01.sol

# 01.sol - Industrial Engineering Fall Integer Programming So...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Industrial Engineering Fall Integer Programming So utions to Homework Prob em . De ne y i = if box i is used, otherwise for all i = , . . . , m ; x ji = if item j is put into box i , otherwise for all i = , . . . , m and j = , . . . , n . Consider the integer program maximize subject to m i = b i y i ≤ Q , n j = a j x ji ≤ b i y i for all i = , . . . , m , m i = x ji = for all j = , . . . , n , x ji ∈ { , } for all i = , . . . , m and j = , . . . , n , y i ∈ { , } for all i = , . . . , m . e above integer program is feasible if and only if the move is possible. Prob em . For j = , . . . , n , let a j , . . . , a j k ( j ) denote the support points of the functions { f i j ∶ i = , . . . , m } ; i.e., the functions { f i j ∶ i = , . . . , m } are linear on the intervals {[ a j ℓ , a j ℓ + ] ∶ ℓ = , . . . , k ( j ) - } . It follows that k ( j ) ≤ ( m + )( μ- ) + . en, the following integer program is valid: minimize n j = k ( j ) ℓ = λ j l f , j ( a j ℓ ) subject to n j = k ( j ) ℓ = λ j l f i , j ( a j ℓ ) ≤ b i for i = , . . . , m , k ( j ) ℓ = λ j ℓ = for all j = , . . . , n , λ j ≤ y j for all j = , . . . , n , λ j ℓ ≤ y j ℓ- + y j ℓ for all j = , . . . , n and ℓ = , . . . , k ( j ) - , λ j k ( j ) ≤ y j k ( j )- for all j = , . . . , n , k ( j )- ℓ = y j ℓ = for all j = , . . . , n , λ j ℓ ≥ for all j = , . . . , n and ℓ = , . . . , k ( j ) , y j ℓ ∈ { , } for all j = , . . . , n and ℓ = , . . . , k ( j ) - . Prob em . a. Let e be a vector of ones,...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

01.sol - Industrial Engineering Fall Integer Programming So...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online