Minimum-cost staffing plan for PharmaPlus

 

To determine the minimum-cost staffing plan for PharmaPlus, we must analyze the current staffing levels, forecasted prescription loads, attrition rates, and salary information provided. We will also ensure that the staffing plan adheres to the service quality guidelines.

Part (a): Minimum-Cost Staffing Plan

Current Staffing Levels:

– Full-time equivalent pharmacists (P_current): 85
– Full-time equivalent technicians (T_current): 175

Attrition:

– Expected pharmacist attrition: 10
– Expected technician attrition: 30

Staffing Requirements:

1. Total Required Staff: At least 250 full-time-equivalent employees (P + T).
2. New Pharmacist Requirement: At least 15 new pharmacists must be hired.
3. Technician to Pharmacist Ratio: No more than 2 technicians per licensed pharmacist, which translates to ( T \leq 2P ).

Calculating New Staff Requirements:

1. Post-Attrition Staffing Levels:

– Pharmacists after attrition: ( P = 85 – 10 = 75 )
– Technicians after attrition: ( T = 175 – 30 = 145 )

2. New Staff Needed to Meet Total Requirement:

– Total staff after attrition: ( 75 + 145 = 220 )
– Required additional staff to meet the total of 250: ( 250 – 220 = 30 )

3. Minimum New Pharmacists:

– Since at least 15 new pharmacists must be hired, we can denote the number of new pharmacists as ( x ). Therefore, total pharmacists will be ( P = 75 + x ).

4. Calculating Technicians Based on Pharmacists:

– From the technician-to-pharmacist ratio: ( T \leq 2P ) implies ( T \leq 2(75 + x) ).

5. Total Staff Equation:

– The total staff equation becomes:
[
(75 + x) + T = 250
]
– Rearranging gives us:
[
T = 250 – (75 + x) = 175 – x
]

6. Combining Technician Constraints:

– Given the technician ratio, we substitute ( T ) into the ratio constraint:
[
175 – x \leq 2(75 + x)
]
– Simplifying this inequality:
[
175 – x \leq 150 + 2x
]
[
175 – 150 \leq 3x
]
[
25 \leq 3x
]
[
x \geq \frac{25}{3} \approx 8.33
]

Since ( x ) must be an integer, the minimum value is ( x = 9 ). Thus, at least 9 new pharmacists must be hired.

7. Calculating Required Technicians:- Substituting ( x = 9 ):- Total pharmacists: ( P = 75 + 9 = 84 )
– Now substituting back to find technicians:
[
T = 250 – P = 250 – 84 = 166
]

– Checking technician ratio:- ( T = 166) is acceptable since ( T = 2P = 2(84) = 168).

Summary of Part (a):

– Full-time equivalent pharmacists needed: 84
– Full-time equivalent technicians needed: 166

Part (b): New Hires and Payroll Impact

New Hires:

1. New pharmacists needed:

– Current pharmacists: 85
– Target pharmacists: 84
– Difference due to attrition is covered by hiring exactly 9 new pharmacists.

2. New technicians needed:

– Current technicians: 175
– Target technicians after attrition: 145
– Target technicians required: 166
– New technicians required:
[
New\ technicians = Target\ technicians – Current\ technicians + attrition\ adjustment = 166 – 145 = 21
]

Payroll Impact Calculation:

1. Salaries:

– Pharmacist salary: $40/hour
– Technician salary: $10/hour

2. Total Payroll Calculation:

– For new pharmacists:

– Total new pharmacists hired: 9
– Assuming full-time hours per year (e.g., 40 hours/week for about 52 weeks):
[
Annual\ salary\ per\ pharmacist = 40\ hours/week * 52\ weeks/year * $40/hour = $83,200
]
– Total new pharmacist payroll:
[
New\ pharmacist\ payroll = 9 * $83,200 = $748,800
]

– For new technicians:

– Total new technicians hired: 21
– Annual salary per technician:
[
Annual\ salary\ per\ technician = 40\ hours/week * 52\ weeks/year * $10/hour = $20,800
]
– Total new technician payroll:
[
New\ technician\ payroll = 21 * $20,800 = $436,800
]

Total Payroll Impact:

– Total new payroll impact due to hiring:
[
Total\ new\ payroll = New\ pharmacist\ payroll + New\ technician\ payroll = $748,800 + $436,800 = $1,185,600
]

Conclusion for Part (b):

To reach the recommended staffing levels, PharmaPlus must hire 9 new pharmacists and 21 new technicians, resulting in an increase in payroll of approximately $1,185,600 annually.