Government Operational Research Service (GORS) Assessment Core Operational Research Techniques Syllabus

Core Operational Research Techniques syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Core Operational Research Techniques in Government Operational Research Service (GORS) Assessment, not a summary of it.

1. 1

   Optimisation and mathematical programming

   4 topics

   • Linear programming
     • Formulating objective functions and constraints
     • Graphical and simplex solution intuition
     • Sensitivity analysis and shadow prices
   • Integer and mixed-integer programming
   • Network optimisation
     • Shortest path and minimum spanning tree
     • Transportation and assignment problems
     • Maximum flow
   • Heuristics and metaheuristics for hard problems
2. 2

   Probability, statistics and forecasting

   4 topics

   • Probability distributions and key concepts
     • Discrete and continuous distributions
     • Expectation, variance and the central limit theorem
   • Statistical inference and hypothesis testing
     • Confidence intervals and p-values
     • Common pitfalls and misinterpretation
   • Regression and correlation
   • Time series analysis and forecasting methods
3. 3

   Stochastic modelling and simulation

   4 topics

   • Queueing theory
     • M/M/1 and M/M/c models
     • Little's Law and utilisation
   • Markov chains and transition models
   • Monte Carlo simulation
   • Discrete event simulation
     • Modelling capacity, flow and bottlenecks
     • Verification and validation
4. 4

   Decision analysis and multi-criteria methods

   4 topics

   • Decision trees and expected value of information
   • Decisions under uncertainty and risk
     • Maximin, maximax and minimax regret criteria
   • Multi-Criteria Decision Analysis (MCDA)
     • Weighting and scoring approaches
     • Analytic Hierarchy Process
   • Cost-benefit analysis and the HM Treasury Green Book
5. 5

   Systems, scheduling and other OR tools

   4 topics

   • System dynamics modelling
   • Project scheduling: critical path method and PERT
   • Inventory and supply chain models
   • Game theory and strategic interaction basics

Core Operational Research Techniques flashcards for Government Operational Research Service (GORS) Assessment

23 of 70 cards from the Core Operational Research Techniques deck — real questions with worked answers.

1. What is the standard form of a linear programming (LP) problem?

   Maximize (or minimize) a linear objective $z = \vec{c}^{\,T}\vec{x}$ subject to linear constraints $A\vec{x} \leq \vec{b}$ and non-negativity $\vec{x} \geq \vec{0}$. The objective and all constraints must be linear functions of the decision variables.

2. In linear programming, where does the optimal solution always occur (if one exists)?

   At a vertex (extreme point) of the convex feasible region. Because the feasible region is a convex polytope and the objective is linear, an optimum lies at a corner point — the basis of the Simplex method.

3. What does the Simplex method do, and what is its complexity behaviour?

   It moves along edges of the feasible polytope from vertex to vertex, improving the objective until no adjacent vertex is better. It is exponential in the worst case but very efficient in practice (typically polynomial-like).

4. State the relationship between a primal LP and its dual (weak and strong duality).

   Weak duality: any feasible dual objective bounds the primal objective ($\vec{c}^{\,T}\vec{x} \leq \vec{b}^{\,T}\vec{y}$ for a min dual). Strong duality: if the primal has a finite optimum, so does the dual, and their optimal values are equal.

5. What is the economic interpretation of a dual variable (shadow price) in LP?

   The shadow price is the rate of change of the optimal objective per unit increase in a constraint's right-hand side — the marginal value of relaxing that resource constraint by one unit, valid within the allowable RHS range.

6. How does Integer Programming (IP) differ from LP, and why is it harder?

   IP requires some or all decision variables to take integer values, removing the convexity that LP relies on. IP is NP-hard; you cannot simply round the LP relaxation, since rounding may be infeasible or sub-optimal.

7. What is a Mixed-Integer Programming (MIP) problem?

   An optimisation problem in which some decision variables are constrained to be integers while others may take continuous values. It generalises both LP (all continuous) and pure IP (all integer).

8. Describe the branch-and-bound method for integer programming.

   Solve the LP relaxation to get a bound; if a variable is fractional, branch by adding constraints (e.g. $x \leq \lfloor v \rfloor$ and $x \geq \lceil v \rceil$), creating sub-problems. Prune branches whose bound is worse than the best known integer solution, until the optimal integer solution is proven.

9. What role do binary (0–1) variables play in MIP modelling?

   They model yes/no decisions — e.g. whether to open a facility, select a project, or enforce logical conditions. They enable fixed costs, either/or constraints, and indicator/big-M formulations.

10. What is the shortest-path problem in network optimisation, and a standard algorithm?

    Find the minimum-total-weight path between two nodes in a weighted graph. Dijkstra's algorithm solves it for non-negative edge weights in $O(E + V\log V)$ with a priority queue; Bellman–Ford handles negative weights.

11. What is a minimum spanning tree (MST) and name two algorithms for it.

    A subset of edges connecting all nodes of a connected graph with minimum total weight and no cycles. Kruskal's algorithm (add cheapest edges avoiding cycles) and Prim's algorithm (grow a tree from a start node) both find it.

12. State the max-flow min-cut theorem.

    In a flow network, the maximum value of flow from source to sink equals the minimum capacity over all cuts separating source from sink: $\max \text{flow} = \min \text{cut}$. The Ford–Fulkerson method exploits this.

13. What characterises the transportation and assignment problems?

    Transportation: minimise cost of shipping from supply nodes to demand nodes subject to supply/demand limits. Assignment: a special case matching $n$ agents to $n$ tasks one-to-one; the Hungarian algorithm solves it in polynomial time.

14. What are heuristics, and why are they used for hard problems?

    Heuristics are rule-of-thumb methods that find good (not necessarily optimal) solutions quickly for problems that are intractable to solve exactly (e.g. NP-hard). They trade guaranteed optimality for computational feasibility.

15. Define a metaheuristic and give three examples.

    A metaheuristic is a high-level, problem-independent strategy that guides subordinate heuristics to escape local optima and explore the solution space. Examples: simulated annealing, genetic algorithms, tabu search (also ant colony, particle swarm).

16. How does simulated annealing avoid getting stuck in local optima?

    It accepts worse solutions with probability $p = e^{-\Delta E / T}$, where $\Delta E$ is the objective worsening and $T$ is a 'temperature' that decreases over time. Early high $T$ allows exploration; cooling gradually focuses on exploitation.

17. What are the core operators of a genetic algorithm?

    Selection (favour fitter individuals), crossover (combine two parents' genes), and mutation (random small changes). A population of candidate solutions evolves over generations toward higher fitness.

18. State the difference between local search and tabu search.

    Local search moves to the best neighbouring solution and stops at a local optimum. Tabu search continues past local optima by allowing non-improving moves while keeping a short-term 'tabu list' of recently visited solutions to prevent cycling back.

19. For a continuous random variable, how are the PDF and CDF related?

    The CDF is the integral of the PDF: $F(x) = \int_{-\infty}^{x} f(t)\,dt$, and conversely $f(x) = \frac{d}{dx}F(x)$. Also $P(a \leq X \leq b) = \int_{a}^{b} f(x)\,dx$.

20. Give the mean and variance of a Binomial$(n,p)$ distribution.

    Mean $\mu = np$ and variance $\sigma^{2} = np(1-p)$. It counts the number of successes in $n$ independent Bernoulli trials each with success probability $p$.

21. State the PMF, mean and variance of a Poisson distribution.

    $P(X = k) = \frac{\lambda^{k} e^{-\lambda}}{k!}$ for $k = 0,1,2,\dots$, with mean $= \lambda$ and variance $= \lambda$. It models the number of rare independent events in a fixed interval.

22. What is the memoryless property and which distributions have it?

    $P(X > s + t \mid X > s) = P(X > t)$ — the future is independent of elapsed time. The exponential distribution (continuous) and geometric distribution (discrete) are the only ones with this property.

23. State the Central Limit Theorem (CLT).

    For i.i.d. random variables with mean $\mu$ and finite variance $\sigma^{2}$, the sample mean's distribution approaches Normal as $n \to \infty$: $\bar{X} \approx N\!\left(\mu, \frac{\sigma^{2}}{n}\right)$, regardless of the original distribution's shape.

See more Core Operational Research Techniques flashcards →

Planning Core Operational Research Techniques for Government Operational Research Service (GORS) Assessment

Core Operational Research Techniques (Government Operational Research Service (GORS) Assessment) FAQ