4: Linear Programming (Modeling Examples)

Standard Form

requires all variables to be to the left of the inequality and numeric values to the right.

Standard Form

requires that fractional relationships between variables be eliminated.

double-subscripted variable

is simply another form of variable name. Example: Xij

Balanced Transportation Model

supply equals demand such that all constraints are equalities

Unbalanced Transportation Model

supply does not equal demand, and one set of constraints is ≤

Profit

maximized in the objective function by subtracting cost from revenue.

Shadow Price

is the marginal economic value of one additional unit of a resource.

Systematic Approach to Model Formulation

is first to define decision variables, then construct the objective function, and finally develop each constraint separately; don’t try to “see” it all at once.