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

24 sample cards from the Core Operational Research Techniques deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. What is a decision tree and how is it evaluated?

   A diagram with decision nodes (squares, choices), chance nodes (circles, probabilistic outcomes), and end payoffs. It is evaluated by 'rolling back' (backward induction): take expected values at chance nodes and the best choice at decision nodes.

2. Define the Expected Value of Perfect Information (EVPI).

   $\text{EVPI} = (\text{expected payoff with perfect information}) - (\text{expected payoff of the best action without information})$. It is the maximum a rational decision-maker should pay for information that fully removes uncertainty.

3. State the maximin, maximax, and minimax-regret decision criteria under uncertainty.

   Maximin: choose the action with the best worst-case payoff (pessimistic). Maximax: choose the action with the best best-case payoff (optimistic). Minimax regret: minimise the maximum opportunity loss (regret) across states.

4. Distinguish 'decisions under risk' from 'decisions under uncertainty'.

   Under risk, probabilities of outcomes are known, so you can use expected value / expected utility. Under uncertainty, probabilities are unknown, so criteria like maximin, maximax, Hurwicz, or minimax regret are applied instead.

5. What is Multi-Criteria Decision Analysis (MCDA) and the basic weighted-sum model?

   A framework for evaluating options against multiple, often conflicting, criteria. The weighted-sum (linear additive) model scores each option as $S_j = \sum_i w_i \, s_{ij}$, where $w_i$ are criterion weights ($\sum_i w_i = 1$) and $s_{ij}$ are normalised scores.

6. What is the Analytic Hierarchy Process (AHP) in MCDA?

   An MCDA method that structures a decision into a hierarchy (goal, criteria, alternatives) and derives weights from pairwise comparisons using a 1–9 scale. It computes priorities from the principal eigenvector and checks a consistency ratio.

7. What is cost-benefit analysis (CBA) and the role of Net Present Value?

   CBA appraises options by valuing all costs and benefits in monetary terms over time. The decision rule uses Net Present Value: $NPV = \sum_{t=0}^{T} \frac{B_t - C_t}{(1+r)^{t}}$; accept projects with $NPV > 0$ (or the highest NPV).

8. What is the HM Treasury Green Book and its recommended discount rate?

   The UK government's guidance on appraisal and evaluation of policies, programmes and projects. It recommends a standard Social Time Preference Rate (discount rate) of 3.5% for most appraisals (declining for very long horizons), and use of social (not just financial) value.

9. In the Green Book, what is optimism bias and how is it handled?

   Optimism bias is the demonstrated tendency for appraisers to be over-optimistic about costs, benefits and timescales. The Green Book requires explicit, empirically based uplift adjustments to costs to counteract it.

10. What are the building blocks of system dynamics modelling?

    Stocks (accumulations/levels), flows (rates that change stocks), feedback loops (reinforcing R and balancing B), and time delays. It models how nonlinear feedback and accumulation drive system behaviour over time.

11. Distinguish reinforcing and balancing feedback loops in system dynamics.

    Reinforcing (positive) loops amplify change, producing exponential growth or decline (e.g. compound interest). Balancing (negative) loops counteract change, seeking equilibrium or a goal (e.g. a thermostat). Their interaction generates complex dynamics.

12. What is the Critical Path Method (CPM) and the critical path?

    A project-scheduling technique that finds the longest sequence of dependent activities (the critical path), which determines the minimum project duration. Activities on it have zero float/slack; delaying any of them delays the whole project.

13. How is total float (slack) of an activity calculated in CPM?

    Total float $= LS - ES = LF - EF$, where ES/EF are earliest start/finish and LS/LF are latest start/finish. It is the amount an activity can be delayed without delaying project completion; critical activities have zero float.

14. How does PERT estimate an activity's expected time and variance?

    Using three estimates — optimistic $a$, most likely $m$, pessimistic $b$: expected time $t_e = \frac{a + 4m + b}{6}$ and variance $\sigma^{2} = \left(\frac{b - a}{6}\right)^{2}$. PERT treats durations probabilistically (Beta distribution).

15. State the Economic Order Quantity (EOQ) formula and what it minimises.

    $EOQ = \sqrt{\dfrac{2DS}{H}}$, where $D$ = annual demand, $S$ = ordering cost per order, $H$ = holding cost per unit per year. It minimises the total of ordering plus holding costs, where these two costs are equal at the optimum.

16. What is the reorder point in inventory control (with safety stock)?

    Reorder point $= d \cdot L + SS$, where $d$ is average demand per unit time, $L$ is lead time, and $SS$ is safety stock held to buffer against demand/lead-time variability. An order is placed when inventory falls to this level.

17. What is the bullwhip effect in supply chains?

    The amplification of demand variability as orders move upstream from retailer to manufacturer: small fluctuations in consumer demand cause progressively larger swings in orders and inventory upstream, driven by batching, forecasting lags, and price fluctuations.

18. What is a Nash equilibrium in game theory?

    A set of strategies (one per player) where no player can improve their payoff by unilaterally changing their own strategy, given the others' strategies. Each player's choice is a best response to the others'.

19. Explain the Prisoner's Dilemma and its key lesson.

    Two players each choose cooperate or defect; mutual cooperation beats mutual defection, but defecting dominates individually. Both rationally defect, reaching a Pareto-inferior Nash equilibrium — illustrating how individual rationality can produce a collectively worse outcome.

20. Distinguish a dominant strategy from a dominated strategy.

    A dominant strategy yields a player a payoff at least as high as any other strategy regardless of opponents' choices. A dominated strategy is always worse than some alternative and can be eliminated. Rational players play dominant strategies and avoid dominated ones.

21. What is the difference between a pure strategy and a mixed strategy?

    A pure strategy deterministically selects one action. A mixed strategy assigns probabilities over actions, randomising the choice. Nash's theorem guarantees that every finite game has at least one equilibrium in (possibly mixed) strategies.

22. What is sensitivity analysis in an LP/optimisation context?

    Examining how the optimal solution and objective value change as model inputs (objective coefficients, RHS values, constraints) vary. It identifies ranges over which the current basis/solution stays optimal and quantifies robustness to data uncertainty.

23. What is the difference between expected value and expected utility decision-making?

    Expected value weights monetary outcomes by probability and assumes risk-neutrality. Expected utility applies a utility function $u(x)$ first (often concave for risk-aversion), so $E[u(X)]$ can rank a sure smaller payoff above a risky larger-EV gamble.

24. What is autocorrelation and why does it matter in time series and regression?

    Autocorrelation is the correlation of a series with its own lagged values. In time series it reveals structure (used in ARIMA identification via ACF/PACF); in regression it violates the independence-of-errors assumption, biasing standard errors (tested via Durbin–Watson).

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