Indian Statistical Service Examination (with Indian Economic Service) · India · Union Public Service Commission
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 Indian Statistical Service Examination spread across the units of Optimization Techniques for Statisticians. Difficulty: 13 easy, 36 medium, 8 hard.
| Simplex method, Big-M and two-phase methods | 10 | |
| Transportation and assignment problems | 9 | |
| Duality and sensitivity analysis | 8 | |
| Integer programming: branch and bound | 8 | |
| Linear programming: formulation and graphical solution | 7 | |
| Dynamic programming | 6 | |
| Non-linear programming: Lagrange multipliers and Kuhn-Tucker conditions | 4 | |
| Goal programming for multi-objective farm planning | 3 | |
| Quadratic programming and risk programming (MOTAD) | 2 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Which assumption of LP is violated when fractional animals cannot be kept?
D. Divisibility
Divisibility allows fractional activity levels; integer requirements need integer programming.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
Which variable converts a ≤ constraint into an equation in the simplex method?
C. A slack variable
Slack = unused resource, added to ≤ constraints; surplus is subtracted from ≥ constraints.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
Why do modern solvers also use interior-point methods for very large LPs?
D. Polynomial worst-case complexity
Simplex is fast in practice but has exponential worst cases; interior-point methods have polynomial complexity and suit very large sparse problems.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
A balanced transportation problem has 3 sources and 4 destinations. How many basic (allocated) cells does a non-degenerate basic solution have?
B. 6
m + n − 1 = 3 + 4 − 1 = 6.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
Which algorithm solves the assignment problem efficiently?
C. The Hungarian method
The Hungarian method exploits the assignment structure; NW corner and Vogel give initial transportation solutions.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
In the Hungarian method, when has an optimal assignment been reached?
D. When n lines cover the zeros
n covering lines guarantee n independent zeros for a complete assignment.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
When is a branch-and-bound node fathomed?
A. Infeasible, integral, or no better bound
Each of the three conditions shows that no better integer solution can lie in that branch.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
A binary-variable model requires that at most 2 of 5 irrigation projects be chosen. How is this written?
D. δ₁ + δ₂ + δ₃ + δ₄ + δ₅ ≤ 2
With δⱼ ∈ {0, 1}, the sum counts chosen projects.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
What does the Lagrange multiplier of a constraint measure?
B. The constraint's marginal value
λ = ∂f*/∂b, the shadow price of the constraint.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
Which methods solve a Markov decision process?
C. Value and policy iteration
Both iterate the Bellman equation for expected values.
Further reading: Taha, Operations Research: An Introduction; Hazell and Norton, Mathematical Programming for Economic Analysis in Agriculture; Nocedal and Wright, Numerical Optimization
Ten here, 57 in the app. The Laisha app has every practice question we have written to Indian Statistical Service Examination in this subject, marked as you go, with timed papers, a jump-to-unanswered list and a certificate when you pass at 70 per cent.
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