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Resource planning and allocation: How many service technicians does it take?

Resource planning/allocation: How many service technicians does it take?

Assumptions/factors:

- Available working hours: 8AM - 5PM Monday - Friday, with one hour off for lunch (time not fixed), and two 15-minute breaks (times not fixed).

- Scope of work includes receiving a dispatch (ticket), contacting and visiting user, verifying/clarifying issue, troubleshooting to isolate problem area/cause, repairing or replacing defective items as most appropriate.

- They must successfully resolve 90% of all events within 4 business hours, which can span two business days (example: 1 hour Monday, 3 hours Tuesday). The 4 hours is measured between receipt of dispatch (ticket) and problem/event resolution.

- Historically average (mean) event working time duration: 1.42 hours, with a range of 0.5 hours to 4.0 (or more) hours. Typically less than 2% (assume 2%) require more than 4 business hours to resolve. Assume normal distribution of event durations.

- Assume all times stated above include logistics/comms/prep/cleanup, etc. - no additional tasks remain. Assume no travel or related issues (already at same site as event).

- Average (mean) number of events per month: 3204. Average (mean) number of working days per month: 20.9. Average (mean) number of events per day = 153.3.

- Assume equal competency, skills, and tools by all technicians - no other know variables.

Request:

I need a formula that accurately predicts minimum number of technicians needed to staff to guarantee 90% of all resolutions will occur within the 4-hour business hour window, and how to account for the following changes:

a. Average event working time (example: increases from 1.42 to 2.5 hours per event)
b. Changes in service level (the 90% or the time window) affect the calculation. For example, if the service level changed from 90% to 95%, or the resolution time requirement changed from 4 hours to 8 hours, how should I account for those changes when recomputing staffing requirements?
c. Changes in available working hours; for example, if work hours change from 8AM - 5PM to 9AM to 5PM, how do I account for that in the staffing model?

Solution Preview

Please refer to the attachment for graphics.

Actually we are to calculate the minimum working hours a day to fulfill the task.

Now, Average number of events per day = 153.3. And average event working time duration=1.42 hours, with a range of 0.5 hours to 4.0 (or more) hours. Less than 2% require more than 4 business hours to resolve.

Since event durations are normal distribution, we can find the standard deviation "s" by interpreting it into standard normal ...

Solution Summary

The solution is very detailed showing the formulas and calculations. The narrative portion is very understandable.

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