Chapter 7

• A variable whose only possible values are 0 and 1

  Binary variable
• A binary variable that represents a yes-or-no decision by assigning a value of 1 for choosing yes and a value of 0 for choosing no

  Binary decision variable
• A type of problem or model that fits linear programming except that it uses binary decision variables

  Binary integer programming
• A BIP model where all the variables are restricted to be binary variables

  Pure BIP model
• A BIP model where only some of the variables are restricted to be binary variables

  Mixed BIP model
• A general BIP model involves ‘how much decisions’ and only make sense if their decision values are integers
• Since binary variables only provide two choices, they are ideally suited to be the decision variables when dealing with yes-or-no decisions
• Trial-and-error or parameter report can be performed for what-if-analysis for integer programming problems
• Requires that the decision variables can take on any nonnegative values (not just integer values) within its feasible range

  Continuous variables assumption
• A group of alternatives where choosing any one alternative excludes choosing any of the others

  Mutually Exclusive Alternatives
• A yes-or-no decision is a contingent decision if it can be yes only if a certain other yes-or-no decision is yes
• A constraint that requires the sum of certain binary variables to be greater than or equal to 1

  Set covering constraint
• A type of BIP model where the objective is to minimize some quantity such as total cost and all the functional constraints are set covering constraints

  Set covering problem
• What does BIP mean?

  Binary Interger Programming
• In a BIP problem with 3 mutually exclusive alternatives, x1, x2, and x3, what constraint should be added to the formulation?

  x1 + x2 + x3 ≤ 1