STPM Management Mathematics 950 key terms

The set of all points satisfying every constraint of a linear programming problem simultaneously, including non-negativity conditions. Its corner points, called vertices, are the candidates that must be tested when optimising a linear objective.

A corner point of the feasible region obtained by setting enough variables to zero so that the remaining system can be solved uniquely, with all values non-negative. The simplex method moves between such solutions until the objective can no longer improve.

The rate at which the optimal objective value changes when the right-hand side of one constraint is relaxed by a small amount, holding all else fixed. It reveals the marginal worth of a scarce resource and is read from the dual solution.

A companion linear programme in which each primal constraint becomes a variable and each primal variable becomes a constraint. Its optimal value equals the primal optimum, and its variables give the shadow prices directly.

Examination of how the optimal solution and objective value respond to changes in coefficients, resource limits, or the addition of new constraints. It answers practical questions about how robust a recommended plan is.

An iterative algebraic procedure that starts at a basic feasible solution and pivots to adjacent vertices, improving the objective each time, until an optimality test is satisfied. It handles many variables and constraints without drawing graphs.

The amount by which the objective would improve if a currently non-basic variable were forced into the solution by one unit. A zero reduced cost signals alternative optima; a favourable sign signals that improvement is still possible.

A special linear programme that allocates supplies from several origins to demands at several destinations at minimum total cost. It is solved by initial methods such as the north-west corner rule followed by stepping-stone or MODI improvement checks.

A transportation model in which each source is matched to exactly one destination, typically one worker to one job. The Hungarian method solves it by row and column reductions and covering of zeros.

The longest-duration chain of dependent activities through a project network, which fixes the shortest possible project completion time. Any delay on an activity in this chain delays the whole project unless the plan is revised.

The amount of spare time an activity can absorb without delaying the project or violating a successor's timing. Total float uses the latest allowable finish; free float is the smaller slack before the next activity's earliest start.

The soonest an activity can begin, equal to the maximum earliest finish time of all its immediate predecessors. It is found by a forward pass through the network from the start node.

The latest an activity may end without delaying the project, obtained by a backward pass from the final node. Comparing it with the earliest finish reveals the float and identifies critical activities.

A network planning method that uses three time estimates, optimistic, most likely, and pessimistic, to model uncertain activity durations. It computes an expected duration and variance for each activity and hence a probability of meeting a target date.

The probability-weighted average of the payoffs of a decision alternative, used to rank alternatives under risk. It is the standard rollback criterion when probabilities of states of nature are known and repeated decisions are assumed.

A branching diagram with square decision nodes and circular chance nodes, read from left to right and evaluated from right to left. It structures sequential decisions and the uncertain events that follow them.

The most a decision maker should pay for reliable information about which state of nature will occur. It equals the expected payoff with perfect foresight minus the best expected monetary value without it.

A pessimistic rule that selects the alternative whose worst possible payoff is as good as possible, often called the Wald criterion. It suits decision makers who wish to guarantee a floor on outcomes under uncertainty.

A rule that first builds an opportunity-loss table by subtracting each payoff from the best in its column, then chooses the alternative whose largest regret is smallest. It limits the disappointment from a wrong choice.

The order size that minimises the sum of annual ordering cost and annual holding cost, found at the point where the two are equal. Under constant demand and instantaneous replenishment it equals the square root of twice annual demand times order cost divided by holding cost per unit per year.

The stock level at which a fresh order is placed, set to cover expected demand during the lead time plus a safety margin. It triggers replenishment before stock runs out.

Extra inventory held to absorb demand variability or lead-time uncertainty, reducing the risk of a stock-out. Higher safety stock lowers shortage costs but raises holding costs.

The interval between placing an order and receiving it into usable stock. It determines how much demand the reorder level must protect against.

The cost of keeping one unit in stock for a period, covering storage, insurance, deterioration, and the opportunity cost of tied-up capital. It rises with average inventory and therefore penalises large order sizes.

In a queueing model, the ratio of arrival rate to service rate, denoted rho, measuring how busy the server is. Values approaching one cause queue length and waiting time to grow sharply.

Another name for the ratio of mean arrival rate to mean service capacity in a queueing system; it must be below one for a stable single-server queue. It expresses the fraction of time the server is occupied.

A general result stating that the average number of customers in a system equals the average arrival rate multiplied by the average time each spends there. It links queue length and waiting time without assuming a particular distribution.

A single-server model with Poisson arrivals, exponential service times, and unlimited waiting capacity. Steady-state formulas give the mean number in the system as rho divided by one minus rho.

An entry in a payoff matrix that is simultaneously the smallest in its row and the largest in its column, giving the value of a pure-strategy zero-sum game. Neither player can improve by changing strategy alone.

A randomised plan in which a player chooses among pure strategies with specified probabilities, used when no saddle point exists. Optimal mixing makes the opponent indifferent between their options.

A reduction rule that removes a strategy that is never better, and sometimes worse, than another available strategy. Repeated dominance can shrink a large payoff matrix before solving.

A forecast formed by averaging the most recent fixed number of observations and updating the window each period. It smooths random fluctuation, and a longer window gives steadier but slower-reacting forecasts.

A recursive forecast that blends the latest actual value with the previous forecast using a smoothing constant between zero and one. A high constant reacts quickly to change; a low one produces a stable, lagging series.

The average of the absolute differences between actual values and their forecasts, used to compare forecasting methods. Smaller values indicate a better fit, though the measure ignores the direction of errors.

A multiplicative or additive factor expressing how far a period's typical value sits above or below the trend. It is estimated from ratios to moving averages and used to deseasonalise data or adjust forecasts.

A weighted price index that values a fixed basket of base-period quantities at current prices relative to base-period prices. It overstates price change because it ignores substitution away from items that became dearer.

A price index that weights each item by current-period quantities rather than base-period quantities. It reflects present spending patterns but requires fresh quantity data every period.

A series formed by linking period-to-period index relatives multiplicatively, so each link compares consecutive periods. It is useful when the basket or base changes and a long fixed-base series would mislead.

The sum of a project's future cash flows discounted to today at a required rate, minus the initial outlay. A positive value means the project is expected to add value at that discount rate.

The discount rate at which a project's net present value equals zero, found by solving or interpolating. It is compared with a hurdle rate to accept or reject, though multiple sign changes can give several roots.

A series of equal payments made at regular intervals, either at the end of each period or at the start. Its present and future values are obtained from standard compound-interest factors.

A fund built by regular equal deposits so that a specified sum is available at a future date, often to repay a loan. The required deposit is found from the future value of an annuity factor.