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Compute capacity, staffing trade-offs, and break-even

Capital OneData Scientist · HR Screen
MediumData ScientistHR ScreenAnalytics & Experimentation

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This question tests the ability to model operational costs, evaluate staffing trade-offs between overtime and contracting, and perform break-even analysis under varying volume assumptions.

The Problem

You are analyzing the capacity of a customer support team that handles an average of 10,000 inquiries per week. Each inquiry takes 30 minutes to resolve. Currently, the team has 125 full-time employees (FTEs) who work 40 hours per week.

Constraints & Costs:

  • An FTE costs $2,000 per week (fully burdened).
  • Overtime pay is 1.5x the hourly rate of an FTE. You must calculate the hourly rate based on a 40-hour work week.
  • Alternatively, you can hire contractors at a flat rate of $60 per hour, but they require 5 hours of training (unpaid to them, but requires an FTE supervisor) per 40 hours of work.

Your Task:

  1. Determine the current capacity utilization rate of the team.
  2. If inquiry volume increases by 20% next month, calculate the cost difference between meeting the demand via mandatory overtime versus hiring contractors.
  3. Identify the "break-even" volume increase (percentage) where the cost of hiring a new permanent FTE becomes cheaper than continuing with contractor labor.

Assumptions:

  • FTEs operate at 90% efficiency (10% of time is spent on non-inquiry tasks).
  • Assume a 50-week working year.
  • Training requires 5 hours of an FTE's time per contractor hired.

Hints

Hint 1

First, calculate the hourly rate of an FTE and compare it to the total cost of contractor labor including the supervisor training overhead.

Hint 2

Calculate the total man-hours required for the 20% increase in volume and convert those into FTE equivalents vs. overtime hours.

Hint 3

For the break-even analysis, set up an equation where Cost(FTE) = Cost(Contractors) based on the variable volume increase x.

Follow-up questions

  • How would your recommendation change if the inquiry volume were highly seasonal versus experiencing steady, long-term growth?
  • If contractor efficiency is only 75% compared to the 90% efficiency of FTEs, how does this impact your break-even point?
  • What qualitative factors—beyond just labor cost—should we consider when choosing between overtime and contractors?