these financial thresholds supports strategic decisions about expanding or reducing specific service offerings or adjusting pricing structures.

Staffing Needs for Contracted Pre-Employment Physicals

Exercise 8-3 evaluates the staff time required for performing 50 pre-employment physicals per week, with specified time estimates per physical at each station. Given the times—0.20 hours reception/discharge, 0.45 hours nursing/testing, and 0.20 hours medical examination—the total weekly work hours per station are calculated by multiplying the per-physicals hours by 50.

Specifically, reception/discharge requires 10 hours (0.20 x 50), nursing/testing 22.5 hours (0.45 x 50), and medical examination 10 hours (0.20 x 50). These totals reflect the additional workload imposed on the current staff, eligible for comparison to existing staffing levels.

Subsequently, the clinic's staffing by role can be calculated based on 35 hours scheduled per employee, determining the number of employees needed in each category by dividing total hours required by scheduled hours per employee. This enables the clinic to align staffing levels with contractual obligations efficiently.

Impact of Visit Ratio Changes on Staffing

In exercise 8-4, the current visit volume is 250 weekly, with 50% being return visits. The analysis explores how alterations in return visit ratios influence staffing requirements. If return visits decrease to 10%, the number of first visits increases, affecting the workload distribution across physicians, nurses, and receptionists.

With the contract for pre-employment physicals, additional staffing calculations are required. The total workload per staff type is computed based on the combined visit and physicals volumes, divided by the scheduled hours per employee. Should the number of physicals decrease or increase to 35 weekly, the staff requirements adjust proportionally, assuming staff productivity remains constant.

Such analysis aids managers in adjusting staffing plans dynamically, balancing workload with available resources to maintain operational efficiency and quality patient care.

Effects of Processing Time Modifications

Exercise 8-5 examines how changes in processing times impact capacity. Increasing nursing and testing time to 0.50 hours per visit and reducing medical exam/treatment time to 0.30 hours for first visits and 0.20 hours for return visits alter the bottleneck analysis. The new processing times may shift the capacity constraints, requiring reevaluation of staffing and facility capacity.

Queuing Theory Applications

Turning to exercises 9-1 and 9-2, queuing theory models provide a method for analyzing patient flow as an M/M/1 system—single server, single queue. For Alpha Walk-in Clinic, with an average arrival rate λ of 7 patients/hour and a service rate μ of 7 patients/hour, calculations of system metrics follow standard formulas.

For instance, the probability the system is idle (P0) equals 1 - (λ/μ). In this case, as λ = μ, the system is at capacity, and P0 tends to zero, indicating the system is always busy or nearly so.

The average number of patients in the system (L) is λ / (μ - λ); however, since λ = μ, the formula indicates an unstable or infinitely growing queue, signifying the need for increased capacity.

The average time in the system (W) and in queue (Wq), as well as the probability of waiting upon arrival (Pw), are derived similarly, providing critical insights into patient wait times and system efficiency. These metrics inform decisions about system improvements, such as increasing staff or expanding capacity.

Cost and Capacity Optimization for Pharmacy Services

In exercise 9-2, the pharmacy operates as an M/M/1 queue with different operational periods. Adjusting the service rate by increments of 50 prescriptions per hour, at an additional $100 cost per increment, the hospital can analyze the trade-offs between capacity and expenses.

Calculations involve determining the current utilization, probability the system is idle, average number of prescriptions in the system, and average waiting times. When the service rate is increased, the probability that a patient must wait diminishes, but costs rise accordingly.

Applying these insights, the management should evaluate whether the cost of increasing capacity justifies the reductions in patient waiting time and queue length. If the marginal benefit of decreased wait times aligns with the additional expenses, capacity expansion is justified; otherwise, maintaining or reducing capacity might be more economical.

Summary and Recommendations

The integration of capacity analysis and queuing theory in healthcare operations supports evidence-based decision-making. For Durham Health Clinic, expanding bottleneck stations like nursing/testing, based on capacity frontiers, can raise throughput and patient satisfaction. Financial analyses such as break-even points guide resource allocation and staffing levels. When modeling patient flow with queuing theory, understanding the impact of staff and process adjustments enables the clinic to optimize performance economically.

In hospital pharmacy operations, carefully balancing service capacity and costs can significantly improve patient experience and operational efficiency. Overall, these analytical frameworks assist managers in making strategic choices that align resource deployment with organizational goals, ensuring sustainable and effective healthcare delivery.

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