Lecture Notes – Chapter 3
Linear Programming –Steps
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Identify the decision variable
Quantify the objective and constraints
Construct a model
Solve the model
A crucial step in building a mathematical model is determining those factors in the
decision-making process over which the decision maker has control. These are known as
the controllable inputs or decision variables. For example in a manufacturing process,
the quantity of goods produced or the amount of overtime assigned during the week. The
number of machines in the plant, the amount of resources needed to make one unit of the
product and the overall plant capacity are factors outside the control of the decision
maker, and are called uncontrollable inputs. These are also called constraints to the
problem.
In many cases, determining the appropriate decision variable is the hardest part of
building the mathematical model. Naturally, the rest of the modeling process flows quite
smoothly once the decision variable has been properly defined.
Linear programming models possess a number of properties. These are;
 Proportionality – the level of each activity is multiplied by a constant factor
corresponding to the coefficient.
 Additivity – the sum of the contributions from the various activities to a particular
constraint equals the total contribution to the constraint.
 Divisibility – implies that both integer and non-integer values are allowed in the
solution.
 Linearity – All decision variables are raised to the first power. The linearity
assumption subsumes all the three properties listed above.
Solving LP Models
 Graphical solution
 Spreadsheet modeling
Special Cases of LP
 Alternate Optimal Solution – More than one solution (not a unique solution)
 Infeasibility – No feasible region exists
 Unbounded solution – An infinite feasible region