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ESI 6912 HW 2 1

# ESI 6912 HW 2 1 - Problem 1 Floor planning problem(1 Data L...

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Problem 1 : . Floor planning problem (1) : Data : ; L length of the available space : ; W width of the available space : ={ , , , , } R set of 5 different rectangular rooms R 1 2 3 4 5 : . Amin set of minimum of the above 5 rooms : . lmin the minimum of length : . lmax the maximum of length : . wmin the minimum of width : . wmax the maximum of width : ( < ) ; fij the flow between room i and j i j : M an arbitrarily large real number (2) : Variable : - , ∀ ∈ . xi1 x coordinate of left point of room i i R : - , ∀ ∈ . xi2 x coordinate of right point of room i i R : - , ∀ ∈ . yi1 y coordinate of lower point of room i i R : - , ∀ ∈ . yi2 y coordinate of upper point of room i i R : , ∀ , ∈ . rijl binary variable indicates whether room i is in the left of room j i j R : , rijr binary variable indicates whether room i is in the right of room j ∀ , ∈ i j R : , riju binary variable indicates whether room i is on the top of room j ∀ , ∈ i j R : rijd binary variable indicates whether room i is under the bottom of room , ∀ , ∈ j i j R : , ∀ ∈ . li length of room i i R

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: , ∀ ∈ . wi width of room i i R : , ∀ ∈ . Ai area of room i i R : , ∀ ∈ , ∈ , ≠ . dij distance between room i and j i R j R and i j (3) : IVR +, ∀ ∈ . xi1 R i R +, ∀ ∈ . xi2 R i R +, ∀ ∈ . yi1 R i R +, ∀ ∈ . yi2 R i R , , ∀ , ∈ rijl 0 1 i j R ∈ , ,∀ , ∈ rijr 0 1 i j R ∈ , ,∀ , ∈ riju 0 1 i j R ∈ , ,∀ , ∈ rijd 0 1 i j R +, ∀ ∈ . li R i R +,∀ ∈ . wi R i R +, ∀ ∈ . Ai R i R +,∀ ∈ . dij R i R (4) : Constraints < ,∀ ∈ xi1 xi2 i R < , ∀ ∈ yi1 yi2 i R - : ; The x coordinate of left point of each room should be xi1 0 - : ; The x coordinate of right point of each room should be xi2 L - , I assume x direction is the length and it is 12l
- : The y coordinate of upper point of each room should be yi1 0 - : The y coordinate of down point of each room should be yi2 W - , I assume y direction is the width and it is 11l : = - ,∀ ∈ The length of each room defined as li xi2 xi1 i R : = - ,∀ ∈ The width of each room defined as wi yi2 yi1 i R : , ∀ ∈ The length of each room should be lmin li lmax i R : , ∀ ∈ The width of each room should be wmin wi wmax i R : = × The area of each room is Ai wi li : The area of each room should be larger than minimum requirement Ai Aimin : The sum of 5 room should not be larger than the available space × i RAi W L : The distance between two center point is = + - + +( + ) -( + ) ∀ ∈ , ∈ , dij xi1 xi22 xj1 xj222 yi1 yi2 2 yj1 yj2 22 i R j R and i j Any two room have one and only one position : + + + = , ∀ , ∈ relationship rijl rijr riju rijd 1 i j R : I formulate the if and else relationship as + - × ,∀ , ∈ , xi2 xj1 1 rijl M i j R and i j - - × ,∀ , ∈ , xi1 xj2 1 rijr M i j R and i j + - × ,∀ , ∈ , yi2 yj1 1 rijd M i j R and i j - - × ,∀ , ∈ , yi1 yj2 1 riju M i j R and i j (5) : Objective < × Minimize transporting goods i jfij dij

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(6) Solutions Ro o m i xi 1 xi 2 yi 1 yi 2 li wi Ai 1 . 4 1 8 2 . 7 4 0 1 0
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