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$ Optimal Design of Multiproduct Batch Plants
$ Ignacio E. Grossmann
$
$ CACHE Process Design Case Studies
$ M. Morari and I.E. Grossmann
$
$ Optimal Solution: 167,428
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DECLARATION {{
INDEX {i,j,k};
SET I = |1:2|; #products
SET J = |1:3|; #stages
SET K = |1:3|; #potential number of parallel units
PARA q(I) = {200000, 150000}; #demand of product i [kg]
PARA alpha(J) = {250, 500, 340}; #cost coefficient
PARA beta(J) = {0.6, 0.6, 0.6}; #cost exponent
PARA s(I,J) = {2,3,4, #size factor of product i in stage j [L/kg]
4,6,3};
PARA t(I,J) = {8,20,4, #processinig time of product i in stage j [h]
10,12,3};
XVAR {v(J), #volume of stage j [L]
b(I), #batch size of product i [kg]
tl(I), #cycle time of product i [h]
n(J) #number of unit in parallel stage j
};
LBDS v(J) = ;
UBDS v(J) = ;
LBDS b(I) = *;
UBDS b(I) = **;
LBDS tl(I) = **;
UBDS tl(I) = **;
LBDS n(J) = ;
UBDS n(J) = ;
YVAR {y(K,J)}; #existence of stage
BINA {y(K,J)};
}}
MODEL {{
MIN: <>;
#Volume requirement in stage j
l1(i E I, j E J): v(j) =g= log[s(i,j)] + b(i);
#Cycle time for each product i
l2(i E I, j E J): n(j) + tl(i) =g= log[t(i,j)];
#Constraint for production time
n1: <**> =l= 6000;
#Relating number of units to 0-1 variables
l3(j E J): n(j) =e= <>;
#Only one choice for parallel units is feasible
l4(j E J): <> =e= 1;
}}
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