Selecting Skill Development Partners under Budget and Equity Constraints
The Haryana Skill Development Mission has ₹4.0 crore for 1,200 short-term training slots in one district. Four partners submit bids: A-₹32,000 per slot, 78% placement, 18% SC trainees, 60% retention at six months; B-₹40,000, 85% placement, 26% SC, 70% retention; C-₹28,000, 65% placement, 30% SC, 55% retention; D-₹36,000, 80% placement, 22% SC, 75% retention. The mission must ensure at least 25% SC trainees overall and at least 40% women, but the bids do not report gender. A preliminary note proposes selecting A and B because they have the highest placement rates. The finance officer warns that the budget cannot exceed ₹4.0 crore and that placement claims are self-reported. The mission director asks for a reasoned selection of two partners, a feasible slot allocation, and a data improvement plan.
1. Test the preliminary note's proposal to select A and B. Show the arithmetic and identify the binding constraint.
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The A+B proposal fails on cost. The average cost per slot is (₹32,000 + ₹40,000) ÷ 2 = ₹36,000. For 1,200 slots, the cost is 1,200 × ₹36,000 = ₹4.32 crore, which exceeds the ₹4.0 crore ceiling by ₹32 lakh. Even a 50:50 split is infeasible; any mix of A and B costs at least ₹32,000 and at most ₹40,000, and the minimum A+B average is above ₹33,333.
The binding constraint is therefore budget, not placement. The note optimised only one criterion and ignored feasibility. I would also check other pairs: B+C averages ₹34,000, so 1,200 slots cost ₹4.08 crore, still infeasible. A+D averages ₹34,000 and is infeasible. B+D is ₹38,000 and infeasible. The feasible pairs are A+C (average ₹30,000, ₹3.60 crore) and C+D (average ₹32,000, ₹3.84 crore).
This is the key judgement: a high-placement partner can be unaffordable at the required scale. The mission must choose among feasible pairs, not rank bids in isolation.
2. Select two partners and allocate 1,200 slots. Check the SC quota and calculate the expected placement rate.
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I would select C and D, with 600 slots each, subject to conditions.
Cost: 600 × ₹28,000 = ₹1.68 crore; 600 × ₹36,000 = ₹2.16 crore; total ₹3.84 crore, within ₹4.0 crore.
SC share: C gives 30% of 600 = 180; D gives 22% of 600 = 132; total 312 of 1,200 = 26%, above the 25% floor but with only a 1 percentage-point margin.
Placement: C gives 65% of 600 = 390; D gives 80% of 600 = 480; total 870 of 1,200 = 72.5%.
Retention: weighted average is 65% (C 55%, D 75%), better than A+C's 57.5%.
Why not A+C? A+C is cheaper at ₹3.56 crore and can meet the SC quota if A is capped at 500 slots, but its placement is only 70.4% and retention 57.5%. C+D gives better employment outcomes for ₹28 lakh more, still within budget.
The risk is that D's SC share is below 25%, so the overall quota depends on C. I would fix the 600:600 split in the contract and require monthly SC enrolment reporting; if D falls short, slots shift to C.
3. What data gaps would you close before releasing the second tranche, and how would you avoid punishing honest reporting?
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Gender: the bids do not report women's share, so the 40% requirement cannot be verified. Require sex-disaggregated enrolment and completion data before tranche two.
Placement verification: self-reported placement is weak. Require employer confirmation, PF/ESI records where available, and a random audit of at least 10% of placed trainees. Do not rely on a placement certificate alone.
Retention: the six-month retention figures need a defined denominator and proof of employment. Ask for month-wise follow-up, not a single percentage.
Cost and quality: verify trainer qualifications, lab access, and dropout rates. A low-cost partner may be cheap because it screens out weaker trainees.
To avoid punishing honest reporting, I would separate data correction from penalty. First tranche is released on enrolment; second tranche on verified data, with a 30-day cure period. Partners that self-report a shortfall and submit a remedial plan should not be treated the same as partners that conceal it. Publish the audit method in advance so everyone knows the rules.