Meeting a 1,000-certification target with fixed batch costs, dropout and a seat-rental offer
A department must certify 1,000 employees in basic computer literacy. Each batch has a fixed cost of ₹1,10,000 (trainer, lab and materials) and a variable cost of ₹500 per enrolled candidate. The lab has 32 working seats per batch. Historically 20% of enrolled candidates drop out before certification. The sanctioned budget is ₹50,00,000. A vendor offers to add eight seats per batch by renting neighbouring lab space for ₹18,000 per batch, which would allow 40 seats per batch. The department can also run a two-day retention drive at ₹60,000 in total, which is expected to cut dropout from 20% to 18%. The training calendar allows at most 40 batches in the financial year, and the lab cannot run more than one shift.
1. Calculate the number of batches and the cost under the current 32-seat configuration, and state whether the target can be met.
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To certify 1,000 candidates at a 20% dropout rate, the department must enrol 1,000 ÷ 0.80 = 1,250 candidates.
At 32 seats per batch, 1,250 ÷ 32 = 39.06, so 40 batches are needed if every batch is filled. Cost:
- Fixed: 40 × ₹1,10,000 = ₹44,00,000
- Variable: 1,250 × ₹500 = ₹6,25,000
- Total: ₹50,25,000
That is ₹25,000 over the ₹50,00,000 budget. If only 39 batches are run, capacity is 39 × 32 = 1,248, and expected certification is 1,248 × 0.80 = 998, two short of the target. Cost would be 39 × ₹1,10,000 = ₹42,90,000 plus 1,248 × ₹500 = ₹6,24,000, a total of ₹49,14,000, leaving ₹86,000 but missing the target by two.
So the current configuration cannot meet the target within budget unless dropout falls slightly, seats are added, or the target is renegotiated. The arithmetic, not the calendar, is the binding constraint: 40 batches are within the 40-batch ceiling.
2. Compare the two options (renting seats versus the retention drive) and recommend one, with numbers.
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Option 1: rent eight seats per batch. With 40 seats, 1,250 ÷ 40 = 31.25, so 32 batches are needed. Fixed cost per batch becomes ₹1,10,000 + ₹18,000 = ₹1,28,000. Total fixed = 32 × ₹1,28,000 = ₹40,96,000; variable = 1,250 × ₹500 = ₹6,25,000; total = ₹47,21,000. Cost per certified candidate = ₹4,721.
Option 2: retention drive to 18% dropout. Enrolment needed = 1,000 ÷ 0.82 = 1,219.5, so 1,220. At 32 seats, 1,220 ÷ 32 = 38.125, so 39 batches. Fixed = 39 × ₹1,10,000 = ₹42,90,000; variable = 1,220 × ₹500 = ₹6,10,000; retention drive = ₹60,000; total = ₹49,60,000. Expected certification = 1,220 × 0.82 = 1,000.4, so 1,000. Cost per certified candidate = ₹4,960.
Recommendation: rent the seats, because it delivers the target for about ₹2.39 lakh less and uses 32 batches instead of 39. The retention drive is administratively attractive but leaves only a two-candidate margin of error and costs more per certified person.
3. What non-financial factors might reverse your recommendation?
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Several factors could outweigh the ₹2.39 lakh saving:
- Learning quality at 40 seats. A batch of 40 in a lab designed for 32 reduces hands-on time per candidate and may raise dropout above the historical 20%. If dropout rises to 24%, enrolment needed becomes 1,316 and the rental option loses its cost advantage.
- Vendor reliability and data security. The neighbouring lab is an external site; if it is unavailable for even two batches, the 32-batch plan has no slack, whereas the 39-batch plan has more room to absorb disruption. Employee data and screen access also need a written confidentiality arrangement.
- Sustainability. The retention drive builds internal capability and may reduce dropout in future programmes; renting seats builds a recurring dependency.
- Verification risk. A certification target met by larger batches may be questioned if assessments are not independent. The non-financial question is whether the certificate means the same thing in a 40-seat room as in a 32-seat room.
A reasonable compromise is to rent seats for a pilot of five batches, measure dropout and assessment scores, and then decide. That converts an assumption into evidence before committing the full budget.