# 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.

Example: