STPM Management Mathematics 950 flashcards
STPM Management Mathematics 950 · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Reduced cost
- For a non-basic variable, c̄ⱼ = cⱼ − c_BᵀB⁻¹Aⱼ. In a maximisation, a positive reduced cost means bringing that variable into the basis improves the objective.
- Shadow price
- The optimal dual value of a resource constraint: the increase in the objective per one-unit increase in that resource's availability, valid while the current basis remains optimal.
- Unbounded solution test
- In the simplex ratio test, if every entry in the entering variable's column is zero or negative, no leaving variable exists and the objective can increase without limit.
- Total float
- Latest start minus earliest start, equivalently latest finish minus earliest finish. It is the delay an activity can absorb without delaying the whole project.
- Free float
- Earliest start of the successor minus earliest finish of the activity. It is the delay possible without affecting any successor's earliest start date.
- PERT expected time
- tₑ = (a + 4m + b)/6, a weighted average of optimistic, most likely and pessimistic estimates, with variance ((b − a)/6)² used to find project completion probabilities.
- Cost slope
- (Crash cost − normal cost) divided by (normal time − crash time). It measures the extra cost per unit of time saved when shortening an activity.
- Dummy activity
- A zero-duration arrow drawn to express a precedence relationship that cannot be shown by the real activities alone; it consumes no time or resources.
- Expected value of perfect information
- The expected payoff with perfect foresight minus the best expected monetary value without it. It caps the amount worth spending on additional information.
- Minimax regret
- A decision rule under uncertainty: build an opportunity-loss table, find each alternative's maximum regret, and choose the alternative whose maximum regret is smallest.
- Indifference probability
- The probability of one state of nature at which two alternatives have equal expected monetary value, marking the switch point in sensitivity analysis.
- Economic order quantity
- EOQ = √(2DS/H), the order size minimising the sum of annual ordering cost and annual holding cost, where D is demand, S ordering cost and H holding cost.
- Reorder level
- The inventory position at which a new order is placed: demand per period multiplied by lead time, plus any safety stock held against uncertainty.
- Safety stock
- Extra inventory held to cover demand or lead-time variability; it raises holding cost but reduces the probability of a stockout during the replenishment cycle.
- Production run model EPQ
- EPQ = √(2DS/(H(1 − d/p))), used when inventory builds up gradually at rate p while being consumed at rate d, rather than arriving all at once.
- Little's law
- L = λW and Lq = λWq: average number in the system equals arrival rate times average time in the system, for any stable queueing system.
- M/M/1 queue length
- With utilisation ρ = λ/μ < 1, average number in the system is L = ρ/(1 − ρ) and average number waiting is Lq = ρ²/(1 − ρ).
- M/M/c stability condition
- A multi-server queue is stable only if λ < cμ, so utilisation ρ = λ/(cμ) is below one; otherwise the waiting line grows without bound.
- Kendall notation
- A/B/c/K/N/D notation recording arrival distribution, service distribution, number of servers, system capacity, calling population and queue discipline.
- Saddle point
- An entry that is simultaneously the minimum of its row and the maximum of its column. Its existence means both players have an optimal pure strategy.
- Value of a game
- The expected payoff to the row player when both players use their optimal strategies. A zero value means the game is fair.
- Dominance in games
- Removing a strategy that can never do better than another: for the maximising player, delete a row whose entries are all less than or equal to another row's.
- Exponential smoothing
- F_{t+1} = αYₜ + (1 − α)Fₜ, a weighted average where the smoothing constant α between 0 and 1 controls responsiveness to recent observations.
- Seasonal index
- A factor expressing the typical percentage deviation of a season from the trend; for quarterly multiplicative data the four indices average 100 and sum to 400.
- Tracking signal
- The running sum of forecast errors divided by mean absolute deviation. Large absolute values indicate persistent bias and call for model revision.
- Laspeyres index
- A weighted aggregate index using base-period quantities: (Σpₙq₀ / Σp₀q₀) × 100. Because weights are fixed, it tends to overstate price increases.
- Paasche index
- A weighted aggregate index using current-period quantities: (Σpₙqₙ / Σp₀qₙ) × 100. It tends to understate price rises relative to Laspeyres.
- Fisher's ideal index
- The geometric mean of the Laspeyres and Paasche indices. It satisfies both the time-reversal and factor-reversal tests, making it theoretically preferred.
- Deflating a value
- Converting a nominal money amount to real terms by dividing by a price index and multiplying by 100, so values from different years become comparable.
- Effective annual rate
- (1 + r/m)^m − 1, the true yearly growth factor when nominal rate r is compounded m times per year; it allows fair comparison of compounding conventions.
- Net present value
- The sum of discounted future cash flows minus the initial outlay. A positive NPV means the project returns more than the required rate.
- Sinking fund payment
- R = FV · i/[(1 + i)ⁿ − 1], the equal periodic deposit that accumulates to a specified future sum when interest is compounded each period.