Model Parameter¶

Definition¶

A model parameter is a given numerical input to the optimization model. In the course's LP notation, parameters include objective coefficients $c_j$ , constraint coefficients $a_{ij}$ , and right-hand sides $b_i$ .

Interpretation¶

Parameters describe the circumstances under which decisions are made. A parameter may be an estimate even though the optimization treats its supplied value as fixed.

A linear program written out with its parts labelled: the objective, the functional constraints and the domain restrictions; decision variables are coloured blue and parameters red.

The objective function $f(\boldsymbol{x})$ is the quantity to maximize (for example, profit) or minimize (for example, cost). Functional constraints describe what an allowed decision must satisfy, such as resource limits or demand requirements. Domain restrictions specify signs or integrality.

In the diagram, blue identifies decision variables, whose values the model determines; red identifies model parameters, the given data $c_j$ , $a_{ij}$ and $b_i$ . In general, the model is $\max/\min\ f(\boldsymbol{x})$ subject to $\boldsymbol{x}\in F$ $F$ , where the constraints define the feasible set $F$ . A solution assigns values to all variables.

Key Results¶

Changing parameters can change both the optimal decision and the optimal value.
Units must agree within an equation or inequality.
Sensitivity analysis investigates the effect of parameter changes.

Examples¶

The coefficient $3$ in $3x_s+2x_t$ is profit per soldier.
The right-hand side $100$ in $2x_s+x_t\le100$ is available finishing time.

Prerequisites¶

Sources¶

OR Modelling · Week 1

Aliases: input parameter Symbols: element of

Last updated: 17 October 2026 21:53