The Flyer Deadline
Nomsa has promised a client 7,200 A5 flyers by 2 pm tomorrow. Work starts at 9 am, and both staff take a 30-minute lunch together, leaving 270 working minutes before 2 pm. Both operators work the whole period. Printer A prints 22 sheets per minute but jams roughly every 400 sheets, costing 6 minutes to clear. Printer B prints 15 sheets per minute and has not jammed in a year. Trimming runs at 25 sheets per minute and can begin as soon as sheets come off either printer. The invoice is R14,400. The client has offered an alternative: 3 pm delivery at a 10% discount. A second trimmer can be hired for R650 for the day, but would need 15 minutes of instruction first.
1. Where is the bottleneck, and can the job be delivered by 2 pm with the current two staff? Show the arithmetic.
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Step 1 - effective printing rate. Printer A completes 400 sheets in (400 / 22) + 6 = 18.2 + 6 = 24.2 minutes, i.e. 16.5 sheets/min. Printer B runs at 15 sheets/min. Combined, if both run continuously: 31.5 sheets/min.
Step 2 - printing time. 7,200 / 31.5 = 229 minutes (finishes about 12:49).
Step 3 - trimming time. 7,200 / 25 = 288 minutes, and one trimmer cannot go faster than 25/min however fast the printers run.
Conclusion: the bottleneck is trimming, not printing. Printing has 41 minutes of slack before the 2 pm cut-off; trimming needs 288 minutes against 270 available. The job misses 2 pm by roughly 18-20 minutes, and no amount of printer speed closes the gap.
Note the jam rate on Printer A is not the constraint here - the 41 minutes of printing slack absorbs about six additional jams before printing becomes binding.
2. Advise Nomsa: hold the 2 pm promise, accept the 3 pm delivery and the discount, or hire the second trimmer? Use the numbers.
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Compare the three outcomes on cost, not on pride.
- Hold 2 pm with current staff - not available. The work finishes around 2:20 pm. Promising 2 pm means a late delivery plus a damaged relationship.
- Accept 3 pm at a 10% discount. Discount = 0.10 x R14,400 = R1,440. Trimming still needs 288 minutes, ending about 13:48 - inside the 3 pm window with roughly 40 minutes to spare. Cost: R1,440.
- Hire the second trimmer (R650). Trim rate becomes 50/min, so trimming needs 7,200 / 50 = 144 minutes. Printing is now the constraint at 229 minutes, finishing about 12:49 - comfortably before 2 pm. Deduct the 15-minute instruction from the working window (270 - 15 = 255 available minutes) and printing still fits with 26 minutes to spare. Cost: R650.
Recommendation: hire the second trimmer. R650 against a R1,440 discount leaves the shop about R790 better off and keeps the 2 pm promise intact. The instruction time must be given to the second trimmer before 9 am or during printing, otherwise the 26-minute buffer is at risk.
Accept the 3 pm discount only if the second trimmer cannot be found - it is the fallback, not the plan.
3. Which assumption in your recommendation is the most fragile, and what would you do about it?
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The most fragile assumption is that the 255 usable minutes are uninterrupted.
- With the second trimmer, printing finishes at about 12:49 against a 2 pm deadline: a buffer of roughly 71 minutes from 9 am, but only about 26 minutes after allowing the 15-minute instruction. A single stoppage over about 26 minutes - a paper jam it takes two attempts to clear, a delivery arriving late, toner, a power trip - breaks the 2 pm promise.
- The jam rate is an average; jams cluster. Ten extra jams on Printer A would add 60 minutes to that printer alone, though the combined rate means B keeps producing in the meantime, so the true effect is smaller than 60 minutes but not zero.
What to do:
- Run the 15-minute instruction before 9 am, restoring the full 71-minute buffer.
- Load and check paper and toner for both printers the afternoon before.
- Set an internal checkpoint: if printing is not complete by 11:30, call the client immediately and move to the 3 pm option while the discount is still negotiable - rather than discovering the shortfall at 13:50.
The decision rule is to protect the promise with an early checkpoint, not to assume the average case will hold.