The 28-Page Urgency and the Arithmetic of Revision
You coordinate translation of a 28-page draft regulation for a Council working party. The text averages 650 words per page, so 18,200 words. The team has three translators: A can produce 420 words/hour, B 360 words/hour, and C 500 words/hour but is available only 50% of the time because of parallel duties. A working day is 7.5 hours; the deadline is three working days from now. The team also has 5,200 words of previously committed urgent work that must be delivered in the same window. One reviser can revise 800 words/hour and has 1,000 words of other revision already booked. The rule is that no translation may be sent to the working party without full revision. You cannot authorise overtime without the head of unit’s approval, and approval takes one working day.
1. Calculate the team’s net translation capacity in the three-day window after deducting committed work. Is the 18,200-word job feasible for translation alone?
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Gross translation capacity: A = 420 × 7.5 × 3 = 9,450 words; B = 360 × 7.5 × 3 = 8,100 words; C = 500 × 7.5 × 3 × 0.5 = 5,625 words. Total gross = 23,175 words. Deduct the 5,200 words of committed urgent work: net capacity = 17,975 words. The new job is 18,200 words, so translation alone is short by 225 words. That is a small but real shortfall: it cannot be closed by assuming that the team will 'work a bit faster', because the rates already build in normal working speed. The translation side is therefore not feasible on the stated assumptions unless 225 words are added through overtime, a temporary translator, or a reduction in the committed work. The answer should show the arithmetic rather than simply saying that the team is 'close'.
2. Calculate the reviser’s net capacity and identify the binding constraint. What does this imply for the deadline?
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Reviser’s gross capacity: 800 × 7.5 × 3 = 18,000 words. Deduct 1,000 words already booked: net revision capacity = 17,000 words. The new job needs 18,200 words revised, so revision is short by 1,200 words. Translation is short by only 225 words. The binding constraint is therefore revision, not translation. This matters because the rule forbids sending unrevised text, so extra translation capacity alone would not save the deadline. Even if translators produce all 18,200 words, the reviser cannot fully revise them within three days at the stated rate. The implication is that the deadline cannot be met in full compliance with the revision rule unless the revision resource is increased or the scope is reduced. A plan that relies on skipping revision would breach the stated control.
3. Recommend a course of action that respects the revision rule and the one-day approval lead time. Include one numerical option.
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Send the approval request today, because a one-day approval lead time means that any overtime or external reviser must be authorised on day 1 to be useful on days 2–3. A numerical option: add 1,200 words of revision capacity, which at 800 words/hour is 1.5 hours of additional reviser time, plus 225 words of translation, which at A’s 420 words/hour is about 32 minutes. In practice, request a second reviser for half a day, which covers the 1,200-word gap with a margin, and ask A for one hour of overtime. If approval is refused, do not silently miss the deadline: inform the working party that full revision cannot be completed by day 3 and propose a staged delivery, with the revised text delivered as far as capacity allows and the remainder immediately after. The recommendation should state the trade-off explicitly rather than pretending that the arithmetic works.