ASRB Agricultural Research Service (ARS) - Agricultural Statistics scientist · India · Agricultural Scientists Recruitment Board (ICAR)
Original practice questions written to the published syllabus · not past papersThe optimisation theory statisticians use: linear programming with simplex and duality, transportation and assignment, integer and goal programming for farm and crop planning, non-linear optimisation with Kuhn-Tucker conditions, and the numerical optimisers inside likelihood estimation. The Agribusiness track teaches operations research for managers; this goes to the theory.
In the exams: AICE-JRF Ag Stat Unit 2 'linear programming: formulation, graphical, simplex, duality, transportation and assignment' (heavy); UPSC ISS Statistics III operations research (heavy, reported); ASRB NET Ag Stat (present)
How our questions for ASRB Agricultural Research Service spread across the units of Optimization Techniques for Statisticians. Difficulty: 0 easy, 23 medium, 9 hard.
| Quadratic programming and risk programming (MOTAD) | 9 | |
| Goal programming for multi-objective farm planning | 8 | |
| Linear programming: formulation and graphical solution | 3 | |
| Duality and sensitivity analysis | 3 | |
| Dynamic programming | 3 | |
| Integer programming: branch and bound | 2 | |
| Numerical optimisation: gradient, Newton and quasi-Newton methods | 2 | |
| Transportation and assignment problems | 1 | |
| Non-linear programming: Lagrange multipliers and Kuhn-Tucker conditions | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Land has a shadow price of 20 thousand currency units per hectare. Renting more land costs 15 per hectare. What should the farmer do?
C. Rent more, within the RHS range
Each extra hectare adds 20 at a cost of 15, but only within the range over which the shadow price stays valid.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
Mustard's return stays at 30. Over what range of wheat return does the plan (4, 8) remain optimal?
A. 30 to 60
The plan stays optimal while c_wheat/c_mustard lies between the slopes 1 (land) and 2 (labour), i.e. 30 to 60.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
An assignment problem maximises yields of varieties at sites. How is it converted for the Hungarian method?
B. Subtract entries from the maximum
Regret = maximum − entry turns maximisation into minimisation; negating also works but the standard device is subtraction from the maximum.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
In a goal constraint f(x) + d⁻ − d⁺ = g, what does d⁻ measure?
B. Shortfall below target
d⁻ ≥ 0 is the shortfall below the target; d⁺ the excess above it.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
With 12 ha and a 20-day labour limit, wheat (40/ha, 2 days) and mustard (30/ha, 1 day), can an income goal of 450 be met?
A. No; the maximum is 440
Maximising 40x + 30y with x + y ≤ 12 and 2x + y ≤ 20 gives (8, 4) and 440 < 450, so the goals conflict and weights decide the compromise.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
A variance component must stay positive during optimisation. What is a standard device?
C. Optimise over its logarithm
Transforming constrained parameters (log σ², logit p) lets unconstrained optimisers work.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
A mixed model reports non-convergence. Which cause is most common?
B. Over-parameterisation
Unidentifiable or boundary parameters make the objective flat or constrained; simplifying or reparameterising usually helps.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
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