Planning with limiting factors (Chapter 6) – VOCABULARY flashcards

Key vocabulary for planning with limiting factors, including concepts like shadow prices, slack, iso-contribution lines, and linear programming insights.

Limiting factor

A resource or factor whose limited availability constrains the production plan and determines what can be produced.

Scarce resource

A resource that is in short supply and can become a limiting factor in planning.

One limiting factor

A situation with a single resource constraint; allocate by ranking products by contribution per unit of the scarce resource.

Multiple limiting factors

Two or more scarce resources that limit production; require linear programming to optimize.

Linear programming

A mathematical method for optimizing a linear objective function subject to linear constraints.

Feasible region

The set of all variable combinations that satisfy all constraints; feasible solutions lie within or on its boundary.

Corner solution

An optimal solution located at a vertex (corner) of the feasible region.

Shadow price (dual price)

The increase in the objective value from one additional unit of a limiting factor at its current cost; zero for non‑critical constraints.

Slack

The amount by which a resource is under-utilised at the optimum; occurs when the optimum point is not on the constraint line.

Critical constraint

A constraint with zero slack at the optimum; increasing it can improve the solution.

Non-critical constraint

A constraint with slack at the optimum; changing it has little or no effect on the optimum.

Iso-contribution line

A line showing all (x, y) pairs that yield the same total contribution; used to locate the optimal solution within the feasible region.

Intercepts

Points where constraint lines cross the axes; used to plot lines on a graph.

Decision variables

Variables representing quantities to produce (e.g., x and y) that are chosen to optimize the objective.

Non-negativity constraint

Constraint that decision variables must be ≥ 0 (no negative production).

Objective function

The function to maximize or minimize (e.g., maximise total contribution).

Contribution per unit

Selling price minus total variable costs per unit; the unit’s contribution to profit.

Hours per unit

The amount of a scarce resource (in hours) required to produce one unit of a product.

Contribution per hour

Contribution per unit divided by hours per unit; measures profit per unit of scarce resource used.

Feasible region boundary orientation

For constraints of the form ≤, feasible solutions lie on/under the constraint line (left/below in a graph).