Homework 9

Homework 9 Question 1: Suppose we have a building that is 183 by 200 feet and we want to place 6 departments. The flows between these six departments are shown in the following table a) Use AMPL to develop an integer programming model to solve this layout problem approximately. Use the above data to create a data file. Solve the problem.

Mod: reset ; option solver gurobi ; set departments; param area{i in departments}; param LowerLength; param UpperLength; param LowerWidth; param UpperWidth; param buildingX; param buildingY; param M; param perimeterLower{i in departments} := 0.99*4* sqrt (area[i]); param perimeterUpper{i in departments} := 1.01*4* sqrt (area[i]); param v{i in departments, j in departments}; var x{i in departments}>=0; var l{i in departments}>=0; var y{i in departments}; var w{i in departments}; var a{i in departments, j in departments}; var b{i in departments, j in departments}; var zX{i in departments, j in departments} binary ; var zY{i in departments, j in departments} binary ; minimize distTimesflow: sum {i in departments, j in departments}v[i,j]*(a[i,j]+b[i,j]); subject to perimeterBound{i in departments}: perimeterLower[i]<=(2*(w[i]+l[i]))<= perimeterUpper[i]; subject to lengthBound{i in departments}: LowerLength<=l[i]<= UpperLength; subject to widthBound{i in departments}: LowerWidth<=w[i]<= UpperWidth; subject to buildingLimit{i in departments}: x[i]<=(buildingX- l[i]);

subject to buildingLimit2{i in departments}: y[i]<=(buildingY- w[i]); subject to overlap{i in departments,j in departments: i!=j}: x[i]+l[i]<=x[j]+M*(1 - zX[i,j]); subject to overlap3{i in departments,j in departments: i!=j}: y[i]+w[i]<=y[j]+M*(1 - zY[i,j]); subject to summationConstraint{i in departments, j in departments: i<j}: zX[i,j]+zX[j,i]+zY[i,j]+zY[j,i]>=1; subject to absConstraint{i in departments, j in departments}: a[i,j] >= x[i]+(0.5*l[i])- x[j]-(0.5*l[j]); subject to absConstraint2{i in departments, j in departments}: a[i,j] >= -1*(x[i]+(0.5*l[i])-x[j]-(0.5*l[j])); subject to absConstraint3{i in departments, j in departments}: b[i,j] >= y[i]+(0.5*w[i])-y[j]-(0.5*w[j]); subject to absConstraint4{i in departments, j in departments}: b[i,j]>= -1*(y[i]+(0.5*w[i])-y[j]-(0.5*w[j])); data HW9.dat ; solve ; display _varname, _var; display distTimesflow; display x, y, l, w; Dat: set departments:= 1 2 3 4 5 6; param area:=