Two Support Teams and a Consultant's 8% Promise
Northgate's customer support runs two teams. Team A has 10 agents handling 6,000 tickets a month at an average handle time of 9 minutes. Team B has 10 agents handling 4,200 tickets a month at 14 minutes. Each agent works 21 days a month at 7 productive hours a day - 8,820 productive minutes.
A consultant recommends moving two agents from A to B, predicting an 8% rise in total tickets handled, and cites B's "higher workload per ticket." Team B carries a backlog of 900 tickets that is not shrinking; Team A clears its queue daily. Team B's rework rate is 11% against Team A's 6% - that is, 11 of every 100 tickets B closes are reopened and reworked at the same handle time. The operations director must approve or reject the move by Friday and wants to know what would actually raise throughput.
1. Compute utilisation for both teams, including rework, and state whether capacity is the binding constraint.
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Productive capacity per agent-month is 8,820 minutes; per team of 10, 88,200 minutes.
- Team A: 6,000 × 9 = 54,000 minutes → 61.2%. Rework adds 6%: 54,000 × 1.06 = 57,240 → 64.9%.
- Team B: 4,200 × 14 = 58,800 minutes → 66.7%. Rework adds 11%: 58,800 × 1.11 = 65,268 → 74.0%.
Translate capacity into tickets: A can absorb 88,200 ÷ 9 = 9,800; B can absorb 88,200 ÷ 14 = 6,300. B's demand including backlog is 4,200 + 900 = 5,100, still below 6,300.
So neither team is capacity-bound. The numbers show a real problem - B is running hotter once rework is priced in, and its backlog is growing - but the constraint is arrivals and rework, not headcount. Reallocating agents between two teams that both have unused capacity cannot increase total output.
2. Test the 8% claim arithmetically. Where does the consultant's reasoning fail?
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Total productive minutes are fixed: 20 agents × 8,820 = 176,400, and moving an agent does not create a minute. After the move, A has 8 agents (capacity 8 × 8,820 ÷ 9 = 7,840 tickets, demand 6,000) and B has 12 (capacity 12 × 8,820 ÷ 14 = 7,560, demand plus backlog 5,100). Both remain in surplus, so expected completions change by zero, not 8%.
An 8% gain would require queued demand pressing against capacity somewhere - that is the hidden assumption, and the figures contradict it. The consultant also confuses handle time with workload: A processes more tickets per agent (600 vs 420), B spends more minutes per ticket. Neither team is idler, so "higher workload per ticket" describes the work's shape, not spare capacity.
The only route to a genuine throughput gain visible here is B's rework: 4,200 × 14 × 0.11 ≈ 6,468 minutes a month, roughly 0.73 of an agent, spent redoing work already counted as done. Cutting B's rework toward A's rate buys more than moving people does.
3. Which single additional measure would most change your recommendation, and why that one?
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Net weekly arrivals minus completions for Team B - the backlog trend, not the backlog level.
Why this one dominates:
- If arrivals exceed completions, the backlog grows regardless of how agents are allocated between teams, and the fix is either added headcount or rework reduction. Any reallocation is then at best irrelevant and at worst harms A, which currently absorbs spikes and clears daily.
- If arrivals are at or below completions and the backlog is a legacy from an earlier spike, the correct action is to let B drain it and fix the rework cause; adding agents to B would be paying twice for the same problem.
The director already knows A handles 6,000 and B 4,200 - those are completions. Without arrivals, an allocation decision is being made on output data alone, which cannot distinguish a stable system from a deteriorating one. Cheaper measures such as utilisation or handle time cannot substitute, because both are downstream of the arrival rate.