QAT1 Chapter 11 Integer Linear Programming

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0-1 integer linear program

An all-integer or mixed-integer linear program in which the integer variables are only permitted to assume the values 0 or 1. Also called binary integer program.

k out of n alternatives constraint

An extension of the multiple-choice constraint. This constraint requires that the sum of n 0-1 variables equals k.

all-integer linear program

An integer linear program in which all variables are required to be integer.

capital budgeting problem

A 0-1 integer programming problem that involves choosing which possible projects or activities provide the best investment return.

conditional constraint

A constraint involving 0-1 variables that does not allow certain variables to equal 1 unless certain other variables are equal to 1.

corequisite constraint

A constraint requiring that two 0-1 variables be equal. Thus, they are both either in or out of solution together.

distribution system design problem

A mixed-integer linear program in which the binary integer variables usually represent sites selected for warehouses or plants and continuous variables represent the amount shipped over arcs in the distribution network.

fixed cost problem

A 0-1 mixed-integer programming problem in which the binary variables represent whether an activity, such as a production run, is undertaken (variable = 1) or not (variable = 0).

integer linear program

A linear program with the additional requirement that one or more of the variables must be integer.

location problem

A 0-1 integer programming problem in which the objective is to select the best locations to meet a stated objective. Variations of this problem (see the bank location problem in Section 11.3) are known as covering problems.

LP Relaxation

The linear program that results from dropping the integer requirements for the variables in an integer linear program.

mixed-integer linear program

An integer linear program in which some, but not necessarily all, variables are required to be integer.

multiple-choice constraint

A constraint requiring that the sum of two or more 0-1 variables equals 1. Thus, any feasible solution makes a choice of which variable to set equal to 1.

mutually exclusive constraint

A constraint requiring that the sum of two or more 0-1 variables be less than or equal to 1. Thus, if one of the variables equals 1, the others must equal 0. However, all variables could equal 0.

product design and market share optimization problem

Sometimes called the share of choice problem, it involves choosing a product design that maximizes the number of consumers preferring it.

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